Large Amplitude Breaking Internal Solitary Waves: Their Origin and Dynamics

2003 ◽  
Author(s):  
David M. Farmer
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Internal Solitary Waves

scholarly journals Optimal transient growth in thin-interface internal solitary waves

2018 ◽  
Vol 840 ◽  
pp. 342-378 ◽  
Author(s):  
Pierre-Yves Passaggia ◽  
Karl R. Helfrich ◽  
Brian L. White
Keyword(s):  
Solitary Waves ◽  
Carrier Frequency ◽  
Large Amplitude ◽  
Stokes Equations ◽  
Normal Growth ◽  
Energy Gain ◽  
Wkb Approximation ◽  
Internal Solitary Waves ◽  
Transient Growth ◽  
Optimal Disturbances

The dynamics of perturbations to large-amplitude internal solitary waves (ISWs) in two-layered flows with thin interfaces is analysed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct–adjoint iterations of the Navier–Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin–Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity $c$ (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough $c$) of potentially unstable Richardson number, $Ri<0.25$. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with $c$. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local Wentzel–Kramers–Brillouin (WKB) approximation for spatially growing Kelvin–Helmholtz (K–H) waves through the $Ri<0.25$ zone. The WKB approach is able to capture properties (e.g. carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K–H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave. Two-dimensional numerical calculations of the nonlinear evolution of optimal disturbance packets leads to the generation of large-amplitude K–H billows that can emerge on the leading face of the wave and that break down into turbulence in the lee of the wave. The nonlinear calculations are used to derive a slowly varying model of ISW decay due to repeated encounters with optimal or free wave packets. Field observations of unstable ISW by Moum et al. (J. Phys. Oceanogr., vol. 33 (10), 2003, pp. 2093–2112) are consistent with excitation by optimal disturbances.

scholarly journals Structure of Large-Amplitude Internal Solitary Waves

2000 ◽  
Vol 30 (9) ◽  
pp. 2172-2185 ◽  
Author(s):  
Vasiliy Vlasenko ◽  
Peter Brandt ◽  
Angelo Rubino
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Internal Solitary Waves

scholarly journals Convectively induced shear instability in large amplitude internal solitary waves

2008 ◽  
Vol 20 (12) ◽  
pp. 126601 ◽  
Author(s):  
M. Carr ◽  
D. Fructus ◽  
J. Grue ◽  
A. Jensen ◽  
P. A. Davies
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Shear Instability ◽  
Internal Solitary Waves

scholarly journals A model for large-amplitude internal solitary waves with trapped cores

2010 ◽  
Vol 17 (4) ◽  
pp. 303-318 ◽  
Author(s):  
K. R. Helfrich ◽  
B. L. White
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Matching Condition ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Ambient Flow ◽  
The Core ◽  
Core Boundary

Abstract. Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of depression (elevation) these solutions may develop recirculating cores for wave speeds above a critical value. As typically modeled, these recirculating cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trapped-core solitary waves is reformulated. A finite core of homogeneous density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The flow outside the core satisfies the DJL equation. The flow in the core is given by a vorticity-streamfunction relation that may be arbitrarily specified. For simplicity, the simplest choice of a stagnant, zero vorticity core in the frame of the wave is assumed. A pressure matching condition is imposed along the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. Numerical solutions of time-dependent non-hydrostatic equations initiated with the new stagnant-core DJL solutions show that for the ambient stratification considered, the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Steadily propagating trapped-core waves formed by lock-release initial conditions also agree well with the theoretical wave properties despite the presence of a "leaky" core region that contains vorticity of opposite sign from the ambient flow.

scholarly journals Nonlinear Phenomena in Propagation of Large-Amplitude Internal Solitary Waves

2014 ◽  
Vol 70 (2) ◽  
pp. I_6-I_10
Author(s):  
Kei YAMASHITA ◽  
Taro KAKINUMA ◽  
Asuki YOSHIMOTO ◽  
Ryo YOSHIKAWA
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Internal Solitary Waves ◽  
Nonlinear Phenomena

scholarly journals Large-Amplitude Internal Solitary Waves Observed in the Northern South China Sea: Properties and Energetics

2014 ◽  
Vol 44 (4) ◽  
pp. 1095-1115 ◽  
Author(s):  
Ren-Chieh Lien ◽  
Frank Henyey ◽  
Barry Ma ◽  
Yiing Jang Yang
Keyword(s):  
Kinetic Energy ◽  
South China Sea ◽  
Energy Flux ◽  
Solitary Waves ◽  
South China ◽  
Large Amplitude ◽  
Northern South China Sea ◽  
Vertical Displacement ◽  
Internal Solitary Waves ◽  
Background Shear

Abstract Five large-amplitude internal solitary waves (ISWs) propagating westward on the upper continental slope in the northern South China Sea were observed in May–June 2011 with nearly full-depth measurements of velocity, temperature, salinity, and density. As they shoaled, at least three waves reached the convective breaking limit: along-wave current velocity exceeded the wave propagation speed C. Vertical overturns of ~100 m were observed within the wave cores; estimated turbulent kinetic energy was up to 1.5 × 10−4 W kg−1. In the cores and at the pycnocline, the gradient Richardson number was mostly &lt;0.25. The maximum ISW vertical displacement was 173 m, 38% of the water depth. The normalized maximum vertical displacement was ~0.4 for three convective breaking ISWs, in agreement with laboratory results for shoaling ISWs. Observed ISWs had greater available potential energy (APE) than kinetic energy (KE). For one of the largest observed ISWs, the total wave energy per unit meter along the wave crest E was 553 MJ m−1, more than three orders of magnitude greater than that observed on the Oregon Shelf. Pressure work contributed 77% and advection contributed 23% of the energy flux. The energy flux nearly equaled CE. The Dubriel–Jacotin–Long model with and without a background shear predicts neither the observed APE &gt; KE nor the subsurface maximum of the along-wave velocity for shoaling ISWs, but does simulate the total energy and the wave shape. Including the background shear in the model results in the formation of a surface trapped core.

An Analytical Model of Large Amplitude Internal Solitary Waves

2015 ◽  
pp. 191-201
Author(s):  
Nikolay I. Makarenko ◽  
Janna L. Maltseva
Keyword(s):  
Analytical Model ◽  
Solitary Waves ◽  
Large Amplitude ◽  
Internal Solitary Waves

scholarly journals Large Amplitude Internal Solitary Waves due to Solitary Resonance regarding the Change in Amplitude

2012 ◽  
Vol 68 (2) ◽  
pp. I_1-I_5
Author(s):  
Keisuke NAKAYAMA ◽  
Taro KAKINUMA ◽  
Hidekazu TSUJI ◽  
Masayuki OIKAWA
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Internal Solitary Waves

scholarly journals NONLINEAR OBLIQUE INTERACTION OF LARGE AMPLITUDE INTERNAL SOLITARY WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 19
Author(s):  
Keisuke Nakayama ◽  
Taro Kakinuma ◽  
Hidekazu Tsuji ◽  
Masayuki Oikawa
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Large Amplitude ◽  
Numerical Study ◽  
Incident Angle ◽  
Resonant Interaction ◽  
Internal Solitary Waves ◽  
Weakly Nonlinear ◽  
Wave Angle ◽  
The One

Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including ‘freak waves’). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called “resonant interaction” because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amplitude wave due to the interaction (“stem” wave) at the wall and its dependency of incident angle. For the case of internal waves, analyses using weakly nonlinear model equation (ex. Tsuji and Oikawa, 2006) suggest also qualitatively similar result. Therefore, the aim of this study is to investigate the strongly nonlinear interaction of internal solitary waves; especially whether the resonant behavior is found or not. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude. In contrast, a "stem" was not found to occur when the incident wave angle was more than the critical angle, which has been demonstrated in the previous studies.

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