scholarly journals Two-Dimensional Gravity Waves in a Stratified Ocean

1967 ◽  
Vol 10 (3) ◽  
pp. 482 ◽  
Author(s):  
T. Yao-Tsu Wu
Keyword(s):  
Gravity Waves ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Stratified Ocean

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

Scattering of internal tides by irregular bathymetry of large extent

2014 ◽  
Vol 747 ◽  
pp. 481-505 ◽  
Author(s):  
Yile Li ◽  
Chiang C. Mei
Keyword(s):  
Gravity Waves ◽  
Method Of Characteristics ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stratified Ocean ◽  
Stationary Random Function

AbstractWe present an analytical theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on a linearized approximation, the idealized case of constant mean sea depth and Brunt–Väisälä frequency is considered. The depth fluctuation is assumed to be a stationary random function of space, characterized by small amplitude and a correlation length comparable to the typical wavelength. For both one- and two-dimensional topographies the effects of scattering on the wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Bühler & Holmes-Cerfon (J. Fluid Mech., vol. 678, 2011, pp. 271–293), computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

Gravity waves in flowing water

1955 ◽  
Vol 231 (1187) ◽  
pp. 496-504 ◽  
Keyword(s):  
Gravity Waves ◽  
Flowing Water ◽  
Two Dimensional ◽  
First Derivative ◽  
Linear Waves ◽  
Dimensional Gravity ◽  
Uniform Current ◽  
Velocity Of Propagation ◽  
The One ◽  
A Current

Some particular cases of the effect of a non-uniform current on two-dimensional gravity waves are considered. For linear waves on a current varying as the one-seventh power of the depth, the velocity of propagation can be found as a power series in the square root of the Froude number. For the non-linear solitary and cnoidal waves, both the profile and the velocity are found to depend on the value at the free surface of the current and its first derivative.

Wind effects on the nonlinear evolution of slowly varying gravity—capillary waves

1994 ◽  
Vol 267 ◽  
pp. 221-250 ◽  
Author(s):  
Tetsu Hara ◽  
Chiang C. Mei
Keyword(s):  
Gravity Waves ◽  
Evolution Equations ◽  
Modulational Instability ◽  
Peak Frequency ◽  
Capillary Waves ◽  
Initial Growth ◽  
Two Dimensional ◽  
Spectral Evolution ◽  
Unequal Rates ◽  
Dimensional Gravity

A train of uniform two-dimensional gravity waves in deep water is known to be unstable to certain sideband disturbances. If the time of propagation is sufficiently long for the fourth-order terms to be important, the sidebands may grow at unequal rates, resulting in a downward shift of peak frequency. But this shift is only a temporary phase of a recurrent evolution process. Recent work by us (Hara & Mei 1991) has shown that wind and dissipation can help maintain this downshift at large time. In this paper we examine a similar two-dimensional problem for capillary–gravity waves. The basic flow in air and water is assumed to be steady, horizontally uniform and turbulent; the wave-induced flow in both media is assumed to be laminar. Evolution equations are deduced with wind and dissipation included in such a way that their influence is comparable to the asymmetric spectral evolution. After finding the initial growth rates of unstable sidebands, the nonlinear development of modulational instability is examined by integrating the evolution equations numerically. Computed results show that persistent downshift of frequency can happen for relatively long waves, but upshift occurs for very short waves.

scholarly journals Two-dimensional generalized solitary waves and periodic waves under an ice sheet

2011 ◽  
Vol 369 (1947) ◽  
pp. 2957-2972 ◽  
Author(s):  
Jean-Marc Vanden-Broeck ◽  
Emilian I. Părău
Keyword(s):  
Solitary Waves ◽  
Gravity Waves ◽  
Ice Sheet ◽  
Periodic Waves ◽  
Two Dimensional ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Dimensional Gravity ◽  
Nonlinear Solutions

Two-dimensional gravity waves travelling under an ice sheet are studied. The flow is assumed to be potential. Weakly nonlinear solutions are derived and fully nonlinear solutions are calculated numerically. Periodic waves and generalized solitary waves are studied.

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

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