The effect of a background shear current on large amplitude internal solitary waves

2006 ◽  
Vol 18 (3) ◽  
pp. 036601 ◽  
Author(s):  
Wooyoung Choi
Keyword(s):  
Solitary Waves ◽  
Large Amplitude ◽  
Internal Solitary Waves ◽  
Shear Current ◽  
Background Shear

scholarly journals The evolution of mode-2 internal solitary waves modulated by background shear currents

2018 ◽  
Vol 25 (2) ◽  
pp. 441-455 ◽  
Author(s):  
Peiwen Zhang ◽  
Zhenhua Xu ◽  
Qun Li ◽  
Baoshu Yin ◽  
Yijun Hou ◽  
...  
Keyword(s):  
Wave Packet ◽  
Shear Layer ◽  
Solitary Waves ◽  
Average Rate ◽  
Propagation Distance ◽  
Internal Solitary Waves ◽  
Long Wave ◽  
Shear Current ◽  
Mode 2 ◽  
Background Shear

Abstract. The evolution of mode-2 internal solitary waves (ISWs) modulated by background shear currents was investigated numerically. The mode-2 ISW was generated by the “lock-release” method, and the background shear current was initialized after the mode-2 ISW became stable. Five sets of experiments were conducted to assess the sensitivity of the modulation process to the direction, polarity, magnitude, shear layer thickness and offset extent of the background shear current. Three distinctly different shear-induced waves were identified as a forward-propagating long wave, oscillating tail and amplitude-modulated wave packet in the presence of a shear current. The amplitudes of the forward-propagating long wave and the amplitude-modulated wave packet are proportional to the magnitude of the shear but inversely proportional to the thickness of the shear layer, as well as the energy loss of the mode-2 ISW during modulation. The oscillating tail and amplitude-modulated wave packet show symmetric variation when the background shear current is offset upward or downward, while the forward-propagating long wave was insensitive to it. For comparison, one control experiment was configured according to the observations of Shroyer et al. (2010); in the first 30 periods, ∼ 36 % of total energy was lost at an average rate of 9 W m−1 in the presence of the shear current; it would deplete the energy of initial mode-2 ISWs in ∼ 4.5 h, corresponding to a propagation distance of ∼ 5 km, which is consistent with in situ data.

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 <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 > 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.

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.

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