Propagation of low-frequency sound across a warm core ring-enhanced oceanic front at lower horizontal grazing angles is presented. The data were collected from an experimental source tow conducted during the New England Shelf Break Acoustics (NESBA) experiments in spring 2021. The 3 h tow track provides spatiotemporal measurements of acoustic propagation through the front across varying geometries. Coincident oceanographic measurements are used to estimate the strong temperature gradient of the water column and three-dimensional (3D) sound speed field. Two-dimensional (2D) adiabatic mode and full-field sound propagation models are utilized to investigate the acoustic sensitivity to the frontal structure. Then, the joint effects of acoustic ducting and bathymetric slope refraction are examined using 3D sound propagation models. Key components of the measured acoustic impulse response are captured in the 3D numerical model, and the sensitivity of low-frequency propagation to the front geometry is demonstrated.

Oceanic fronts occurring on the continental shelf or shelf slope can cause strong sound speed fronts due to sharp temperature, density, and salinity gradients.1–4 These features strongly influence acoustic propagation through reflection, refraction, and ducting along and across the front. The far-field sound propagation effects of oceanic fronts along the shelf slope have been examined theoretically and through numerical simulation of the ocean acoustic environment.3,5–7 In this study, experimental measurements of low-frequency, low horizontal grazing angle sound propagation into a front at the New England shelfbreak are presented to contextualize existing numerical studies in the region and add to a limited set of observational acoustic experiments recording continental shelf sound propagation along frontal boundaries.4 These experimental results are supplemented by two-dimensional (2D) and three-dimensional (3D) numerical modeling to demonstrate the dominant physical phenomena in this region.

One of the most significant acoustic propagation experiments in the New England shelfbreak area took place during the 1996–1997 PRIMER experiment, where extensive oceanographic measurements complemented moored acoustic source transmissions across spring, summer, and winter seasons. The effect of the shelfbreak front and seasonal variation on acoustic propagation was examined in detail using 2D range-dependent range-dependent acoustic model (RAM) parabolic equation simulations.8,9 For a shallow source, near-surface sound ducting was predicted for the spring and winter seasons, with intensification of the duct occurring in the winter season. In the summer, conditions over 6 days in the summer 1996 demonstrated variation due to shifts in the front position. Ducting was predicted down to 200 Hz for spring and winter. The experimental transmissions from the summer 400 Hz deep moored source were analyzed and demonstrated modal propagation in the lower water column with possible coupling into an upper duct.4 The PRIMER experiment was the first field effort to show the importance of the Cold Pool, the sub-thermocline shelf water mass, as a persistent source of ducts over the outer continental shelf and upper continental slope.

Motivated by the success of the PRIMER experiment in combining acoustic and oceanographic data, and an observed shift in oceanographic conditions on the New England shelf over the recent decade,13,15 the New England Shelf Break Acoustic (NESBA) experiments were conducted in spring 2021 using a network of acoustic and oceanographic instruments. Temperature and salinity gradients across the shelfbreak front were enhanced by a warm core ring (WCR), an anticyclonic eddy of warm saline water originating in the Gulf Stream current.10–14 Recent observations have shown increasing temperature and salinity over the upper continental slope as a result of the increasing number of WCRs.13,15 A significant changeover over the upper shelf is the presence of frontal features that advect northward from the Gulf Stream [Fig. 1(a)]. During the PRIMER experiment, the shelfbreak front was primarily a boundary between shelf and slope water masses. The increasing presence of Gulf Stream near-surface water masses has substantially increased temperature and salinity gradients in recent years, thus directly affecting sound speed fields and acoustic propagation. As part of this experiment, a low-frequency (105–160 Hz), upper water column acoustic source tow was conducted in a region 20–60 km due west of the PRIMER 1996–1997 study area [Figs. 1(a) and 1(b)]. The acoustic source was towed onshore into the cooler shelf waters. Synchronous horizontal and vertical arrays deployed ∼18 km away from the source inside the WCR received source transmissions during the 3 h tow. The front was characterized by a surface temperature change of approximately 6 °C over 3 km, corresponding to a lateral sound speed change of nearly 30 m/s over 3 km. Conductivity, temperature, and depth (CTD) and expendable bathythermograph (XBT) measurements provided point measurements of the three-dimensional (3D) temperature and salinity structure of the WCR-enhanced front. The acoustic transmissions received at the array during the tow provide a unique high-resolution sampling of the WCR-enhanced front and its effect on low-frequency 3D sound propagation.

FIG. 1.

(Color online) (a) Satellite images of sea surface temperature on March 20–22, 2021 indicate the evolution of WCR water filaments and shelf water (data courtesy of Center for Ocean Observing Leadership, Department of Marine and Coastal Sciences, Rutgers University). The experiment region is shown with a black box. (b) Geographic locations of acoustics and oceanographic measurements from March 20–22, 2021. The source tow was conducted on March 21, 2021, 01:04-04:19 GMT. (c) Diagram of the L-array mooring design in the y–z plane. An inset shows the estimated x–y positions (top down view) of the horizontal array elements in meters. Positive y is nominally magnetic north. Hydrophone positioning errors are denoted by thin-line ellipses.

FIG. 1.

(Color online) (a) Satellite images of sea surface temperature on March 20–22, 2021 indicate the evolution of WCR water filaments and shelf water (data courtesy of Center for Ocean Observing Leadership, Department of Marine and Coastal Sciences, Rutgers University). The experiment region is shown with a black box. (b) Geographic locations of acoustics and oceanographic measurements from March 20–22, 2021. The source tow was conducted on March 21, 2021, 01:04-04:19 GMT. (c) Diagram of the L-array mooring design in the y–z plane. An inset shows the estimated x–y positions (top down view) of the horizontal array elements in meters. Positive y is nominally magnetic north. Hydrophone positioning errors are denoted by thin-line ellipses.

Close modal

The range-dependent physics of acoustic propagation into the front is examined using 2D and 3D numerical approaches in this paper. An adiabatic mode model16 and the 2D RAM parabolic Eq. (9) model are used to demonstrate the effect of surface ducting caused by the bottom intrusion of the warm ring water onto the shelf. Using these models, features observed in the experimental impulse response are simulated with a range-dependent sound speed field. We examine how duct thickness affects the frequency- and mode-dependent propagation. Then, the 3D effects of bathymetric refraction on the modes is examined using vertical-mode horizontal-ray theory. Last, full-field 3D sound propagation is simulated with a 3D parabolic equation model17,18 that incorporates the near-front sound speed field and realistic bathymetry.

This paper is organized as follows. Section II examines the WCR feature and presents the oceanographic and acoustic measurements taken during one of the NESBA experiments in March 2021. Section III presents 2D and 3D parabolic equation model simulations in the NESBA environment, including an approach for approximating the 3D sound speed field, and discusses the effects of the range-dependent duct on modal propagation. Additional considerations, including choice of the modeled front location, observation of mode-ray duality, the effect of frequency-dependent propagation in the duct, and the prediction and observation of 3D bathymetric refraction are discussed in Sec. IV.

WCRs are anticylonic eddies that form from steep meanders of western boundary currents. In the Mid-Atlantic Bight region, they have been shown to interact with the topography and turn towards the shelf, where they may deform and develop small-scale flow features.11,14 Historically, WCRs were observed in deeper waters off the New England shelf.10,11 However, onshore intrusions were recently described and have been observed to occur with increasing regularity since 2000,12,13,19–21 corresponding to overall warming and increased salinity of the upper continental slope.13,15 The shelfward ring water can cause small-scale filament flows12 leading to regions of cooler, fresher water streamer overlying and mixing with the warm, dense ring water, forming a strong near-surface acoustic duct. On the downstream side, the shelf water can be advected beneath the warm ring water, producing multi-duct conditions. The features can evolve in a few days, with filaments moving with the front up to 500 m/hr (10–12 km/d).13 

During the March 2021 experiment, the front location relative to the ship was identified using satellite sea surface temperature (SST) images [Fig. 1(a)] and shipboard temperature profilers [Fig. 2(a)]. The presence of a WCR was later confirmed by examining multi-day timeseries. Figure 2(a) shows the spatial and temporal variation of the vertical temperature distribution near the front using CTD and XBT casts from March 20–22, 2021. South of 38.5°N, measurements were within the front and characterized by homogeneous vertical temperature between 14.5 °C and 15 °C and salinity of 36 practical salinity units (PSU) down to 250 m. A mass of cooler (off-shelf) slope water near 8.5° and 35.3 PSU mixed with the ring water below 250 m, beyond the acoustic propagation depth range between the towed source and L-array. North of 40.05°N, shelf water between 6 °C and 6.5 °C with salinity near 33 PSU defined the acoustic surface duct that extended nearly to the ocean bottom, warming slightly as it mixed with the warm ring water below. Between these extremes, the surface duct thickness varied and was characterized by stratified layers of mixed water masses at intermediate temperature.

FIG. 2.

(Color online) (a) Vertical temperature profiles taken from March 20–22 using XBT and CTD instruments. (b), (c) Echograms of 38 kHz backscatter (EK80, Kongsberg) taken on March 20 and 22 within the experiment region. High backscatter indicates sharp density contrasts. The CTD and XBT cast locations are shown with vertical lines.

FIG. 2.

(Color online) (a) Vertical temperature profiles taken from March 20–22 using XBT and CTD instruments. (b), (c) Echograms of 38 kHz backscatter (EK80, Kongsberg) taken on March 20 and 22 within the experiment region. High backscatter indicates sharp density contrasts. The CTD and XBT cast locations are shown with vertical lines.

Close modal

Acoustic backscattering of the water column by a 38 kHz shipboard EK80 provides a spatially continuous view of the shelf water depth [Figs. 2(b) and 2(c)]. Strongly reflected layers represent strong density contrasts, assumed to correspond to the steep temperature gradients observed in CTD and XBT profiles in Fig. 2(a). Early on March 20, the eastern EK80 track shows the shelf water layer reaching the surface and disappearing near 40°N [top, Fig. 2(b)]. The satellite image taken 12 h later [Fig. 1(b)] recorded the front location on the sea surface along the eastern EK80 track at 39.93°N, about 6–7 km south. Figure 2(c) shows the front location on the sea surface along the western EK80 track on March 22, 2 days later, to be near 39.9°N, where it had migrated over 10 km southward compared to its observed SST location in Fig. 1(b) on March 20. These measurements are consistent with expected movement of the WCR small-scale features13 and demonstrate the importance of understanding the acoustic cross-front variability due to the frontal dynamics.

A 32-element hydrophone L-array [Figs. 1(b) and 1(c)] was deployed inside the front of the WCR to receive signals from an upper water-column towed source outside the front at 18 km range. The L-array consisted of a 16-element vertical array (VLA) with 3.75 m spacing between the top 8 hydrophones and 7.5 m spacing between the bottom 8 hydrophones. The shallowest hydrophone (VLA hydrophone 1) was located at 96 m depth, with the bottom-mooring depth of 180 m estimated by a shipboard acoustic survey. The 16-element bottom-mounted horizontal array (HLA) was spaced at 15 m and oriented close to due north. HLA hydrophone 1 denotes the HLA hydrophone closest to the sled bottom-mooring. The true HLA hydrophone positions [Fig. 1(c), inset] were estimated by correlating the ship noise between the first and nth hydrophone during a circular localization survey, then applying iterative least squares with error ellipses to find the relative positions in x and y (Easting, Northing). An atomic clock on the array was synchronized to global positioning system (GPS) prior to deployment.

The linear frequency-modulated (LFM) source (105–160 Hz) was towed from the ship stern at about 10 m depth with 4 s upsweep followed by 4 s off [Fig. 1(b)]. The ship transited inshore from the front for 3 h, with the source transmitting between 01:16–04:19 GMT. Throughout the tow, the source was located inside the cool shelf water surface duct. A reference hydrophone mounted on the tow body at a nominal distance of 1 m was used to obtain the transmitted acoustic signals for deconvolving the signals received at the array to obtain impulse responses. The source and reference hydrophone were synchronized to the GPS clock to ensure precise signal timing.

The sound propagation impulse response measured on the L-array, VLA hydrophone 13 (152 m depth), and HLA hydrophone 1 (bottom, near mooring, see Fig. 1) during the source tow is shown in Fig. 3. High signal-to-noise ratio signals were received throughout the experiment. The first arrival time corresponds closely to the source–receiver distance, which varied between 18.3–18.6 km during the tow. The banding pattern on the individual sensor impulse responses in Figs. 3(b) and 3(c) is attributed to a transition from modal arrivals to ray arrivals, which can be represented as a sum of higher-order modes. During the tow, the source–receiver topography shifted from mildly upslope to downslope propagation [Fig. 1(b)], which reduced the arrival time spread. A twisting pattern is observed in the early arrivals, with aperiodic fluctuations in the received amplitude across the tow. This twisting pattern results in part from intermodal interference and will be discussed in Secs. III C, III D, and IV.

FIG. 3.

(Color online) HLA and VLA measured impulse response for transmissions along the source tow track for (a) both HLA and VLA coherently averaged for 5 pulse transmissions at 01:45, 02:30, and 04:19 GMT, (b) across the source tow at VLA hydrophone 13, and (c) HLA hydrophone 1 (at Shark sled).

FIG. 3.

(Color online) HLA and VLA measured impulse response for transmissions along the source tow track for (a) both HLA and VLA coherently averaged for 5 pulse transmissions at 01:45, 02:30, and 04:19 GMT, (b) across the source tow at VLA hydrophone 13, and (c) HLA hydrophone 1 (at Shark sled).

Close modal

The propagation effects of an evolving acoustic duct at the edge of the New England shelf were simulated. First, oceanographic measurements of temperature and salinity were used to construct an idealized 3D sound speed model. Two-dimensional sound speed slices were extracted from each source position every 1 min along the source–receiver track to conduct 2D propagation modeling. Then, the response of both adiabatic (Kraken mode model16) and coupled-mode propagation [2D split-step Padè parabolic equation (PE) model RAM9] to the surface duct thickness was examined. Full-field RAM9 was used to examine the sensitivity of low-frequency acoustic propagation to the duct geometry. Last, a 3D PE model17,18 was used to simulate the horizontal effects of the 3D sound speed field and bathymetry. Realistic bathymetry was incorporated using data from the global multi-resolution topography (GMRT) dataset.22 All scenarios modeled the ocean bottom as a homogeneous medium of nominal sound speed 1700 m/s and attenuation α=0.3 dB/λ, which corresponds to a homogeneous sand bottom. Shear speed was neglected.

The 3D structure of sound speed within the experiment region was estimated using XBT and CTD casts taken from March 20–22 along with satellite sea surface temperature data [Fig. 1(b)]. EK80 acoustic reflection data were examined and found to agree with the XBT and CTD data. However, these EK80 data were not quantitatively incorporated in the SSP model due to the challenge of inferring temperature information from the EK80 reflection surfaces at depth, and due to a shift in the front location between the March 20 acoustic tow and the March 22 EK80 survey.

First, idealized temperature profiles were created by approximating the surface duct as an upward-refracting duct warming linearly in depth between the surface and bottom layers in the water column [Fig. 4(a)]. Both the measured and idealized temperature profiles capture the presence of a range-dependent, upward-refracting sound duct near the surface resulting from shelf water overlaying warm core ring water. Then, a realistic 2D vertical temperature slice was constructed for comparison by interpolating the XBT and CTD temperature measurements in the cross-shelf direction (along latitude) [Fig. 4(b)]. An idealized 2D temperature slice [Fig. 4(c)] was created by interpolating the idealized temperature profiles in the same manner as the realistic 2D slice. The idealized duct narrowed from its maximum depth on the shelf until vanishing at the front, where its width was fixed at 0 m. The 2D idealized temperature slice was extended to 3D by assuming a laterally invariant duct continuing along the WCR-enhanced front. The front was approximated as linear, with a tilt angle of 9°W of N [Fig. 1(b)] estimated from sea surface satellite data near the source track. The 3D temperature profile was extrapolated inside the front by assuming a vertically uniform temperature profile.

FIG. 4.

(Color online) (a) Estimated temperature vs depth at the marked ranges, for SSP interpolated from CTD and XBT measurements and the idealized linear-duct model. (b) Range-depth temperature slice along the source–receiver track using linearly interpolated oceanographic measurements projected along the source track, with CTD and XBT measurement positions are marked by vertical lines. (c) An idealized range-dependent temperature profile with linearly deepening surface duct. (d) Map of surface temperatures for the 3D idealized model.

FIG. 4.

(Color online) (a) Estimated temperature vs depth at the marked ranges, for SSP interpolated from CTD and XBT measurements and the idealized linear-duct model. (b) Range-depth temperature slice along the source–receiver track using linearly interpolated oceanographic measurements projected along the source track, with CTD and XBT measurement positions are marked by vertical lines. (c) An idealized range-dependent temperature profile with linearly deepening surface duct. (d) Map of surface temperatures for the 3D idealized model.

Close modal

The 3D temperature map was converted to sound speed using a one-to-one empirical relationship between sound speed and temperature determined from the CTD data taken on March 22 in shelf water in the experiment region. The mapping was validated by conducting the same procedure with an independent CTD dataset taken on March 21, which produced comparable results. This approach is assumed to yield accurate local sound speed since small errors in salinity have been observed to have a negligible contribution to sound speed errors in the New England shelf waters.8 The CTD reference sound speed values were computed using the Chen and Millero sound speed relation.23 

For 2D sound propagation modeling, a vertical 2D sound speed slice was interpolated along each line-of-sight path between the moving source and the fixed receiver array. The duct thickness of the 2D slices for different source positions agrees well with the duct thickness measured during the along-tow XBTs in Fig. 2(a). In addition, the front location just north of the L-array matches the front location observed in SST satellite measurement [Fig. 1(b)].

During the source tow, the change in surface duct thickness between the source and receiver due to changing source position directly influenced the vertical distribution of modal energy in the water column. The local adiabatic modal effects of duct narrowing are shown for modes 1–4 at 160 Hz in Fig. 5. Compared to a uniform profile, the presence of a 100 m duct concentrates low-order modal energy near the surface [Fig. 5(a)] and alters the mode shapes. As the duct thickness decreases, the proportion of trapped energy decreases. For a duct thickness of 25 m, the mode shapes in the bottom of the water column are nearly identical to a uniform profile, with the largest differences observed in Mode 1. The effects of ducting on modal group speed is demonstrated in Fig. 5(b). For sufficiently deep ducts, the lowest modes may theoretically travel more slowly than higher modes, while narrower ducts decrease the overall modal group velocity.

FIG. 5.

(Color online) Local vertical modes 1–4 at 160 Hz for upward-refracting ducts of varying thickness: 100 m, 50 m, 25 m, and 0 m (no duct, uniform), and corresponding local modal group velocity. Lower modes are more sensitive to narrow ducts.

FIG. 5.

(Color online) Local vertical modes 1–4 at 160 Hz for upward-refracting ducts of varying thickness: 100 m, 50 m, 25 m, and 0 m (no duct, uniform), and corresponding local modal group velocity. Lower modes are more sensitive to narrow ducts.

Close modal

Modal coupling occurs when energy is exchanged between modes in a range-dependent waveguide. Coupling can occur at interfaces or features of sharp sound speed or density contrast, such as bathymetric ridges, oceanic internal gravity waves, or sound speed fronts.4 In Fig. 6, the effect of modal coupling due to the NESBA 2021 WCR-enhanced front is examined by comparing the pressure fields simulated at 160 Hz with the Kraken16 adiabatic mode model and the RAM full-field PE model9 for a source–receiver track at the source tow position of 04:19 GMT, March 21, 2021. The reduced (corrected for spreading loss) transmission loss (TL) is shown to emphasize the differences due to modal coupling. Figures 6(b) and 6(c) show that, due to the gradual variation of the surface duct, strong modal coupling is not predicted. However, weak modal coupling is observed when the duct narrows to a thickness shorter than the modal wavelength. The coupling is evident between 15 km and 19 km where TL increases (energy decrease) in the bottom third of the water column and decreases (energy increase) in the mid-water column [Fig. 6(c)] compared to the lower TL in the bottom third of the water column in the adiabatic model [Fig. 6(b)]. At closer ranges where the duct is sufficiently thick to support modes (<10 km range), coupling is absent, and the modal propagation is predominantly adiabatic.

FIG. 6.

(Color online) Reduced transmission loss at 160 Hz for the sound speed field shown in (a) with (b) adiabatic Kraken mode model, (c) RAM full-field PE model. The section is estimated for the source position at tow time 04:19 GMT, March 21, 2021.

FIG. 6.

(Color online) Reduced transmission loss at 160 Hz for the sound speed field shown in (a) with (b) adiabatic Kraken mode model, (c) RAM full-field PE model. The section is estimated for the source position at tow time 04:19 GMT, March 21, 2021.

Close modal

The sensitivity of low-frequency (160 Hz) propagation to the surface duct geometry was carried out using a 2D full-field PE model9 (Fig. 7). First, a range-independent, upward-refracting surface duct with linearly increasing sound speed to 100 m depth was used to demonstrate the effect of the duct on acoustic propagation [Figs. 7(b), 7(e), and 7(h)] compared to a uniform sound speed environment [Figs. 7(a), 7(d), and 7(g)]. Near the ocean surface, ducted lower-order modes can be observed as lower TL [Fig. 7(e)]. At the near-bottom receiver, the modal energy is split between the surface duct and the lower water column, reflecting a decrease in lower-order modal energy near the bottom as demonstrated in the modal sensitivity analysis (Fig. 5). As a result, modal group velocity is slower. Comparing the first arrivals of the broadband impulse response at 152 m depth for the final tow position (along travel time axis), it is clear that the modeled signal in the uniform environment [Fig. 7(g)] arrives at least 0.1 s earlier than in the duct environment [Fig. 7(h)].

FIG. 7.

(Color online) Simulated acoustic sensitivity to an idealized shelf duct using the RAM PE model for (a) uniform sound speed, (b) duct with linearly increasing sound speed to 100 m depth, (c) duct with linearly increasing sound speed narrowing from 100 m to surface along the source–receiver bathymetry for the source tow position at 04:19 GMT. (d)–(f) Reduced transmission loss at 160 Hz along the source–receiver track corresponding to the sound speed profiles in (a)–(c). (g)–(i) Broadband impulse response simulated at VLA channel 13 (152 m depth) every 1 min across the source tow, with duct conditions in (a)–(d) and realistic source–receiver bathymetry.

FIG. 7.

(Color online) Simulated acoustic sensitivity to an idealized shelf duct using the RAM PE model for (a) uniform sound speed, (b) duct with linearly increasing sound speed to 100 m depth, (c) duct with linearly increasing sound speed narrowing from 100 m to surface along the source–receiver bathymetry for the source tow position at 04:19 GMT. (d)–(f) Reduced transmission loss at 160 Hz along the source–receiver track corresponding to the sound speed profiles in (a)–(c). (g)–(i) Broadband impulse response simulated at VLA channel 13 (152 m depth) every 1 min across the source tow, with duct conditions in (a)–(d) and realistic source–receiver bathymetry.

Close modal

Next, the effect of a range-variable surface duct [Figs. 7(c), 7(f), and 7(i)] was modeled by using 2D vertical slices from the 3D reconstructed sound speed model, as discussed in Sec. III A. As the duct thickness decreases in range, fewer modes are supported in the surface channel and the proportion of modal energy in the lower water column increases [Fig. 7(f)]. Near the receiver, almost all of the modal energy is contained in the lower water column due to the negligible surface duct [Fig. 7(f)]. The increased modal energy near the bottom across the track increases group velocity of all modes compared, which is observed in an earlier first arrival in the range-variable duct impulse response [Fig. 7(i)] compared to the constant-duct [Fig. 7(h)]. The differential effect of variable duct thickness between lower- and higher-order modes results in acoustic interference at the receiver, a distinct twisting or braiding pattern as seen in Fig. 7(i) similar to that observed in the experimental impulse response [Fig. 3(b)]. Modeled impulse response levels are up to 5 dB higher than the constant-duct environment due to the constructive interference [Fig. 7(i)].

A 3D full-field parabolic equation (PE) model17,18 was used to simulate acoustic propagation within the experiment region, including lateral mode coupling resulting from the 3D sound speed gradients and horizontal bathymetric refraction due to the seafloor slope. This 3D approach enables modeling of the exchange of acoustic energy between the horizontal and vertical planes, which cannot be simulated with the 2D method, assuming line-of-sight propagation.

Simulated transmission loss computed by the 3D PE model for a single source position is shown with fixed slices across the computation domain in Fig. 8(a). The along-slope (along-track) slice shows modal propagation similar to that predicted by the 2D method. However, as shown in the horizontally sliced TL field close to the ocean surface and bottom [Fig. 8(b)], curved wave fronts resulting from horizontal refraction of vertical modes in response to the shelf slope are observable. The horizontal refraction of modes will be further examined using mode-ray theory later in the paper, with sound bending away from shallower depths in accordance with the frequency, local bathymetric gradient, and vertical-mode wavenumber (see Sec. IV for details). Differences between the 2D and 3D PE modeling results are in part attributed to the ability of the 3D modeling to simulate refracted modal paths instead of the 2D modeling that assumes line-of-sight propagation.

FIG. 8.

(Color online) Volumetric view of transmission loss at 160 Hz simulated with a 3D PE model shown as (a) along and cross sections between source and receiver, (b) horizontal slices at 10 m and 152 m depth.

FIG. 8.

(Color online) Volumetric view of transmission loss at 160 Hz simulated with a 3D PE model shown as (a) along and cross sections between source and receiver, (b) horizontal slices at 10 m and 152 m depth.

Close modal

The broadband impulse response at 152 m for 3D propagation across the source tow is shown in Fig. 9(b), along with an inset displaying a horizontal slice of the 3D sound speed field at the source depth of 10 m [see Sec. III A, Fig. 4(b)]. The 3D PE model agrees with the data better than the 2D PE model. In the 3D PE model, later higher-order modal arrivals diminish near the end of the tow (>12.5 s, from 03:00 on) as observed in the data [see Fig. 3(b)], but this effect is not observed in the 2D PE model [Fig. 7(i)]. This discrepancy suggests that 3D effects are more profound for higher-order modes, which will be investigated more through vertical-mode horizontal-ray modeling later in Sec. IV. As a matter of fact, one can even see at the beginning of track that the signal level of higher-order arrivals in the 2D PE is much higher than for the 3D PE and the data. This mismatch on higher-order modal arrivals is a key feature of the 3D sound propagation effects. In Sec. IV, horizontal beamforming of the L-array data will be demonstrated to confirm the horizontal refraction of higher-order modes caused by the seafloor slope. There is also similarity between 2D and 3D PE model results relating to vertical-mode propagation. For example, the twisting/braiding pattern of modal interference in the early arrivals is replicated in both the 2D and 3D models. This indicates the modal interference resulting from changing surface duct geometry, which was discussed in Sec. III C, is in fact a 2D effect.

FIG. 9.

(Color online) Impulse response simulated at the L-array location with depth 152 m (VLA hydrophone 13) for the given 3D sound speed across the source tow using a 3D parabolic equation model. The inset shows the tilted front SSP model at 10 m depth, with color bar from 1480 to 1510 m/s.

FIG. 9.

(Color online) Impulse response simulated at the L-array location with depth 152 m (VLA hydrophone 13) for the given 3D sound speed across the source tow using a 3D parabolic equation model. The inset shows the tilted front SSP model at 10 m depth, with color bar from 1480 to 1510 m/s.

Close modal

In this study, experimental low-frequency source tow propagation through a WCR-enhanced front at the New England shelfbreak and complementary modeling enabled the observation of multiple interacting propagation effects. The effects of the front geometry are further examined by simulating a longitudinally invariant front with no rotation (Fig. 10, the flat front case) and with a rotation of 9° counterclockwise (Fig. 9, the tilted front case). The flat front results in a wider apparent surface duct between source and receiver, leading to the twisting pattern of modal interference occurring throughout the source tow. For the tilted front, the twisting pattern is absent in the first 15–30 min of the tow, matching more closely with the measured impulse response. The lack of twisting pattern can be attributed to a narrow apparent surface duct when the source is near the front, such that modal propagation in the duct is not supported. The sensitivity of the low-order modes to the exact front geometry emphasizes the importance of and need for increased experimental oceanographic and acoustic measurements, particularly in regions with dynamic oceanographic fronts.

FIG. 10.

(Color online) Impulse response simulated at the L-array location with depth 152 m (VLA hydrophone 13) for the given 3D sound speed across the source tow using a 3D parabolic equation model. The inset shows the flat front SSP model at 10 m depth, with color bar from 1480 to 1510 m/s.

FIG. 10.

(Color online) Impulse response simulated at the L-array location with depth 152 m (VLA hydrophone 13) for the given 3D sound speed across the source tow using a 3D parabolic equation model. The inset shows the flat front SSP model at 10 m depth, with color bar from 1480 to 1510 m/s.

Close modal

The impulse response arrivals (Figs. 3, 7, 9, and 10) demonstrate the effect of mode-ray duality24 within the wide low-frequency bandwidth of the experimental source (linear chirp with a center frequency of 132.5 Hz and a bandwidth of 55 Hz). In this case, modal arrivals become indistinguishable for higher-order modes and are characterized as acoustic rays. A RAM full-field PE9 broadband simulation of the acoustic impulse response across depth in Fig. 11 shows this transition from modal to ray-based propagation. Distinct mode shapes become wavefronts whose arrival angles are visible across the pulse. On the single hydrophone impulse response, the mode-ray transition appears as a tightly banded pattern in the later arrivals.

FIG. 11.

(Color online) Impulse response simulated with the 2D RAM PE at the receiver range across depth for the source tow position at time 04:19 GMT. The source depth is 10 m.

FIG. 11.

(Color online) Impulse response simulated with the 2D RAM PE at the receiver range across depth for the source tow position at time 04:19 GMT. The source depth is 10 m.

Close modal

Simulations of the modal group velocities in a 100 m idealized surface duct [Fig. 12(a)] demonstrate their strong frequency-dependence across the experimental bandwidth (105–160 Hz). Higher-order modes (modes 9–10) are monotonic, with group velocity decreasing as a function of mode number [Fig. 12(a)]. Below mode 9, the modal group velocity is nonmonotonic and the relative group velocities vary significantly with frequency, leading to a complicated frequency dispersive pattern. The joint effect of broadband, multi-modal propagation have been captured by the modeled time-domain impulse responses shown in Secs. III C and III D. Modal phase speed is shown for reference [Fig. 12(b)].

FIG. 12.

(Color online) Frequency-dependent (a) modal group velocities, (b) modal phase velocities of modes 1–10 at 175 m depth for a uniform sound speed profile (1507 m/s) and a 100 m cool duct (1480 m/s) overlying a warm layer (1507 m/s).

FIG. 12.

(Color online) Frequency-dependent (a) modal group velocities, (b) modal phase velocities of modes 1–10 at 175 m depth for a uniform sound speed profile (1507 m/s) and a 100 m cool duct (1480 m/s) overlying a warm layer (1507 m/s).

Close modal

The apparent 3D effects of propagation are observed with array beamforming and modeled using modal-ray propagation (Fig. 13). Assuming adiabatic mode propagation, the eigenray paths of the modes can be determined with the modal phase speed field,24–26 which is highly sensitive to bathymetry for higher-order modes and is frequency-dependent. To demonstrate the dependency of modal eigenrays on frequencies and mode numbers, the predicted horizontal refractions of modes 5 and 10 within the source frequency band (105–160 Hz) for the most along-shelf track at 01:16 GMT (source at 39.96°N, 71.40°W) are shown in Figs. 13(a) and 13(b). One can clearly observe the frequency and mode number dependencies of shelfward-bending eigenray paths, and the horizontal refraction is stronger for mode 10 than mode 5 at a fixed frequency. When the mode number is fixed, lower frequency has stronger horizontal refraction. Notably, while modal refraction can occur in response to the sound speed gradient, the refraction observed in these data is attributed primarily to bathymetric refraction due to the gradual SSP gradient. No measurable refraction due to SSP was observed in the modal-ray model for uniform vs realistic 3D SSP. Figure 13(c) confirms the existence of refracted modal ray paths in the experimental data by showing agreement between the location of peaks in the horizontal line array beamforming ambiguity surface and the frequency-dependent modal arrival angles (white lines) predicted by the modal-ray model. Across frequency bandwidth, a span of up to 20° total arrival variation in azimuth is observed. A single modal arrival is also predicted to have a frequency-dependent spread of up to 10°. Horizontal line array beamforming assumes plane wave arrivals with a reference phase speed vp = 1500 m/s. As shown in Fig. 12(b), individual modal phase speeds may exceed the reference phase speed, resulting in arrivals occurring beyond the line-of-sight azimuth of 71.5°.

FIG. 13.

(Color online) Mode-ray eigenpaths between the towed source (circle symbol) at 01:16 GMT (39.96°N, 71.40°W) and Shark array (cross-symbol) for (a) mode 5 and (b) mode 10 exhibit frequency-dependent 3D refraction due to the shelf slope. (c) The predicted arrival angles for modes 1, 7, and 10, using vp = 1500 m/s, are shown as white lines from right to left atop the measured frequency-dependent azimuth of the towed source received on the Shark HLA. The line-of-sight azimuth was 71.5°E of N. Beamformed arrivals may occur beyond line-of-sight due to local modal phase speeds.

FIG. 13.

(Color online) Mode-ray eigenpaths between the towed source (circle symbol) at 01:16 GMT (39.96°N, 71.40°W) and Shark array (cross-symbol) for (a) mode 5 and (b) mode 10 exhibit frequency-dependent 3D refraction due to the shelf slope. (c) The predicted arrival angles for modes 1, 7, and 10, using vp = 1500 m/s, are shown as white lines from right to left atop the measured frequency-dependent azimuth of the towed source received on the Shark HLA. The line-of-sight azimuth was 71.5°E of N. Beamformed arrivals may occur beyond line-of-sight due to local modal phase speeds.

Close modal

Last, Figure 14 shows the channel impulse responses of the measured signals, 2D PE, and 3D PE with the realistic SSP model side by side for VLA channel 12 at 145 m depth. The models and data show evidence of mode-ray duality in the twisting interference of modes in the early arrivals and in the banding patterns of the later (ray) arrivals. The 2D and 3D PEs show self-consistent twisting patterns in the early lower-order mode arrivals and agree qualitatively with the data, demonstrating that the upward-refracting duct propagation effect yielding the twisting pattern of lower-order mode arrivals is a 2D effect. In the 3D PE, the slope of the ray arrivals across transmission time, and the lower received levels of the later arrivals relative to the 2D PE, agree better with the measured data. This difference in the later arrivals between 2D and 3D PEs can be attributed to differences in 3D ray propagation paths and indicates the important role of mode-ray horizontal refraction in the experimental propagation environment. The 2D and 3D PE impulse response arrivals occur earlier than in the data due to a small positive bias in the 3D SSP; however, across the entire propagation path, this discrepancy is less than +5 m/s over an average speed of 1505 m/s.

FIG. 14.

(Color online) Impulse response throughout the source tow at the L-array location with depth 145 m (VLA hydrophone 12) for (a) the measured signal, (b) 2D parabolic equation model, (c) 3D parabolic equation model. Both models used the idealized 3D sound speed model shown in Fig. 4.

FIG. 14.

(Color online) Impulse response throughout the source tow at the L-array location with depth 145 m (VLA hydrophone 12) for (a) the measured signal, (b) 2D parabolic equation model, (c) 3D parabolic equation model. Both models used the idealized 3D sound speed model shown in Fig. 4.

Close modal

This study presents data from low-frequency acoustic propagation through a WCR-enhanced front near the New England shelfbreak, conducted in March 2021. Using concurrent oceanographic measurements, a near-front surface duct is identified as a key acoustic feature. A towed source track across-shelf enables observations of changes in the received impulse response due to the apparent source–receiver surface duct and front geometry. An L-shaped hydrophone array captured the variation in depth and range, demonstrating mode and ray arrivals.

An idealized linear surface duct is used to simulate the response of the low-frequency propagation to the surface duct geometry. The adiabatic mode model provides insight into the response of local modes to the duct thickness and the effect of modal coupling. The 2D RAM PE is used to discuss the frequency-dependent response of the full wave field to different types of duct geometry and indicate the ducting conditions observed in the experiment. Then, a full-field 3D PE model is used to simulate the joint effects of frequency-dependent ducting and fully capture the modal horizontal refraction observed in the data, which is also confirmed with vertical-mode horizontal-ray modeling.

Finally, physical phenomena of 3D low-frequency acoustic propagation in the shelfbreak-front environment are further discussed. Simulations demonstrate that propagation is sensitive to the front geometry that can be observed from sea surface temperature satellite images. The effect of mode-ray duality and the mode-ray transition within the experimental source bandwidth are shown using a depth-dependent impulse response. Broadband modal group velocity dispersion shows the strong frequency-dependence of low-order mode relative arrival times and high-order mode interference leading to ray propagation. Evidence of frequency-dependent modal refraction along the shelf slope (3D propagation) is provided with broadband beamforming using modal phase speeds on the horizontal line array data. Modeling of the modal eigenrays confirms the effect of horizontal refraction for higher-order modes and agrees well with the measured arrival azimuths. Propagation effects are summarized in a direct comparison of the impulse response from the measured, 2D PE, and 3D PE models, which show the better data-model agreement for the 3D PE.

The 3D sound speed model (Fig. 4) developed in this paper is used to demonstrate the key acoustic phenomena on the New England shelf along a WCR-enhanced front, and to model the differences between 2D and 3D propagation. However, discrepancies between the real-world ocean sound speed field and the 3D sound speed model can still cause mismatch between the modeled and measured acoustic broadband impulse response.

Ongoing work should continue to explore methods for accurately reconstructing 3D sound speed fields jointly from oceanographic and acoustic measurements. This will include improving interpolation methods for measured data using physically informed models and developing acoustic inversion or data assimilation approaches in the multidimensional domain. In addition, future research will examine signal processing methods for isolating and beamforming modal arrivals within these data using the full L-array. This work can provide estimates of modal wavenumbers and improve knowledge of water column effects on modal refraction.

This work was supported by the Office of Naval Research under the Task Force Ocean program, Grant Nos. N00014-19-1-2663, N00014-19-1-2646, and N00014-21-1-2959. The authors thank Brendan Decourcy, Arthur Newhall, Hunter Akins, and Ryan Saenger for discussion on the implementation of the computational models. Thanks also to the Captain and crew of the R/V Neil Armstrong for their assistance during the field experiment.

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