scholarly journals Numerical simulations of shoaling internal solitary waves of elevation

2016 ◽  
Vol 28 (7) ◽  
pp. 076601 ◽  
Author(s):  
Chengzhu Xu ◽  
Christopher Subich ◽  
Marek Stastna
Keyword(s):  
Numerical Simulations ◽  
Solitary Waves ◽  
Internal Solitary Waves

scholarly journals Combined Effect of Rotation and Topography on Shoaling Oceanic Internal Solitary Waves

2014 ◽  
Vol 44 (4) ◽  
pp. 1116-1132 ◽  
Author(s):  
Roger Grimshaw ◽  
Chuncheng Guo ◽  
Karl Helfrich ◽  
Vasiliy Vlasenko
Keyword(s):  
Solitary Wave ◽  
Wave Packet ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Combined Effect ◽  
Internal Solitary Wave ◽  
Internal Solitary Waves ◽  
De Vries ◽  
Ostrovsky Equation ◽  
Variable Topography

Abstract Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg–de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth’s background rotation is potentially significant. The relevant extension of the Kortweg–de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia–gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal solitary wave. Hence, the combined effects of background rotation and variable topography are examined. Then the Ostrovsky equation is replaced by a variable coefficient Ostrovsky equation whose coefficients depend explicitly on the spatial coordinate. Some numerical simulations of this equation, together with analogous simulations using the Massachusetts Institute of Technology General Circulation Model (MITgcm), for a certain cross section of the South China Sea are presented. These demonstrate that the combined effect of shoaling and rotation is to induce a secondary trailing wave packet, induced by enhanced radiation from the leading wave.

scholarly journals Direct Numerical Simulations on Jets during the Propagation and Break down of Internal Solitary Waves on a Slope

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 671
Author(s):  
Jin Xu ◽  
Eldad J. Avital ◽  
Lingling Wang
Keyword(s):  
Numerical Simulations ◽  
Solitary Waves ◽  
Water Environment ◽  
Direct Numerical Simulations ◽  
Internal Solitary Waves ◽  
Jet Flows ◽  
Strong Mixing ◽  
Internal Interface ◽  
Transport Length ◽  
Moving Interface

Jet flows often have an important role in the water environment. The aim of this research is to study the dilution of jets due to complex velocity fields induced by internal solitary waves in stratified water. Direct numerical simulations are used to study vertical jet flows during the propagation and breaking of internal solitary waves (ISWs) with elevation type on a slope. Energy analysis shows that the internal interface is able to absorb kinetic energy from the jet and that for Re < 10,000 with Ri > 3.7, the ISWs can stay stable during the propagation within the presence of jet flows. The vortices jointly induced by the jets and the ISWs are observed at the bottom behind the ISW’s crest. The transport of the jet’s emitted scalar by the ISWs can be divided into two parts; some is transported by the moving interface and the rest by the bottom vortices. The ultimate transport length scales of two types are defined, and it is found that when the center of the jet inlet approaches the slope, the extension of the bottom vortices into the slope will lead to strong mixing. That causes increasing scalar concentration over the slope of the scalar that originated from the jet.

Numerical simulations of internal solitary waves with vortex cores

1999 ◽  
Vol 25 (6) ◽  
pp. 315-333 ◽  
Author(s):  
A Aigner ◽  
D Broutman ◽  
R Grimshaw
Keyword(s):  
Numerical Simulations ◽  
Solitary Waves ◽  
Internal Solitary Waves

scholarly journals Numerical simulations of the local generation of internal solitary waves in the Bay of Biscay

2010 ◽  
Vol 17 (5) ◽  
pp. 575-584 ◽  
Author(s):  
N. Grisouard ◽  
C. Staquet
Keyword(s):  
Numerical Simulations ◽  
Solitary Waves ◽  
Generation Mechanism ◽  
Internal Solitary Waves ◽  
Bay Of Biscay ◽  
Two Dimensional ◽  
Background Flow ◽  
Nonhydrostatic Model ◽  
Wave Trains ◽  
Local Generation

Abstract. Oceanic observations from the Bay of Biscay, Portugal, Mozambique Channel and Mascarene Ridge have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the thermocline from below – a process referred to as "local generation". Here we present two-dimensional numerical simulations with a fully nonlinear nonhydrostatic model of situations that are relevant for the Bay of Biscay in summer. We show that a beam impinging on a thermocline initially at rest can induce a displacement of the isopycnals, large enough for internal solitary waves to be generated. These internal solitary waves however differ from those observed in the Bay of Biscay through their amplitude and distance between wave trains. We then show that the latter feature is recovered when the background flow around the thermocline as found in the Bay of Biscay is included in the forcing, thereby yielding a more accurate view on the local generation mechanism.

scholarly journals Calculating Energy Flux in Internal Solitary Waves with an Application to Reflectance

2009 ◽  
Vol 39 (3) ◽  
pp. 559-580 ◽  
Author(s):  
Kevin G. Lamb ◽  
Van T. Nguyen
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Numerical Simulations ◽  
Energy Flux ◽  
Solitary Waves ◽  
Internal Solitary Waves ◽  
Available Potential Energy ◽  
Correct Account ◽  
Velocity Pressure ◽  
Reflectance Ratio

Abstract The energetics of internal solitary waves (ISWs) in continuous, quasi-two-layer stratifications are explored using fully nonlinear, nonhydrostatic numerical simulations. The kinetic energy of an internal solitary wave is always greater than the available potential energy, by as much as 30% for the stratifications considered. Because of different spatial distributions of the kinetic and available potential energy densities, however, the fluxes are quite different. The available potential energy flux is found to always exceed the kinetic energy flux, by as much as a factor of 5. The sizes of the various fluxes in the wave pseudoenergy (kinetic plus available potential energy) equation are compared, showing that, while the linear flux term (velocity–pressure perturbation) dominates the fluxes, the fluxes of available potential and kinetic energy are significant for large ISWs. Past work on estimating the reflectance (ratio of reflected to incident pseudoenergy flux) associated with internal solitary waves incident on a linearly sloping bottom in laboratory experiments and numerical simulations has incorrectly assumed that the available potential energy flux was equal to the kinetic energy flux. Hence, the sensitivity of reflectance estimates to the way the flux is calculated is investigated. For these low Reynolds number situations, it is found that a correct account of the available potential energy flux reduces the reflectance by as much as 0.1 when the pycnocline is close to the surface.

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