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 Seawater density estimation on surface footprints of internal waves

2020 ◽  
pp. 38-44
Author(s):  
А.И. Алексанин ◽  
В. Ким ◽  
И.О. Ярощук
Keyword(s):  
Density Estimation ◽  
Gravity Waves ◽  
Wave Speed ◽  
Liouville Problem ◽  
Image Data ◽  
Internal Gravity Waves ◽  
Layer Model ◽  
Frequency Model ◽  
Two Layer Model

Рассматривается проблема восстановления плотностной структуры моря на шельфе по проявлениям внутренних гравитационных волн на изображениях поверхности в поляризованном свете. По изображениям рассчитываются скорости распространения волн и их длины. Анализируется 17 случаев регистрации волн, проходивших через станции с вертикально расположенными датчиками температуры. Используется две модели вертикальной изменчивости плотности: однослойная с постоянной частотой плавучести и двухслойная с постоянной плотностью в слое. Анализируются точности решения прямых задач на основе сопоставления скоростей распространения волн, рассчитанных по профилям плотности и полученных по изображениям. Рассматриваются два варианта решения прямых задач: на основе решения задачи Штурма–Лиувилля и на основе уравнения Кортевега де Вриза. Демонстрируется возможность выбора модели среды по изменчивости скорости распространения волн на шельфе с меняющейся глубиной дна. Показывается, что при двухслойной модели среды с нижним слоем со значительно меньшей толщиной, чем у верхнего, оба подхода к решению прямых задач дают существенное занижение наблюдаемых скоростей распространения внутренних гравитационных волн. The problem of shallow water density estimation based on the surface images of internal gravity waves is considered. The images are used for calculation of internal gravity waves speed and wavelength. The seventeen cases of in-situ wave registration by vertical allocation temperature sensors are analyzed. The standard two-layer model and constant Väisälä-Brunt frequency model are explored. The wave speed is calculated by direct task solution using in situ data and image data separately, and the results are compared. Two kinds of direct task solutions are considered: as a solution of Sturm–Liouville problem and as a solution of Korteweg-de Vries equation. The relation between internal wave speed and the depth can help us to choose the density model. It is shown, that for the two-layer model with upper layer depth much higher than the bottom one both approaches to the solution of the direct task give significantly lower speed than the speed calculated from the image sequences.

The degeneration of large-scale interfacial gravity waves in lakes

2001 ◽  
Vol 434 ◽  
pp. 181-207 ◽  
Author(s):  
D. A. HORN ◽  
J. IMBERGER ◽  
G. N. IVEY
Keyword(s):  
Gravity Waves ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Field Observations ◽  
Layer Model ◽  
Lake Ecology ◽  
Initial Wave ◽  
Basin Scale ◽  
Two Layer Model

Mechanisms for the degeneration of large-scale interfacial gravity waves are identified for lakes in which the effects of the Earth's rotation can be neglected. By assuming a simple two-layer model and comparing the timescales over which each of these degeneration mechanisms act, regimes are defined in which particular processes are expected to dominate. The boundaries of these regimes are expressed in terms of two lengthscale ratios: the ratio of the amplitude of the initial wave to the depth of the thermocline, and the ratio of the depth of the thermocline to the overall depth of the lake. Comparison of the predictions of this timescale analysis with the results from both laboratory experiments and field observations confirms its applicability. The results suggest that, for small to medium sized lakes subject to a relatively uniform windstress, an important mechanism for the degeneration of large-scale internal waves is the generation of solitons by nonlinear steepening. Since solitons are likely to break at the sloping boundaries, leading to localized turbulent mixing and enhanced dissipation, the transfer of energy from an initial basin-scale seiche to shorter solitons has important implications for the lake ecology.

Internal gravity waves generated by oscillations of a sphere

1987 ◽  
Vol 183 ◽  
pp. 439-450 ◽  
Author(s):  
J. C. Appleby ◽  
D. G. Crighton
Keyword(s):  
Gravity Waves ◽  
Separation Of Variables ◽  
Near Field ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Spherical Body ◽  
The Body ◽  
Wave Radiation ◽  
Far Field ◽  
Field Solution

We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.

A note on breaking waves

1988 ◽  
Vol 419 (1857) ◽  
pp. 323-335 ◽  
Keyword(s):  
Phase Velocity ◽  
Gravity Waves ◽  
Turbulent Mixing ◽  
Wave Breaking ◽  
Richardson Number ◽  
Breaking Waves ◽  
Internal Gravity Waves ◽  
Time Interval ◽  
Wave Groups ◽  
Surface Gravity Waves

Some simple general properties of wave breaking are deduced from the known behaviour of surface gravity waves in deep water, on the assumption that breaking occurs in association with wave groups. In particular we derive equations for the time interval, ז, between the onset of breaking of successive waves: ז ═ T / |1 – ( c ⋅ c g )/ c 2 |, and for the propagation vector c b (referred to as the ‘wave-breaking vector’) of the position at which breaking, once initiated, will proceed: c b ═ c (1 – c ⋅ c g / c 2 )+ c g . Here c is the phase velocity, and c g the group velocity, of waves of period T . Interfacial waves, internal gravity waves, inertial waves and planetary waves are considered as particular examples. The results apply not only to wave breaking, but to the movement of any property (e. g. fluid acceleration, gradient Richardson number) that is carried through a medium in association with waves. One application is to describe the distribution, in space and time, of regions of turbulent mixing, or transitional phenomena, in the oceans or atmosphere.

Nonlinear internal gravity waves in a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 497-512 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Main Effect ◽  
Local Wave ◽  
The Mean ◽  
The Waves ◽  
Circulation Theorem

The interaction between internal gravity waves in a rotating frame and the mean flow is discussed for the case when the properties of the mean flow vary slowly on a scale determined by the local wave structure. The principle of conservation of wave action is established. It is shown that the main effect of the waves on the Lagrangian mean velocity is due to an appropriate ‘radiation stress’ tensor. A circulation theorem and a potential-vorticity equation are derived for the mean velocity.

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.

scholarly journals Simulating turbulent mixing caused by local instability of internal gravity waves

2021 ◽  
Vol 915 ◽  
Author(s):  
Yohei Onuki ◽  
Sylvain Joubaud ◽  
Thierry Dauxois
Keyword(s):  
Gravity Waves ◽  
Turbulent Mixing ◽  
Internal Gravity Waves ◽  
Local Instability

Abstract

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
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