The reflection of beams of internal gravity waves at a flat rigid surface

Kistovich, Yu. V.; Chashechkin, Yu. D.

doi:10.1016/0021-8928(95)00067-4

Cited by 15 publications

(9 citation statements)

References 1 publication

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“…Although the form of solutions (3.2) differs significantly from (3.1), all the expressions remain finite. The solutions of the two-dimensional wave emission problem, obtained as the limiting case of the three-dimensional problem, are, in general, consistent with [14].…”

Section: Solutions Of the Dispersion Equation And Their Behavior In Tsupporting

confidence: 73%

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

Vasil’ev¹,

Chashechkin²

2006

Fluid Dyn

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An analytical solution of a linearized problem of the emission of periodic internal waves by part of a plane which oscillates with a small amplitude in an arbitrary direction in a viscous exponentially stratified fluid is constructed. Solutions of the dispersion equation are given for all positions of the emitting surface (arbitrary, vertical, horizontal, and critical when one of the beam propagation directions is collinear with the emitting surface). The possibility of transition to the case of a uniform fluid, which is important for applications, is analyzed.

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Section: Solutions Of the Dispersion Equation And Their Behavior In Tsupporting

confidence: 73%

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

Vasil’ev¹,

Chashechkin²

2006

Fluid Dyn

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“…(The implication of breaking on the fluid is discussed in Section 3.3.) In contrast to these inviscid results, viscosity and diffusion stabilize a steady solution even at the critical angle (Kistovich & Chashechkin 1995).…”

Section: Focusing By Wall Reflectionmentioning

confidence: 67%

INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Staquet

Sommeria

2002

Annu. Rev. Fluid Mech.

315

268

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We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steepening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. The influence of those processes upon the fluid medium by mean flow changes is discussed. The specific properties of wave turbulence, induced by wave-wave interactions and breaking, are illustrated by comparative studies of oceanic and atmospheric observations, as well as laboratory and numerical experiments. We then review the different attempts at a statistical description of internal gravity wave fields, whether weakly or strongly interacting.

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“…where is the kinematic viscosity and K is the magnitude of the wave vector (Kistovich and Chashechkin 1995). After reflection, changes in K must then be compensated with changes in , especially when focusing of the wave rays produces larger values of K. For low-period attractors, viscous diffusion then balances geometrical focusing of the rays and the motion concentrates in a shear layer around the attracting trajectory, as is shown numerically by Dintrans et al (1999) and Rieutord et al (2001).…”

Section: Discussionmentioning

confidence: 98%

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

2006

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Field data and numerical simulations were used to investigate the effects of basin shape, continuous stratification, and rotation on the three-dimensional structure of the dominant natural basin-scale internal-wave modes in Lake Kinneret, a stratified lake large enough so that the earth's rotation influences the wave motion. The structure of the modes was inferred from power spectral density of measured and simulated isotherm vertical displacements and from rotary-power spectral density of isopycnal velocities obtained from numerical simulations. The shape of the lake at the level of the thermocline, in conjunction with the dispersion relationship, determines the horizontal configuration of the natural modes. The dominant response to wind forcing was an azimuthal and vertical mode 1 Kelvin wave with a natural period of 22.6 h that propagated around the entire basin; the second most dominant response was a vertical mode 1 wave with a natural period close to 10.5 h and composed of two counter-rotating Poincaré circular cells. The sloping bottom produced an intensification of vertical displacements and velocities over the slope due to focusing of waves rays after reflection at bottom slopes close to the critical angle. The amplitude of the observed oscillations was very sensitive to the phase of the wind relative to the existing waves; resonance was affected by the cessation time of the wind events because it defines the local forcing period and resets the phase of the observed oscillations.

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The reflection of beams of internal gravity waves at a flat rigid surface

Cited by 15 publications

References 1 publication

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

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