High sensitivity of nonlinear wave structures in the weakly stratified fluid with respect to small perturbations of density in the upstream flow was pointed out by Benney and Ko, Stud. Appl. Math., 59(3), pp. 187–199. In the present paper the influence of fine scale stratification on one of the limiting forms, namely the plateau-shaped solitary waves, is analyzed. It is demonstrated that new limiting forms of solitary waves are possible in the case of continuous stratification close to a linear or an exponential one.

Issue Section:
Technical Papers
Keywords:
stratified flow, nonlinear systems, marine vehicles, solitons, surface waves (fluid), ocean waves
Topics:
Waves, Fluids, Density, Flow (Dynamics)
1.
Benney
,
D. J.
, and
Ko
,
D. R. S.
,
1978
, “
The Propagation of Long Large Amplitude Internal Waves
,”
Stud. Appl. Math.
,
59
(
3
), pp.
187
–
199
.
2.
Amick
,
C. J.
, and
Turner
,
R. E. L.
,
1986
, “
A Global Theory of Internal Solitary Waves in Two-Fluid Systems
,”
Trans. Am. Math. Soc.
,
298
(
2
), pp.
431
–
484
.
3.
Derzho
,
O. G.
, and
Grimshaw
,
R.
,
1997
, “
Solitary Waves with a Vortex Core in a Shallow Layer of Stratified Fluid
,”
Phys. Fluids
,
9
(
11
), pp.
3378
–
3385
.
4.
Benjamin
,
T. B.
,
1971
, “
A Unified Theory of Conjugate Flows
,”
Philos. Trans. R. Soc. London, Ser. A
,
269
, pp.
587
–
643
.
5.
Makarenko
,
N. I.
,
1999
, “
Conjugate Flows and Smooth Bores in a Weakly Stratified Fluid
,”
J. Appl. Mech. Tech. Phys.
,
40
(
2
), pp.
249
–
257
.
6.
Maltseva, J. L., 2000, “Flat Solitary Waves in a Two-Layer Fluid,” Proc. 5th International Symposium on Stratified Flows, G. Lawrence et al., eds., University of British Columbia, Vancouver, Canada, pp. 803–808.
7.
Lamb
,
K. G.
, and
Wan
,
B.
,
1998
, “
Conjugate Flows and Flat Solitary Waves for a Continuously Stratified Fluid
,”
Phys. Fluids
,
26
, pp.
2061
–
2079
.
8.
Bukreev
,
V. I.
, and
Gusev
,
A. V.
,
1998
, “
Forced Smooth Bore in a Continuously Stratified Fluid
,”
Dokl. Ross. Akad. Nauk
,
363
(
3
), pp.
327
–
329
.
9.
Grue
,
J.
,
Jensen
,
A.
,
Rusa˚s
,
P.-O.
, and
Sveen
,
J. K.
,
2000
, “
Breaking and Broadening of Internal Solitary Waves
,”
J. Fluid Mech.
,
413
, pp.
181
–
217
.
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