Effect of Water Vorticity on Wind-Generated Gravity Waves in Finite Depth

Water Waves ◽  
2021 ◽  
Author(s):  
Malek Abid ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Finite Depth ◽  
Effect Of Water

scholarly journals Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part II: Shear Flow with a Critical Level

2010 ◽  
Vol 67 (3) ◽  
pp. 694-712 ◽  
Author(s):  
Ji-Young Han ◽  
Jong-Jin Baik
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Wind Direction ◽  
Critical Level ◽  
Deep Convection ◽  
Vertical Wind Shear ◽  
Finite Depth ◽  
Vertical Displacement ◽  
Two Dimensions ◽  
Three Dimensions

Abstract Convectively forced mesoscale flows in a shear flow with a critical level are theoretically investigated by obtaining analytic solutions for a hydrostatic, nonrotating, inviscid, Boussinesq airflow system. The response to surface pulse heating shows that near the center of the moving mode, the magnitude of the vertical velocity becomes constant after some time, whereas the magnitudes of the vertical displacement and perturbation horizontal velocity increase linearly with time. It is confirmed from the solutions obtained in present and previous studies that this result is valid regardless of the basic-state wind profile and dimension. The response to 3D finite-depth steady heating representing latent heating due to cumulus convection shows that, unlike in two dimensions, a low-level updraft that is necessary to sustain deep convection always occurs at the heating center regardless of the intensity of vertical wind shear and the heating depth. For deep heating across a critical level, little change occurs in the perturbation field below the critical level, although the heating top height increases. This is because downward-propagating gravity waves induced by the heating above, but not near, the critical level can hardly affect the flow response field below the critical level. When the basic-state wind backs with height, the vertex of V-shaped perturbations above the heating top points to a direction rotated a little clockwise from the basic-state wind direction. This is because the V-shaped perturbations above the heating top is induced by upward-propagating gravity waves that have passed through the layer below where the basic-state wind direction is clockwise relative to that above.

New solutions for periodic interfacial gravity waves

2021 ◽  
Vol 928 ◽  
Author(s):  
X. Guan ◽  
J.-M. Vanden-Broeck ◽  
Z. Wang
Keyword(s):  
Integral Equation ◽  
Excellent Agreement ◽  
Gravity Waves ◽  
Global Bifurcation ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Fourier Expansions ◽  
Wave Profiles

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

scholarly journals Capillary–gravity waves on a dielectric fluid of finite depth under normal electric field

2019 ◽  
Vol 77 ◽  
pp. 98-107 ◽  
Author(s):  
Tao Gao ◽  
Alex Doak ◽  
Jean-Marc Vanden-Broeck ◽  
Zhan Wang
Keyword(s):  
Electric Field ◽  
Gravity Waves ◽  
Finite Depth ◽  
Dielectric Fluid ◽  
Normal Electric Field

Nonlinear effects on shoaling surface gravity waves

1984 ◽  
Vol 311 (1515) ◽  
pp. 1-41 ◽  
Keyword(s):  
Wave Field ◽  
Gravity Waves ◽  
Fourier Coefficients ◽  
Nonlinear Models ◽  
Finite Depth ◽  
Surface Gravity ◽  
Spectral Energy ◽  
Frequency Space ◽  
Surface Gravity Waves ◽  
Wide Range

Two nonlinear models that describe the shoaling of unidirectional surface gravity waves are developed. Based on variants of Boussinesq’s equations, the models are cast as a set of coupled evolution equations for the amplitudes and phases of the temporal Fourier modes of the wave field. Triad interactions across the entire wind wave frequency band (0.05-0.25 Hz) provide the mechanism for cross spectral energy transfers and modal phase modifications as the waves propagate shoreward through the shoaling region (10-3 m depth). A field experiment, designed to test the operational validity of the nonlinear shoaling models, provided data on wave parameters over a wide range of conditions. Three representative data sets illustrating different initial spectral shapes and subsequent evolutions are compared with predictions of the nonlinear shoaling models and linear, finite-depth theory. Power spectral comparisons, as well as spectra of coherence and relative phase between model predictions and data, indicate that the nonlinear models accurately predict Fourier coefficients of the wave field through the shoaling region sets. Differences between the predictions of the various models are related to differences in the models' dispersion relations. Although generally inferior to the nonlinear models, linear, finite-depth theory accurately predicts Fourier coefficients in regions of physical and frequency space where nonlinear evolution of the power spectrum is not observed, thus verifying the validity of the linear, finite-depth dispersion relation in limited portions of physical and frequency space in the shoaling region.

scholarly journals Wavemaker theories for acoustic–gravity waves over a finite depth

2017 ◽  
Vol 108 (1) ◽  
pp. 25-35 ◽  
Author(s):  
Miao Tian ◽  
Usama Kadri
Keyword(s):  
Gravity Waves ◽  
Finite Depth ◽  
Acoustic Gravity Waves

The Role of Nonnormality in Overreflection Theory

2010 ◽  
Vol 67 (8) ◽  
pp. 2547-2558 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Brian F. Farrell
Keyword(s):  
Shear Layer ◽  
Gravity Waves ◽  
Finite Depth ◽  
Stimulated Emission ◽  
Incoming Wave ◽  
Propagating Waves ◽  
Three Stages ◽  
Orr Mechanism ◽  
Weak Stratification

Abstract The role of nonnormality in the overreflection of gravity waves is investigated. In the limit of weak stratification, wave packets having a critical level inside a shear layer of finite depth are reflected with amplified energy. This process, which exhibits the characteristics of stimulated emission, occurs in three stages: first, the incoming wave enters the shear layer and excites nonpropagating perturbations leaning with and against the shear. Subsequently, the energy of perturbations leaning against the shear grows in a manner similar to energy growth of perturbations in constant shear flows, indicating that the Orr mechanism that is slightly modified by stratification underlies the observed growth. Finally, the amplified perturbations excite propagating waves originating from the vicinity of the shear layer boundary. The role of nonnormality in this process is also investigated from the perspective of the associated nonorthogonality of the modes of the dynamical system. It is found that the incident wave packet projects on nonorthogonal analytic modes having the structure of a downward propagating wave in the far field below the shear layer and overreflection expressed by the interaction among these nonorthogonal modes.

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
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