Interference and transmission of spatiotemporally locally forced internal waves in non-uniform stratifications

2019 ◽  
Vol 866 ◽  
pp. 350-368
Author(s):  
Rohit Supekar ◽  
Thomas Peacock
Keyword(s):  
Experimental Study ◽  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Laboratory Experiments ◽  
Model Analysis ◽  
Destructive Interference ◽  
Two Dimensional ◽  
Wave Fields ◽  
Spatiotemporal Localization

Studies of the effects of constructive or destructive interference on the transmission of internal waves through non-uniform stratifications have typically been performed for internal wave fields that are spatiotemporally harmonic. To understand the impacts of spatiotemporal localization, we present a theoretical and experimental study of the transmission of two-dimensional internal waves that are generated by a boundary forcing that is localized in both space and time. The model analysis reveals that sufficient localization leads to the disappearance of transmission peaks and troughs that would otherwise be present for a harmonic forcing. The corresponding laboratory experiments that we perform provide clear demonstration of this effect. Based on the group velocity and angle of propagation of the internal waves, a practical criterion that assesses when the transmission peaks or troughs are evident is obtained.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

scholarly journals Interaction Features of Internal Wave Breathers in a Stratified Ocean

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 205
Author(s):  
Ekaterina Didenkulova ◽  
Efim Pelinovsky
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Vries Equation ◽  
Internal Gravity Waves ◽  
Wave Fields ◽  
Tidal Waves ◽  
Stratified Ocean

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.

Estimating pressure and internal-wave flux from laboratory experiments in focusing internal waves

2020 ◽  
Vol 61 (11) ◽  
Author(s):  
Pierre-Yves Passaggia ◽  
Vamsi K. Chalamalla ◽  
Matthew W. Hurley ◽  
Alberto Scotti ◽  
Edward Santilli
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Laboratory Experiments ◽  
Wave Flux

scholarly journals Bispectral Analysis of Energy Transfer within the Two-Dimensional Oceanic Internal Wave Field

2005 ◽  
Vol 35 (11) ◽  
pp. 2104-2109 ◽  
Author(s):  
Naoki Furuichi ◽  
Toshiyuki Hibiya ◽  
Yoshihiro Niwa
Keyword(s):  
Internal Wave ◽  
Wave Field ◽  
Internal Waves ◽  
Internal Tide ◽  
Energy Cascade ◽  
Minor Role ◽  
Two Dimensional ◽  
Bispectral Analysis ◽  
Internal Wave Field ◽  
Oceanic Internal Wave

Abstract Bispectral analysis of the numerically reproduced spectral responses of the two-dimensional oceanic internal wave field to the incidence of the low-mode semidiurnal internal tide is performed. At latitudes just equatorward of 30°, the low-mode semidiurnal internal tide dominantly interacts with two high-vertical-wavenumber diurnal (near inertial) internal waves, forming resonant triads of parametric subharmonic instability (PSI) type. As the high-vertical-wavenumber near-inertial energy level is raised by this interaction, the energy cascade to small horizontal and vertical scales is enhanced. Bispectral analysis thus indicates that energy in the low-mode semidiurnal internal tide is not directly transferred to small scales but via the development of high-vertical-wavenumber near-inertial current shear. In contrast, no noticeable energy cascade to high vertical wavenumbers is recognized in the bispectra poleward of ∼30° as well as equatorward of ∼25°. A new finding is that, although PSI is possible equatorward of ∼30°, the efficiency drops sharply as the latitude falls below ∼25°. At all latitudes, another resonant interaction suggestive of induced diffusion is found to occur between the low-mode semidiurnal internal tide and two high-frequency internal waves, although bispectral analysis shows that this interaction plays only a minor role in cascading the low-mode semidiurnal internal tide energy.

Experimental Study of Ship Internal Waves—The Supersonic Case

1993 ◽  
Vol 115 (1) ◽  
pp. 16-22 ◽  
Author(s):  
H. Ma ◽  
M. P. Tulin
Keyword(s):  
Experimental Study ◽  
Internal Wave ◽  
Wave Field ◽  
Experimental Method ◽  
Internal Waves ◽  
Measured Data ◽  
Density Distributions ◽  
Wave Patterns ◽  
Wave Profiles ◽  
Theoretical Results

Internal waves produced by a ship traveling faster than the fastest internal waves (supersonic case) were investigated experimentally in our laboratory in a wide tank using averaging conductivity wave gages developed for this investigation. The wave gage is similar to the conductivity probe, but has space-averaging electrodes. An array of seven such gages was used in a wave tank with dimensions 12 ft length, 8 ft width, 2 ft depth. The water in the tank was stratified with salt to obtain desired density distributions. A spheroid, split vertically, was towed against and along a sidewall to simulate a moving ship. Simultaneous wave profiles at various distances normal to the track of the ship were obtained for different Froude numbers and density distributions. The internal wave patterns were calculated from the measured data and compared with theoretical results. The amplitude on the first crest of the internal wave field is also plotted against the distance from the ship, and a limited comparison with theory is made. The experimental method developed for this study is sensitive, simple and reliable. It may serve to obtain a data base for ship-generated internal waves under a variety of conditions.

Spectra and Coherence of Wind-Generated Internal Waves

1976 ◽  
Vol 33 (10) ◽  
pp. 2323-2328 ◽  
Author(s):  
R. H. Käse ◽  
C. L. Tang
Keyword(s):  
Energy Density ◽  
Internal Wave ◽  
Internal Waves ◽  
Wind Stress ◽  
Wave Mode ◽  
Wave Number ◽  
Small Scale ◽  
Two Dimensional ◽  
Scale Turbulence ◽  
Main Thermocline

On the basis of a model for an internal wave field that is generated by a randomly varying isotropic wind stress and in which energy is transferred to small-scale turbulence, we derive the two-dimensional energy density function. The coherence scales are determined by the highest order internal wave mode that is not affected by virtual friction in the main thermocline, provided the curl of the wind stress has a white noise wave number spectrum. In general, this mode number scale is increasing monotonically with frequency. As a result of such a frequency dependent mode bandwidth, the vertical coherence drops with increasing frequency.

scholarly journals Generation of mode-2 internal waves in a two-dimensional stratification by a mode-1 internal wave

Wave Motion ◽  
2018 ◽  
Vol 83 ◽  
pp. 227-240
Author(s):  
Jianjun Liang ◽  
Tao Du ◽  
Xiaoming Li ◽  
Mingxia He
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Two Dimensional ◽  
Mode 2

The limiting form of internal waves

1984 ◽  
Vol 394 (1807) ◽  
pp. 329-344 ◽  
Keyword(s):  
Free Surface ◽  
Internal Wave ◽  
Internal Waves ◽  
Solitary Waves ◽  
The Other ◽  
Stokes Wave ◽  
Internal Solitary Waves ◽  
Two Dimensional ◽  
Extreme Form ◽  
Eddy Formation

The bifurcation of two-dimensional internal solitary waves in a perfect density stratified fluid between horizontal walls under gravity is studied near to a point of incipient eddy formation. It is shown that eddies do not attach to the walls. Moreover, along the bifurcating branch there is always a flow with a singular cusped streamline before the formation of eddies. This flow with the cusped streamline is an example of what we call an internal wave of limiting form, by analogy with the Stokes wave of extreme form in the free surface problem. Two examples are given where the primary density stratification ensures the existence of a limiting wave of depression in one case, and of elevation in the other.

scholarly journals A THEORETICAL AND EXPERIMENTAL STUDY OF UNDERTOW

1984 ◽  
Vol 1 (19) ◽  
pp. 151 ◽  
Author(s):  
J. Buhr Hansen ◽  
I.A. Svendsen
Keyword(s):  
Experimental Study ◽  
Mass Flux ◽  
Laboratory Experiments ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rip Currents ◽  
Longshore Currents ◽  
Theoretical Results ◽  
Recent Laboratory

It is well known that on a three-dimensional beach large volumes of water carried shorewards by the breakers feed longshore currents, which eventually escape back through the breaker line, often as rip currents. In a steady two-dimensional situation, however, the mass flux represented by (among other things) the surface roller in the breakers returns as a seaward current close to the bottom. This current is called the undertow. In this paper theoretical results for the undertow are compared with the results of recent laboratory experiments.

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