Internal waves in a two-layer system using fully nonlinear internal-wave equations

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
K. Nakayama ◽  
T. Kakinuma
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Equations ◽  
Layer System ◽  
Nonlinear Internal Wave ◽  
Fully Nonlinear

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

Nonlinear internal wave generation over the Yermak Plateau 

2021 ◽  
Author(s):  
Gabin Urbancic ◽  
Kevin Lamb ◽  
Ilker Fer ◽  
Laurie Padman
Keyword(s):  
Internal Wave ◽  
Arctic Ocean ◽  
Internal Waves ◽  
Wave Generation ◽  
The Arctic ◽  
Nonlinear Internal Wave ◽  
Nonlinear Internal Waves ◽  
The Arctic Ocean ◽  
Yermak Plateau ◽  
Internal Wave Generation

<p>North of the critical latitude (78.4), internal waves of the M<sub>2</sub> tidal frequency can no longer freely propagate, and the energy conversion from the barotropic to the internal tides vanishes. Near the continental slopes around the Arctic Ocean, internal wave energy is enhanced and comparable to values at mid-latitudes (Rippeth et al. 2015, Levine et al. 1985). Observations on the northern flank of the Yermak Plateau (YP) has characterized the region as one of enhanced internal wave activity and nonlinear internal waves have been observed (Czipott et al. 1991, Padman and Dillon 1991).</p><p>The YP is a bathymetry feature stretching out into the Fram Strait north-west of Svalbard. The YP plays a prominent role in the Arctic’s heat balance due to its interaction with the West-Spitsbergen current which is a main contributor to the heat transport into the Arctic Ocean. Nonlinear waves generated over the YP are a significant energy source for mixing and can therefore modulate and force exchange processes.</p><p>To study the nonlinear internal wave generation mechanisms over the YP, we used a high resolution, nonlinear, non-hydrostatic model. We found that nonlinear internal waves are forced not by the M<sub>2</sub> but the K<sub>1</sub> tide which has been observed to have significant variability over the YP (Padman et al. 1992). Barotropic, diurnal shelf waves generated on the eastern side of the YP propagates counter-clockwise, amplifying the cross-slope currents. This amplification is the necessary condition for nonlinear internal wave generation over the YP.</p>

scholarly journals INFLUENCE OF STOKES DRIFT ON SALT WEDGE INTRUSION EVALUATED USING FULLY-NONLINEAR AND STRONGLY-DISPERSIVE WAVE EQUATIONS

2011 ◽  
Vol 1 (32) ◽  
pp. 34 ◽  
Author(s):  
Keisuke Nakayama ◽  
Tetsuya Shintani ◽  
Taro Kakinuma ◽  
Yasuyuki Maruya ◽  
Yoshinori Yonome ◽  
...  
Keyword(s):  
Internal Wave ◽  
Surface Waves ◽  
Wave Equations ◽  
Three Dimensional ◽  
River Mouth ◽  
Stokes Drift ◽  
Radiation Stress ◽  
Fully Nonlinear ◽  
Salt Wedge ◽  
Significant Difference

This paper describes the influence of surface waves on salt-wedge intrusion in terms of radiation stress. Radiation stress may increase salt-wedge intrusion when surface waves propagate up a river. This study thus aims to reveal the effect of radiation stress on the distance of salt-wedge intrusion by using fully nonlinear strongly dispersive internal wave equations and three-dimensional numerical computation model, Fantom3D. Fully nonlinear strongly dispersive internal wave model reveals the possibility that large radiation stress is induced near the river mouth and increases the distance of salt-wedge intrusion. Three-dimensional numerical model also demonstrates that there is a significant difference in the intrusion distance by taking into account radiation stress.

Nonlinear Internal Wave Equations: Spectral Properties and Long-Wave Asymptotics

2009 ◽  
Author(s):  
Nikolay Makarenko ◽  
Zhanna Maltseva ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Internal Wave ◽  
Spectral Properties ◽  
Wave Equations ◽  
Nonlinear Internal Wave ◽  
Long Wave

scholarly journals NUMERICAL ANALYSES ON PROPAGATION OF NONLINEAR INTERNAL WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 24
Author(s):  
Kei Yamashita ◽  
Taro Kakinuma ◽  
Keisuke Nakayama
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Breaking ◽  
Wave Equations ◽  
Vertical Wall ◽  
Submerged Breakwater ◽  
Wave Trough ◽  
Water Region ◽  
Wave Nonlinearity ◽  
Sloping Beach

A set of nonlinear surface/internal-wave equations, which have been derived on the basis of the variational principle without any assumptions concerning wave nonlinearity and dispersion, is applied to compare numerical results with experimental data of surface/internal waves propagating through a shallow- or a deep-water region in a tank. Internal waves propagating over a submerged breakwater or a uniformly sloping beach are also simulated. The internal progressive wave shows remarkable shoaling when the interface reaches the critical level, after which physical variables including wave celerity become unstable near the wave-breaking point. In the case of the internal-wave trough reflecting at the vertical wall, the vertical velocities of water particles in the vicinity of the interface are different from that of the moving interface at the wall near the wave breaking, which means that the kinematic boundary condition on the interface of trough has been unsatisfied.

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