The stability of a sheared density interface

Lawrence, Gregory A.; Browand, F. K.; Redekopp, L. G.

doi:10.1063/1.858175

Cited by 161 publications

(135 citation statements)

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“…Browand and Winant [25] first performed shear flow experiments in a stratified environment under conditions for which Holmboe's instabilities are present. Their investigation has been extended further by more recent experiments [11,26,27,28,29,30,31,32].…”

Section: Pacs Numbersmentioning

confidence: 99%

“…It was first identified by Holmboe [10] in a simplified model of a continuous piece-wise linear velocity profile and a step-function density profile. Several authors have expanded Holmboe's theoretical work [11,12,13,14] by considering different stratification and velocity profiles that do not include the simplifying symmetries Holmboe used in his model. Hazel [15] and more recently Smyth and Peltier [16] and Alexakis [17] have shown that Holmboe's results hold for smooth density and velocity profiles as long as the length scale of the density variation is sufficiently smaller than the length scale of the velocity variation.…”

Section: Pacs Numbersmentioning

confidence: 99%

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Marginally unstable Holmboe modes

Alexakis¹

2007

Physics of Fluids

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Marginally unstable Holmboe modes for smooth density and velocity profiles are studied. For a large family of flows and stratification that exhibit Holmboe instability, we show that the modes with phase velocity equal to the maximum or the minimum velocity of the shear are marginally unstable. This allows us to determine the critical value of the control parameter R (expressing the ratio of the velocity variation length scale to the density variation length scale) that Holmboe instability appears Rcrit = 2. We then examine systems for which the parameter R is very close to this critical value Rcrit. For this case we derive an analytical expression for the dispersion relation of the complex phase speed c(k) in the unstable region. The growth rate and the width of the region of unstable wave numbers has a very strong (exponential) dependence on the deviation of R from the critical value. Two specific examples are examined and the implications of the results are discussed.

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Section: Pacs Numbersmentioning

confidence: 99%

Section: Pacs Numbersmentioning

confidence: 99%

Marginally unstable Holmboe modes

Alexakis¹

2007

Physics of Fluids

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“…If the squared velocity difference exceeds the right-hand side, the surface is unstable and begins to undulate, forming a Kelvin-Helmholtz wave of length L (Figure 1). It has since been appreciated that a variety of hydrodynamic instabilities may develop on a fluid interface within the Richardson number range À3 Ri 1 [Lawrence et al, 1991]. The Richardson number is defined by…”

Section: A Simple Model For Interfacial Instabilitymentioning

confidence: 99%

On interfacial instability as a cause of transverse subcritical bed forms

Venditti

Church

Bennett

2006

Water Resources Research

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Recent experimental results suggest there are at least two distinct bed form initiation processes. Bed forms may be generated from local bed defects that are propagated down and across stream by flow separation processes when sediment transport is patchy and sporadic. Alternatively, bed form development may occur over the whole bed at once when sediment transport is general and widespread. Herein, we critically test a simple model for this latter bed form initiation mode that was originally presented by H.‐K. Liu in 1957 but not tested because of the complex nature of the measurements required. The theory is based on the idea that a moving sand bed might be likened to a dense fluid and that a hydrodynamic instability develops at the interface between the sediment transport layer and the near‐bed fluid, leading to the organization of the transport system into laterally extended, discrete bed forms. Our predicted initial bed form lengths are within 10% of the lengths observed in a series of flume experiments, suggesting that transverse waveforms on sand beds sheared by unidirectional currents can be initiated as an interfacial hydrodynamic instability of Kelvin‐Helmholtz type when the current is sufficiently vigorous to produce general sediment movement, that is, to create a sediment transport layer that acts as a pseudofluid with density composed of solid and fluid components.

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“…Yet, it is conjectured from numerical simulations 15 that their contribution to diapycnal exchange is approximately equal, as the high mixing efficiency is maintained over a longer period during the slower Holmboe development. The presented observations may be compared with DNS and laboratory studies, [16][17][18] for the specific case when the centres of the shear and density interfaces are vertically displaced with respect to each other. This results in asymmetric Holmboe overturning, or cusping, into the weaker stratified layer.…”

Section: Introductionmentioning

confidence: 99%

Stratified turbulence and small-scale internal waves above deep-ocean topography

Haren

2013

Physics of Fluids

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When ocean's internal tidal waves "beach" at underwater topography, they transform from more or less linear into highly nonlinear waves that can break with generation of vigorous turbulent mixing. Although most mixing occurs in the half hour around a steep (bottom-)front leading the upslope moving internal tide phase, relatively large mixing also occurs some distance of several tens of meters off the bottom, just prior to the downslope moving internal tide phase and initiated by highfrequency "small-scale" internal waves. Details of this off-bottom small-scale mixing in a stratified natural environment and some of its variability per tidal period are presented here in two case studies using high-resolution temperature observations (61 sensors at 1 m intervals; <10 −3 • C precision) at a 969 m deep site south of New Zealand. The observations shed some light on stratified turbulence that is generated in a relatively thick (∼30 m) weakly stratified layer and in the strongly stratified interfaces above and below. The interfacial internal waves generate turbulence with largest dissipation rate and temperature variance at the edge of the upper interface and the weakly stratified layer. When these waves steep nonlinearly, immediate moderate turbulence generation is observed below, throughout the weakly stratified layer. Largest turbulence is generated by 25 m high asymmetric Holmboe overturns. C 2013 AIP Publishing LLC. [http://dx

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The stability of a sheared density interface

Cited by 161 publications

References 20 publications

Marginally unstable Holmboe modes

Marginally unstable Holmboe modes

On interfacial instability as a cause of transverse subcritical bed forms

Stratified turbulence and small-scale internal waves above deep-ocean topography

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