Internal Gravity Waves Excited by a Moving Oscilatting Source in a Stratified medium with Variable Buoyancy

2019 ◽  
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Stratified Medium

Excitation and breaking of internal gravity waves by parametric instability

1998 ◽  
Vol 374 ◽  
pp. 117-144 ◽  
Author(s):  
DOMINIQUE BENIELLI ◽  
JOËL SOMMERIA
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Parametric Instability ◽  
Excitation Frequency ◽  
Vertical Plane ◽  
Excitation Amplitude ◽  
Internal Gravity Waves ◽  
Stratified Medium ◽  
Primary Wave ◽  
Maximum Slope

We study the dynamics of internal gravity waves excited by parametric instability in a stably stratified medium, either at the interface between a water and a kerosene layer, or in brine with a uniform gradient of salinity. The tank has a rectangular section, and is narrow to favour standing waves with motion in the vertical plane. The fluid container undergoes vertical oscillations, and the resulting modulation of the apparent gravity excites the internal waves by parametric instability.Each internal wave mode is amplified for an excitation frequency close to twice its natural frequency, when the excitation amplitude is sufficient to overcome viscous damping (these conditions define an ‘instability tongue’ in the parameter space frequency-amplitude). In the interfacial case, each mode is well separated from the others in frequency, and behaves like a simple pendulum. The case of a continuous stratification is more complex as different modes have overlapping instability tongues. In both cases, the growth rates and saturation amplitudes behave as predicted by the theory of parametric instability for an oscillator. However, complex friction effects are observed, probably owing to the development of boundary-layer instabilities.In the uniformly stratified case, the excited standing wave is unstable via a secondary parametric instability: a wave packet with small wavelength and half the primary wave frequency develops in the vertical plane. This energy transfer toward a smaller scale increases the maximum slope of the iso-density surfaces, leading to local turning and rapid growth of three-dimensional instabilities and wave breaking. These results illustrate earlier stability analyses and numerical studies. The combined effect of the primary excitation mechanism and wave breaking leads to a remarkable intermittent behaviour, with successive phases of growth and decay for the primary wave over long timescales.

An investigation of internal gravity waves generated by a buoyantly rising fluid in a stratified medium

1973 ◽  
Vol 57 (02) ◽  
pp. 229 ◽  
Author(s):  
T. I. Mclaren ◽  
A. D. Pierce ◽  
T. Fohl ◽  
B. L. Murphy
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Stratified Medium

Internal Gravity Waves in a Stratified Medium

2021 ◽  
pp. 145-167
Author(s):  
Anatoly Kistovich ◽  
Konstantin Pokazeev ◽  
Tatiana Chaplina
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Stratified Medium

scholarly journals Analytical Approximations of Dispersion Relations for Internal Gravity Waves Equation with Shear Flows

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1865
Author(s):  
Vitaly Bulatov ◽  
Yury Vladimirov
Keyword(s):  
Bessel Function ◽  
Dispersion Equation ◽  
Gravity Waves ◽  
Shear Flows ◽  
Internal Gravity Waves ◽  
Stratified Medium ◽  
Buoyancy Frequency ◽  
Modified Bessel Function ◽  
Analytical Approximations ◽  
Background Shear

The problem of internal gravity waves fields in a stratified medium of finite depth is considered for model distributions of background shear currents. For the analytical solution of the problem, a constant distribution of the buoyancy frequency and various linear dependences of the background shear current on depth were used. The dispersion dependences are obtained, which are expressed in terms of the modified Bessel function of the imaginary index. Under the Miles–Howard stability condition and large Richardson numbers, the Debye asymptotics of the modified Bessel function of the imaginary index were used to construct analytical solutions. The dispersion equation is solved using the proposed analytical approximation. The properties of the dispersion equation are studied and the main analytical characteristics of the dispersion curves are investigated depending on the parameters of background shear flows.

scholarly journals Numerical modelling of tsunami wave run-up and breaking within a two-dimensional atmosphere–ocean two-layer model

2014 ◽  
Vol 2 (5) ◽  
pp. 3397-3421
Author(s):  
S. P. Kshevetskii ◽  
I. S. Vereshchagina
Keyword(s):  
Gravity Waves ◽  
Turbulent Mixing ◽  
Tsunami Wave ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Fluid Mixing ◽  
Stratified Medium ◽  
Layer Model ◽  
Two Layer Model ◽  
Run Up

Abstract. A numerical model of propagation of internal gravity waves in a stratified medium is applied to the problem of tsunami wave run-up onto a shore. In the model, the ocean and the atmosphere is considered as a united continuum whose the density varies with height with a saltus at a water–air boundary. Correct conditions of join at a water–air interlayer are automatically ensured because the solution is searched for as a generalised one. The density stratification in the ocean and in the atmosphere is supposed to be an exponential one, but in the ocean, a scale of stratification of density is large and the density varies slightly. The wave running to a shore is taken as a long solitary wave. The wave evolution is simulated with consideration of time-varying vertical wave structure. Inshore, the wave breaks down, and intensive turbulent mixing develops in water thickness. The effect of breakdown depends on shape of the bottom. If slope of the bottom is small, and inshore the depth grows slowly with distance from a shore, then mixing happens only in the upper stratum of the fluid, thanks to formation of a dead region near the bottom. If the bottom slope inshore is significant, then the depth of fluid mixing is dipped up to 50 metres. The developed model shows the depth of mixing effects strongly depends on shape of a bottom, and the model may be useful for investigation of influences of strong gales and hurricanes on coastline and beaches and investigation of dependence of stability of coastline and beaches on bottom shape.

scholarly journals Generation of Internal Gravity Waves Far from Moving Non-Local Source

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1899
Author(s):  
Vitaly Bulatov ◽  
Yury Vladimirov
Keyword(s):  
Gravity Waves ◽  
Finite Depth ◽  
Internal Gravity Waves ◽  
Radial Symmetry ◽  
Stratified Medium ◽  
Local Source ◽  
Natural Sources ◽  
Model Distribution ◽  
Different Depths ◽  
Non Local

We consider analytical solutions describing the generation of internal gravity waves far from a non-local source of disturbances. We suppose that the source moves on the surface of stratified medium of a finite depth. A model distribution of the non-local source shape with radial symmetry is used. This approximation correctly describes (qualitatively) the main spatiotemporal characteristics of natural sources of generation of internal gravity waves in the ocean. The resulting solution is the sum of wave modes. The solution is presented as a series of eigenfunctions of the spectral problem of internal gravity waves. The results of numerical calculations of internal gravity waves components at different depths are presented and discussed.

Model of the internal gravity waves excited by lithospheric greenhouse effect gases

2001 ◽  
Vol 7 (2s) ◽  
pp. 26-33 ◽  
Author(s):  
O.E. Gotynyan ◽  
◽  
V.N. Ivchenko ◽  
Yu.G. Rapoport ◽  
◽  
...  
Keyword(s):  
Gravity Waves ◽  
Greenhouse Effect ◽  
Internal Gravity Waves
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