Weakly-Nonlinear, Long Internal Gravity Waves in Stratified Fluids of Finite Depth

1978 ◽  
Vol 12 (4) ◽  
pp. 157-165 ◽  
Author(s):  
T. Kubota ◽  
D.R.S. Ko ◽  
L.D. Dobbs
Keyword(s):  
Gravity Waves ◽  
Finite Depth ◽  
Internal Gravity Waves ◽  
Stratified Fluids ◽  
Weakly Nonlinear

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

scholarly journals Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth

1987 ◽  
Vol 184 ◽  
pp. 183-206 ◽  
Author(s):  
Juan A. Zufiria
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Hamiltonian Formulation ◽  
Finite Depth ◽  
Capillary Waves ◽  
Bifurcation Structure ◽  
Low Gravity ◽  
Bifurcation Tree ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Model

A weakly nonlinear model is developed from the Hamiltonian formulation of water waves, to study the bifurcation structure of gravity-capillary waves on water of finite depth. It is found that, besides a very rich structure of symmetric solutions, non-symmetric Wilton's ripples exist. They appear via a spontaneous symmetrybreaking bifurcation from symmetric solutions. The bifurcation tree is similar to that for gravity waves. The solitary wave with surface tension is studied with the same model close to a critical depth. It is found that the solution is not unique, and that further non-symmetric solitary waves are possible. The bifurcation tree has the same structure as for the case of periodic waves. The possibility of checking these results in low-gravity experiments is postulated.

On strongly nonlinear gravity waves in a vertically sheared atmosphere

2021 ◽  
Author(s):  
Georg Sebastian Voelker ◽  
Mark Schlutow
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Wave Drag ◽  
Mean Flow ◽  
Flow Strength ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
The Mean

<p>Internal gravity waves are a well-known mechanism of energy redistribution in stratified fluids such as the atmosphere. They may propagate from their generation region, typically in the Troposphere, up to high altitudes. During their lifetime internal waves couple to the atmospheric background through various processes. Among the most important interactions are the exertion of wave drag on the horizontal mean-flow, the heat generation upon wave breaking, or the mixing of atmospheric tracers such as aerosols or greenhouse gases.</p><p>Many of the known internal gravity wave properties and interactions are covered by linear or weakly nonlinear theories. However, for the consideration of some of the crucial effects, like a reciprocal wave-mean-flow interaction including the exertion of wave drag on the mean-flow, strongly nonlinear systems are required. That is, there is no assumption on the wave amplitude relative to the mean-flow strength such that they may be of the same order.</p><p>Here, we exploit a strongly nonlinear Boussinesq theory to analyze the stability of a stationary internal gravity wave which is refracted at the vertical edge of a horizontal jet. Thereby we assume that the incident wave is horizontally periodic, non-hydrostatic, and vertically modulated. Performing a linear stability analysis in the vicinity of the jet edge we find necessary and sufficient criteria for instabilities to grow. In particular, the refracted wave becomes unstable if its incident amplitude is large enough and both mean-flow horizontal winds, below and above the edge of the jet, do not exceed particular upper bounds.</p>

Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study

1968 ◽  
Vol 34 (3) ◽  
pp. 609-624 ◽  
Author(s):  
Walter L. Jones
Keyword(s):  
Gravity Waves ◽  
Richardson Number ◽  
Numerical Study ◽  
Internal Gravity Waves ◽  
Three Dimensions ◽  
Stratified Fluids ◽  
Reflected Wave ◽  
Horizontal Wave ◽  
Numerical Examination ◽  
Stability Of Waves

A numerical examination has been made of the reflectivity of critical levels with low Richardson number to internal gravity waves propagating in stratified fluids with shear. At sufficiently low positive Richardson numbers the reflected wave may actually be stronger than the incident.The normal mode instabilities of three simple models have also been computed. The results are presented in three dimensions: Richardson number, horizontal wave scale and real wave frequency.

scholarly journals Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility

2020 ◽  
Vol 5 (7) ◽  
Author(s):  
Clément Savaro ◽  
Antoine Campagne ◽  
Miguel Calpe Linares ◽  
Pierre Augier ◽  
Joël Sommeria ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Weakly Nonlinear
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