The method of large-eddy simulation (LES) coupled with the density transport equation is employed to simulate the evolution of a gravity-driven high-density turbidity current and its interaction with a pair of parallel suspended pipes. The LES method is validated first using data of a non-Boussinesq lock-exchange experiment and satisfying agreement between LES and experiment is achieved. The simulations reveal that a shear region forms between high- and low-density fluids each moving in opposite directions which lead to the generation of a series of vortices and a substantial mixing region. Close to the bottom boundary, low-density fluid is entrained near the head of the high-density turbidity current, forming a thin water cushion that separates the turbidity current's head from the seabed, the so-called hydroplaning effect, thereby reducing the density of the head and bottom friction. The current study suggests that the effect of hydroplaning phenomena leads to high speed and long distance of the turbidity current. Further, LES simulations of a turbidity current impacting a pair of parallel suspended pipes with different streamwise spacings are performed and impact forces are quantified. The turbulent wake generated by high-density fluid bypassing pipe 1 promotes velocity fluctuations leading to increased impact forces on pipe 2 with increasing streamwise spacing up to 8 times the pipeline diameter (8D). The results suggest that the streamwise spacing between two parallel pipes should be less than 2D to minimize hydrodynamic loads on pipe 2.

1.
J.
Xu
, “
Turbidity current research in the past century: An overview
,”
Period. Ocean Univ. China
44
,
98
105
(
2014
).
2.
G.
Shanmugam
and
Y.
Wang
, “
The landslide problem
,”
J. Palaeogeogr.
4
,
109
166
(
2015
).
3.
X.
Liu
,
J.
Sun
,
Y.
Lu
, and
X.
Guo
, “
Control of ambient fluid on turbidity current evolution: Mechanisms, feedbacks and influencing factors
,”
Geosyst. Geoenviron.
2
,
100214
(
2023
).
4.
R. G.
Walker
, “
Deep-water sandstone facies and ancient submarine fans: Models for exploration for stratigraphic traps
,”
AAPG Bull.
62
,
932
966
(
1978
).
5.
C.
Pirmez
and
J.
Imran
, “
Reconstruction of turbidity currents in amazon channel
,”
Mar. Pet. Geol.
20
,
823
849
(
2003
).
6.
R.
Ouillon
,
C.
Kakoutas
,
E.
Meiburg
, and
T.
Peacock
, “
Gravity currents from moving sources
,”
J. Fluid Mech.
924
,
A43
(
2021
).
7.
X.
Guo
,
N.
Fan
,
Y.
Liu
,
X.
Liu
,
Z.
Wang
,
X.
Xie
, and
Y.
Jia
, “
Deep seabed mining: Frontiers in engineering geology and environment
,”
Int. J. Coal Sci. Technol.
10
,
23
(
2023
).
8.
J. S.
Salinas
,
S.
Balachandar
,
S. L.
Zúñiga
,
M.
Shringarpure
,
J.
Fedele
,
D.
Hoyal
, and
M.
Cantero
, “
On the definition, evolution, and properties of the outer edge of gravity currents: A direct-numerical and large-eddy simulation study
,”
Phys. Fluids
35
,
016610
(
2023
).
9.
P. D.
Komar
, “
The channelized flow of turbidity currents with application to Monterey deep-sea fan channel
,”
J. Geophys. Res.
74
,
4544
4558
, https://doi.org/10.1029/JC074i018p04544 (
1969
).
10.
G.
Parker
,
Y.
Fukushima
, and
H. M.
Pantin
, “
Self-accelerating turbidity currents
,”
J. Fluid Mech.
171
,
145
181
(
1986
).
11.
J.
Locat
and
H. J.
Lee
, “
Submarine landslides: Advances and challenges
,”
Can. Geotech. J.
39
,
193
212
(
2002
).
12.
J. J.
Hance
, “
Submarine slope stability
,” Ph.D. thesis,
University of Texas at Austin
,
2003
.
13.
P.
Jeanjean
,
E.
Liedtke
,
E.
Clukey
,
K.
Hampson
,
T.
Evans
et al, “
An operator's perspective on offshore risk assessment and geotechnical design in geohazard-prone areas
,” in
Proceedings of the Offshore Technology Conference
(
2005
), pp.
115
143
.
14.
X.
Liu
,
Y.
Wang
,
H.
Zhang
, and
X.
Guo
, “
Susceptibility of typical marine geological disasters: An overview
,”
Geoenviron. Disasters
10
,
10
(
2023
).
15.
P. J.
Talling
,
L. A.
Amy
,
R. B.
Wynn
,
G.
Blackbourn
, and
O.
Gibson
, “
Evolution of turbidity currents deduced from extensive thin turbidites: Marnoso arenacea formation (miocene), italian apennines
,”
J. Sediment. Res.
77
,
172
196
(
2007
).
16.
W.
Schneeberger
, “
Turbidity currents, a new concept in sedimentation and its application to oil exploration
,”
Mines Mag.
45
,
42
62
(
1955
).
17.
P.
Weimer
,
R. M.
Slatt
,
R.
Bouroullec
et al,
Introduction to the Petroleum Geology of Deepwater Setting
(
AAPG/Datapages Tulsa
,
2007
), Vol.
111
.
18.
E.
Meiburg
and
B.
Kneller
, “
Turbidity currents and their deposits
,”
Annu. Rev. Fluid Mech.
42
,
135
156
(
2010
).
19.
D.
Bell
,
E. L.
Soutter
,
Z. A.
Cumberpatch
,
R. A.
Ferguson
,
Y. T.
Spychala
,
I. A.
Kane
, and
J. T.
Eggenhuisen
, “
Flow-process controls on grain type distribution in an experimental turbidity current deposit: Implications for detrital signal preservation and microplastic distribution in submarine fans
,”
Depositional Rec.
7
,
392
415
(
2021
).
20.
A.
Zakeri
,
K.
Høeg
, and
F.
Nadim
, “
Submarine debris flow impact on pipelines—Part I: Experimental investigation
,”
Coastal Eng.
55
,
1209
1218
(
2008
).
21.
M.
Shringarpure
,
M. I.
Cantero
, and
S.
Balachandar
, “
Dynamics of complete turbulence suppression in turbidity currents driven by monodisperse suspensions of sediment
,”
J. Fluid Mech.
712
,
384
417
(
2012
).
22.
X.-s.
Guo
,
T.-k.
Nian
,
Z.-t.
Wang
,
W.
Zhao
,
N.
Fan
, and
H.-b.
Jiao
, “
Low-temperature rheological behavior of submarine mudflows
,”
J. Waterw., Port, Coastal, Ocean Eng.
146
,
04019043
(
2020
).
23.
Z.
Tian
,
Y.
Jia
,
J.
Chen
,
J. P.
Liu
,
S.
Zhang
,
C.
Ji
,
X.
Liu
,
H.
Shan
,
X.
Shi
, and
J.
Tian
, “
Internal solitary waves induced deep-water nepheloid layers and seafloor geomorphic changes on the continental slope of the northern south china sea
,”
Phys. Fluids
33
,
053312
(
2021
).
24.
S.-K.
Hsu
,
J.
Kuo
,
L.
Chung-Liang
,
T.
Ching-Hui
,
W.-B.
Doo
,
C.-Y.
Ku
, and
J.-C.
Sibuet
, “
Turbidity currents, submarine landslides and the 2006 Pingtung earthquake off SW Taiwan
,”
Terr., Atmos. Oceanic Sci.
1
,
1229
(
2008
).
25.
T.-k.
Nian
,
X.-s.
Guo
,
N.
Fan
,
H.-b.
Jiao
, and
D.-y.
Li
, “
Impact forces of submarine landslides on suspended pipelines considering the low-temperature environment
,”
Appl. Ocean Res.
81
,
116
125
(
2018
).
26.
X.
Guo
,
T.
Stoesser
,
C.
Zhang
,
C.
Fu
, and
T.
Nian
, “
Effect of opening and wall boundaries on CFD modeling for submarine landslide-ambient water-pipeline interaction
,”
Appl. Ocean Res.
126
,
103266
(
2022
).
27.
M. G.
Wells
and
R. M.
Dorrell
, “
Turbulence processes within turbidity currents
,”
Annu. Rev. Fluid Mech.
53
,
59
83
(
2021
).
28.
K.
Chikita
, “
A field study on turbidity currents initiated from spring runoffs
,”
Water Resour. Res.
25
,
257
271
, https://doi.org/10.1029/WR025i002p00257 (
1989
).
29.
C.
Gong
,
Y.
Wang
,
W.
Zhu
,
W.
Li
,
Q.
Xu
, and
J.
Zhang
, “
The central submarine canyon in the Qiongdongnan basin, northwestern south China sea: Architecture, sequence stratigraphy, and depositional processes
,”
Mar. Pet. Geol.
28
,
1690
1702
(
2011
).
30.
W.
Ding
,
J.
Li
,
J.
Li
,
Y.
Fang
, and
Y.
Tang
, “
Morphotectonics and evolutionary controls on the pearl river canyon system, south china sea
,”
Mar. Geophys. Res.
34
,
221
238
(
2013
).
31.
M.
Azpiroz-Zabala
,
M.
Cartigny
,
E. J.
Sumner
,
M.
Clare
,
P. J.
Talling
,
D. R.
Parsons
, and
C.
Cooper
, “
A general model for the helical structure of geophysical flows in channel bends
,”
Geophys. Res. Lett.
44
,
11932
11941
, https://doi.org/10.1002/2017GL075721 (
2017
).
32.
X.
Liu
,
Y.
Lu
,
H.
Yu
,
L.
Ma
,
X.
Li
,
W.
Li
,
H.
Zhang
, and
C.
Bian
, “
In-situ observation of storm-induced wave-supported fluid mud occurrence in the subaqueous yellow river delta
,”
J. Geophys. Res.: Oceans
127
,
e2021JC018190
, https://doi.org/10.1029/2021JC018190 (
2022
).
33.
M. A.
Hampton
, “
The role of subaqueous debris flow in generating turbidity currents
,”
J. Sediment. Res.
42
,
775
793
(
1972
).
34.
M. M.
Hotta
,
M. S.
Almeida
,
D. T.
Pelissaro
,
J. R. M. da S.
de Oliveira
,
S.
Tibana
, and
R. G.
Borges
, “
Centrifuge tests for evaluation of submarine-mudflow hydroplaning and turbidity currents
,”
Int. J. Phys. Modell. Geotech.
20
,
239
253
(
2020
).
35.
M. R.
Oshaghi
,
H.
Afshin
, and
B.
Firoozabadi
, “
Experimental investigation of the effect of obstacles on the behavior of turbidity currents
,”
Can. J. Civ. Eng.
40
,
343
352
(
2013
).
36.
Z. F.
Haza
,
I. S. H.
Harahap
, and
L. M.
Dakssa
, “
Experimental studies of the flow-front and drag forces exerted by subaqueous mudflow on inclined base
,”
Nat. Hazards
68
,
587
611
(
2013
).
37.
O. E.
Sequeiros
,
R.
Mosquera
, and
F.
Pedocchi
, “
Internal structure of a self-accelerating turbidity current
,”
J. Geophys. Res.: Oceans
123
,
6260
6276
, https://doi.org/10.1029/2018JC014061 (
2018
).
38.
G. H.
Keulegan
,
Twelfth Progress Report on Model Laws for Density Currents
, The Motion of Saline Fronts in Still Water Vol.
5831
(
U.S. Department of Commerce, National Bureau of Standards
,
1958
).
39.
R.
Kelly
,
R.
Dorrell
,
A.
Burns
, and
W.
McCaffrey
, “
The structure and entrainment characteristics of partially confined gravity currents
,”
J. Geophys. Res.: Oceans
124
,
2110
2125
, https://doi.org/10.1029/2018JC014042 (
2019
).
40.
Z.
He
,
D.
Han
,
Y.-T.
Lin
,
R.
Zhu
,
Y.
Yuan
, and
P.
Jiao
, “
Propagation, mixing, and turbulence characteristics of saline and turbidity currents over rough and permeable/impermeable beds
,”
Phys. Fluids
34
,
066604
(
2022
).
41.
T. B.
Benjamin
, “
Gravity currents and related phenomena
,”
J. Fluid Mech.
31
,
209
248
(
1968
).
42.
V.
Birman
,
J.
Martin
, and
E.
Meiburg
, “
The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations
,”
J. Fluid Mech.
537
,
125
144
(
2005
).
43.
L.
Zhao
,
C.-H.
Yu
, and
Z.
He
, “
Numerical modeling of lock-exchange gravity/turbidity currents by a high-order upwinding combined compact difference scheme
,”
Int. J. Sediment Res.
34
,
240
250
(
2019
).
44.
M.
Maggi
,
C.
Adduce
, and
G.
Lane-Serff
, “
Gravity currents interacting with slopes and overhangs
,”
Adv. Water Resour.
171
,
104339
(
2023
).
45.
P.
Gauer
,
T. J.
Kvalstad
,
C. F.
Forsberg
,
P.
Bryn
, and
K.
Berg
, “
The last phase of the Storegga slide: Simulation of retrogressive slide dynamics and comparison with slide-scar morphology
,”
Mar. Pet. Geol.
22
,
171
178
(
2005
).
46.
K.
Yam
,
W. D.
McCaffrey
,
D. B.
Ingham
, and
A. D.
Burns
, “
CFD modelling of selected laboratory turbidity currents
,”
J. Hydraul. Res.
49
,
657
666
(
2011
).
47.
Z.
Xiu
,
L.
Liu
,
Q.
Xie
,
J.
Li
,
G.
Hu
, and
J.
Yang
, “
Runout prediction and dynamic characteristic analysis of a potential submarine landslide in Liwan 3-1 gas field
,”
Acta Oceanol. Sin.
34
,
116
122
(
2015
).
48.
Z.
Ge
,
W.
Nemec
,
R. L.
Gawthorpe
, and
E. W.
Hansen
, “
Response of unconfined turbidity current to normal-fault topography
,”
Sedimentology
64
,
932
959
(
2017
).
49.
Z.
Ge
,
W.
Nemec
,
A. J.
Vellinga
, and
R. L.
Gawthorpe
, “
How is a turbidite actually deposited?
,”
Sci. Adv.
8
,
eabl9124
(
2022
).
50.
R. I.
Wilson
,
H.
Friedrich
, and
C.
Stevens
, “
Turbulent entrainment in sediment-laden flows interacting with an obstacle
,”
Phys. Fluids
29
,
036603
(
2017
).
51.
D.
Liu
,
Y.
Cui
,
C. E.
Choi
,
N. A.
Bazai
,
Z.
Yu
,
M.
Lei
, and
Y.
Yin
, “
Numerical investigation of deposition mechanism of submarine debris flow
,” in
Proceedings of the 7th International Conference on Debris-Flow Hazards Mitigation
, June 10–13, Golden, Colorado (
2019
).
52.
N.
Fan
,
J.
Jiang
,
Y.
Dong
,
L.
Guo
, and
L.
Song
, “
Approach for evaluating instantaneous impact forces during submarine slide-pipeline interaction considering the inertial action
,”
Ocean Eng.
245
,
110466
(
2022
).
53.
P. A.
Allen
,
R. M.
Dorrell
,
O.
Harlen
,
R. E.
Thomas
, and
W. D.
McCaffrey
, “
Mixing in density-and viscosity-stratified flows
,”
Phys. Fluids
34
,
096605
(
2022
).
54.
Y.
Li
,
Y.
Dong
, and
G.
Chen
, “
A numerical investigation of transformation rates from debris flows to turbidity currents under shearing mechanisms
,”
Appl. Sci.
13
,
4105
(
2023
).
55.
H.
Cheng
,
Y.
Huang
, and
Q.
Xu
, “
Numerical modeling of the submarine debris flows run-out using SPH
,” in
Engineering Geology for Society and Territory
(
Springer
,
2014
), Vol.
4
, pp.
157
160
.
56.
E.
Bertevas
,
T.
Tran-Duc
,
K.
Le-Cao
,
B. C.
Khoo
, and
N.
Phan-Thien
, “
A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport
,”
Phys. Fluids
31
,
103303
(
2019
).
57.
Y.
Dong
,
D.
Wang
, and
L.
Cui
, “
Assessment of depth-averaged method in analysing runout of submarine landslide
,”
Landslides
17
,
543
555
(
2020
).
58.
J.-j.
Shi
,
W.
Zhang
,
B.
Wang
,
C.-y.
Li
, and
B.
Pan
, “
Simulation of a submarine landslide using the coupled material point method
,”
Math. Probl. Eng.
2020
,
4392581
.
59.
S.
Koshizuka
and
Y.
Oka
, “
Moving-particle semi-implicit method for fragmentation of incompressible fluid
,”
Nucl. Sci. Eng.
123
,
421
434
(
1996
).
60.
Y.
Huang
and
C.
Zhu
, “
Numerical analysis of tsunami–structure interaction using a modified MPS method
,”
Nat. Hazards
75
,
2847
2862
(
2015
).
61.
T.
Zhao
,
G.
Houlsby
, and
S.
Utili
, “
Investigation of submerged debris flows via CFD-DEM coupling
,” in
Proceedings of the Geomechanics from Micro to Macro IS Cambridge
(
Taylor and Francis Group
,
Cambridge
,
2014
), pp. 497–502.
62.
J.
Xie
,
P.
Hu
,
C.
Zhu
,
Z.
Yu
, and
T.
Pähtz
, “
Turbidity currents propagating down an inclined slope: Particle auto-suspension
,”
J. Fluid Mech.
954
,
A44
(
2023
).
63.
Y.
Lu
,
X.
Liu
,
J.
Sun
,
X.
Xie
,
D.
Li
, and
X.
Guo
, “
CFD-DEM modeling of turbidity current propagation in channels with two different topographic configurations
,”
Front. Mar. Sci.
10
,
1208739
(
2023
).
64.
Q. A.
Tran
,
G.
Grimstad
, and
S. A. G.
Amiri
, “
MPMICE: A hybrid MPM-CFD model for simulating coupled problems in porous media. Application to earthquake-induced submarine landslides
,” arXiv:2211.12761 (
2022
).
65.
X.
Guo
,
T.
Stoesser
,
D.
Zheng
,
Q.
Luo
,
X.
Liu
, and
T.
Nian
, “
A methodology to predict the run-out distance of submarine landslides
,”
Comput. Geotech.
153
,
105073
(
2023
).
66.
F.
Sahdi
,
C.
Gaudin
,
J. G.
Tom
, and
F.
Tong
, “
Mechanisms of soil flow during submarine slide-pipe impact
,”
Ocean Eng.
186
,
106079
(
2019
).
67.
M.
Nasr-Azadani
and
E.
Meiburg
, “
Turbidity currents interacting with three-dimensional seafloor topography
,”
J. Fluid Mech.
745
,
409
443
(
2014
).
68.
M. I.
Cantero
,
J. R.
Lee
,
S.
Balachandar
, and
M. H.
Garcia
, “
On the front velocity of gravity currents
,”
J. Fluid Mech.
586
,
1
39
(
2007
).
69.
S. D.
An
, “
Interflow dynamics and three-dimensional modeling of turbid density currents in IMHA reservoir, South Korea
,” Ph.D. thesis,
Colorado State University
,
2011
.
70.
G.
Constantinescu
, “
LE of shallow mixing interfaces: A review
,”
Environ. Fluid Mech.
14
,
971
996
(
2014
).
71.
L.
Ottolenghi
,
C.
Adduce
,
R.
Inghilesi
,
V.
Armenio
, and
F.
Roman
, “
Entrainment and mixing in unsteady gravity currents
,”
J. Hydraul. Res.
54
,
541
557
(
2016
).
72.
J.
Pelmard
,
S.
Norris
, and
H.
Friedrich
, “
Les grid resolution requirements for the modelling of gravity currents
,”
Comput. Fluids
174
,
256
270
(
2018
).
73.
R.
Zhu
,
Z.
He
, and
E.
Meiburg
, “
Mixing, entrainment and energetics of gravity currents released from two-layer stratified locks
,”
J. Fluid Mech.
960
,
A1
(
2023
).
74.
C. G.
Johnson
and
A. J.
Hogg
, “
Entraining gravity currents
,”
J. Fluid Mech.
731
,
477
508
(
2013
).
75.
D.
Han
,
Y.
Guo
,
P.
Jiao
,
Y.
Yuan
,
Y.-T.
Lin
, and
Z.
He
, “
Coherent structures, turbulence intermittency, and anisotropy of gravity currents propagating on a rough and porous bed
,”
Phys. Fluids
35
,
016611
(
2023
).
76.
A.
Zakeri
,
K.
Høeg
, and
F.
Nadim
, “
Submarine debris flow impact on pipelines—Part II: Numerical analysis
,”
Coastal Eng.
56
,
1
10
(
2009
).
77.
Y.
Zhang
,
Z.
Wang
,
Q.
Yang
, and
H.
Wang
, “
Numerical analysis of the impact forces exerted by submarine landslides on pipelines
,”
Appl. Ocean Res.
92
,
101936
(
2019
).
78.
X.
Qian
,
J.
Xu
,
Y.
Bai
, and
H. S.
Das
, “
Formation and estimation of peak impact force on suspended pipelines due to submarine debris flow
,”
Ocean Eng.
195
,
106695
(
2020
).
79.
X.
Guo
,
X.
Liu
,
M.
Li
, and
Y.
Lu
, “
Lateral force on buried pipelines caused by seabed slides using a CFD method with a shear interface weakening model
,”
Ocean Eng.
280
,
114663
(
2023
).
80.
R. J.
Lowe
,
J. W.
Rottman
, and
P.
Linden
, “
The non-Boussinesq lock-exchange problem. Part 1. Theory and experiments
,”
J. Fluid Mech.
537
,
101
124
(
2005
).
81.
Y.
Liu
,
T.
Stoesser
, and
H.
Fang
, “
Effect of secondary currents on the flow and turbulence in partially-filled pipes
,”
J. Fluid Mech.
938
,
A16
(
2022
).
82.
Y.
Liu
,
T.
Stoesser
, and
H.
Fang
, “
Impact of turbulence and secondary flow on the water surface in partially filled pipes
,”
Phys. Fluids
34
,
035123
(
2022
).
83.
P.
Ouro
,
B.
Fraga
,
N.
Viti
,
A.
Angeloudis
,
T.
Stoesser
, and
C.
Gualtieri
, “
Instantaneous transport of a passive scalar in a turbulent separated flow
,”
Environ. Fluid Mech.
18
,
487
513
(
2018
).
84.
J.
Bai
,
H.
Fang
, and
T.
Stoesser
, “
Transport and deposition of fine sediment in open channels with different aspect ratios
,”
Earth Surf. Processes Landforms
38
,
591
600
(
2013
).
85.
B.
Chen
,
B.
Fraga
, and
H.
Hemida
, “
Large-eddy simulation of enhanced mixing with buoyant plumes
,”
Chem. Eng. Res. Des.
177
,
394
405
(
2022
).
86.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based on the square of the velocity gradient tensor
,”
Flow, Turbul. Combust.
62
,
183
200
(
1999
).
87.
A. J.
Chorin
, “
Numerical solution of the Navier-Stokes equations
,”
Math. Comput.
22
,
745
762
(
1968
).
88.
M.
Cevheri
,
R.
McSherry
, and
T.
Stoesser
, “
A local mesh refinement approach for large-eddy simulations of turbulent flows
,”
Int. J. Numer. Methods Fluids
82
,
261
285
(
2016
).
89.
P.
Ouro
,
B.
Fraga
,
U.
Lopez-Novoa
, and
T.
Stoesser
, “
Scalability of an Eulerian-Lagrangian large-eddy simulation solver with hybrid MPI/OpenMP parallelisation
,”
Comput. Fluids
179
,
123
136
(
2019
).
90.
R.
McSherry
,
K.
Chua
,
T.
Stoesser
, and
S.
Mulahasan
, “
Free surface flow over square bars at intermediate relative submergence
,”
J. Hydraul. Res.
56
,
825
843
(
2018
).
91.
Q.
Luo
,
G.
Dolcetti
,
T.
Stoesser
, and
S.
Tait
, “
Water surface response to turbulent flow over a backward-facing step
,”
J. Fluid Mech.
966
,
A18
(
2023
).
92.
P.
Ouro
and
T.
Stoesser
, “
Impact of environmental turbulence on the performance and loadings of a tidal stream turbine
,”
Flow, Turbul. Combust.
102
,
613
639
(
2019
).
93.
K. V.
Chua
,
B.
Fraga
,
T.
Stoesser
,
S.
Ho Hong
, and
T.
Sturm
, “
Effect of bridge abutment length on turbulence structure and flow through the opening
,”
J. Hydraul. Eng.
145
,
04019024
(
2019
).
94.
C.
Gualtieri
,
A.
Angeloudis
,
F.
Bombardelli
,
S.
Jha
, and
T.
Stoesser
, “
On the values for the turbulent Schmidt number in environmental flows
,”
Fluids
2
,
17
(
2017
).
95.
V.
Dyakova
and
D.
Polezhaev
, “
Shear instability at the interface between fluid and granular medium in a horizontal rotating cylinder
,”
Phys. Fluids
35
,
043336
(
2023
).
96.
D.
Mohrig
,
C.
Ellis
,
G.
Parker
,
K. X.
Whipple
, and
M.
Hondzo
, “
Hydroplaning of subaqueous debris flows
,”
Geol. Soc. Am. Bull.
110
,
387
394
(
1998
).
97.
T.
Ilstad
,
J. G.
Marr
,
A.
Elverhøi
, and
C. B.
Harbitz
, “
Laboratory studies of subaqueous debris flows by measurements of pore-fluid pressure and total stress
,”
Mar. Geol.
213
,
403
414
(
2004
).
98.
N.
Fan
,
T.-k.
Nian
,
H.-b.
Jiao
,
X.-s.
Guo
, and
D.-f.
Zheng
, “
Evaluation of the mass transfer flux at interfaces between submarine sliding soils and ambient water
,”
Ocean Eng.
216
,
108069
(
2020
).
99.
F.
De Blasio
,
A.
Elverhøi
,
D.
Issler
,
C.
Harbitz
,
P.
Bryn
, and
R.
Lien
, “
Flow models of natural debris flows originating from overconsolidated clay materials
,”
Mar. Geol.
213
,
439
455
(
2004
).
100.
Q.
Zhang
,
S.
Draper
,
L.
Cheng
,
M.
Zhao
, and
H.
An
, “
Experimental study of local scour beneath two tandem pipelines in steady current
,”
Coastal Eng. J.
59
,
1750002
(
2017
).
101.
C.
Von Hirschhausen
,
C.
Gerbaulet
,
C.
Kemfert
,
C.
Lorenz
, and
P.-Y.
Oei
,
Energiewende “Made in Germany”: Low Carbon Electricity Sector Reform in the European Context
(
Springer
,
2018
).
102.
Y.
Li
,
M. C.
Ong
,
D. R.
Fuhrman
, and
B. E.
Larsen
, “
Numerical investigation of wave-plus-current induced scour beneath two submarine pipelines in tandem
,”
Coastal Eng.
156
,
103619
(
2020
).
103.
F.
Zhang
,
Z.
Zang
,
M.
Zhao
,
J.
Zhang
,
B.
Xie
, and
X.
Zou
, “
Numerical investigations on scour and flow around two crossing pipelines on a sandy seabed
,”
J. Mar. Sci. Eng.
10
,
2019
(
2022
).
104.
M.
Huang
,
J.
Xu
,
Z.
Luan
,
M.
Liu
,
X.
Li
, and
B.
Liu
, “
Analysis of DF1-1 subsea pipeline free-span distribution characteristics and rectification effects
,”
Mar. Sci.
45
,
77
87
(
2021
).
105.
X.-s.
Guo
,
D.-f.
Zheng
,
L.
Zhao
,
C.-w.
Fu
, and
T.-k.
Nian
, “
Quantitative composition of drag forces on suspended pipelines from submarine landslides
,”
J. Waterw., Port, Coastal, Ocean Eng.
148
,
04021050
(
2022
).
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