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.

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

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 Enhanced diapycnal mixing with polarity-reversing internal solitary waves revealed by seismic reflection data

2021 ◽  
Vol 28 (3) ◽  
pp. 445-465
Author(s):  
Yi Gong ◽  
Haibin Song ◽  
Zhongxiang Zhao ◽  
Yongxian Guan ◽  
Kun Zhang ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Vertical Direction ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Observation Data ◽  
Diapycnal Mixing ◽  
Seismic Reflection Data ◽  
Spatial Coverage ◽  
Dongsha Atoll ◽  
Diapycnal Diffusivity

Abstract. Shoaling internal solitary waves near the Dongsha Atoll in the South China Sea dissipate their energy and enhance diapycnal mixing, which have an important impact on the oceanic environment and primary productivity. The enhanced diapycnal mixing is patchy and instantaneous. Evaluating its spatiotemporal distribution requires comprehensive observation data. Fortunately, seismic oceanography meets the requirements, thanks to its high spatial resolution and large spatial coverage. In this paper, we studied three internal solitary waves in reversing polarity near the Dongsha Atoll and calculated their spatial distribution of diapycnal diffusivity. Our results show that the average diffusivities along three survey lines are 2 orders of magnitude larger than the open-ocean value. The average diffusivity in internal solitary waves with reversing polarity is 3 times that of the non-polarity reversal region. The diapycnal diffusivity is higher at the front of one internal solitary wave and gradually decreases from shallow to deep water in the vertical direction. Our results also indicate that (1) the enhanced diapycnal diffusivity is related to reflection seismic events, (2) convective instability and shear instability may both contribute to the enhanced diapycnal mixing in the polarity-reversing process, and (3) the difference between our results and Richardson-number-dependent turbulence parameterizations is about 2–3 orders of magnitude, but its vertical distribution is almost the same.

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 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.

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