The refraction of a spectrum of short internal waves by a packet of inertia waves is considered. It is found that a short inertia-wave packet produces a larger net change in a spectrum of short waves than a long inertia-wave packet, provided the short waves are trapped at some time during the interaction. Specifically, an incident narrow-banded short-wave spectrum broadens more quickly and more fully when refracted by the short inertia-wave packet. The results are explained in terms of a frequency conservation law, which constrains short-wave change in the limit of a long inertia-wave packet.
REFERENCES
1.
D.
Bruhwiler
and T.
Kaper
, “Wavenumber transport: Scattering of small-scale internal waves by large-scale wave packets
,” J. Fluid Mech.
289
, 379
(1995
).2.
A.
Lichtenberg
and M.
Lieberman
, Regular and Chaotic Dynamics
, 2nd ed. (Springer-Verlag
, New York
, 1992
).3.
J.
Vanderhoff
, K.
Nomura
, J.
Rottman
, and C.
Macaskill
, “Doppler spreading of internal gravity waves by an inertia-wave packet
,” J. Geophys. Res.
113
, C05018
, doi:10.1029/2007JC004390 (2008
).4.
D.
Broutman
, C.
Macaskill
, M.
McIntyre
, and J.
Rottman
, “On Doppler spreading models of internal waves
,” Geophys. Res. Lett.
24
, 2813
, doi:10.1029/97GL52902 (1997
).5.
D.
Broutman
and W.
Young
, “On the interaction of small-scale oceanic internal waves with near-inertial waves
,” J. Fluid Mech.
166
, 341
(1986
).6.
B.
Chirikov
and V.
Vecheslavov
, “Adiabatic invariance and separatrix: Single separatrix crossing
,” J. Exp. Theor. Phys.
90
, 562
(2000
).7.
D.
Bruhwiler
and J.
Cary
, “Diffusion of particles in a slowly modulated wave
,” Physica D
40
, 265
(1989
).8.
D.
Broutman
and R.
Grimshaw
, “The energetics of the interaction between short small-amplitude internal waves and inertial waves
,” J. Fluid Mech.
196
, 93
(1988
).9.
10.
E.
Kunze
(personal communication).11.
D.
Bruhwiler
and J.
Cary
, “Diffusion of trajectories in a simple Hamiltonian system with slow periodic forcing
,” Comput. Phys. Commun.
65
, 52
(1991
).12.
R.
Pinkel
, “On the use of Doppler sonar for internal wave measurements
,” Deep-Sea Res., Part A
28
, 269
(1981
).13.
E.
Kunze
and T.
Sanford
, “Observations of near-inertial waves in a front
,” J. Phys. Oceanogr.
14
, 566
(1984
).14.
S.
McDonald
and A.
Kaufman
, “Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation
,” Phys. Rev. A
37
, 3067
(1988
).© 2010 American Institute of Physics.
2010
American Institute of Physics
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