Symmetric Holmboe instabilities in a laboratory exchange flow

Tedford, Edmund W.; Pieters, Roger; Lawrence, Gregory A.

doi:10.1017/s0022112009007733

Cited by 36 publications

(50 citation statements)

References 19 publications

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“…The H state, figure 3 H, shows the characteristic cusped structure observed in previous experiments in horizontal channels (Lawrence et al 1991;Tedford et al 2009). This state was observed for small angles (θ 1 • ) and for smaller values of ρ, and exhibited cusped waves travelling in opposite directions on the two sides of the interface, with, in most cases, intermittent breaking at the cusps.…”

Section: Qualitative Resultssupporting

confidence: 63%

“…In the case of a horizontal duct, the pressure differences at the two ends of the duct drive a counterflow, with the dense fluid moving along the bottom of the duct and the light fluid moving along the top. This configuration has been studied by Lawrence and his group (Lawrence, Browand & Redekop 1991;Gu & Lawrence 2005;Tedford, Pieters & Lawrence 2009), particularly in the context of the generation of Holmboe instabilities.…”

Section: Introductionmentioning

confidence: 99%

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Stratified shear flow: experiments in an inclined duct

Meyer

Linden

2014

J. Fluid Mech.

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We present results of experiments on stratified shear flow in an inclined duct. The duct connects two reservoirs of fluid with different densities, and contains a counterflow with a dense layer flowing beneath a less dense layer moving in the opposite direction. We identify four flow states in this experiment, depending on the fractional density differences, characterised by the dimensionless Atwood number, and the angle of inclination θ, which is defined to be positive (negative) when the along-duct component of gravity reinforces (opposes) the buoyancy-induced pressure differences across the ends of the duct. For sufficiently negative angles and small fractional density differences, the flow is observed to be laminar (L state), with an undisturbed density interface separating the two layers. For positive angles and/or high fractional density differences, three other states are observed. For small angles of inclination, the flow is wave-dominated and exhibits Holmboe modes (H state) on the interface, with characteristic cusp-like wave breaking. At the highest positive angles and density differences, there is a turbulent (T state) high-dissipation interfacial region typically containing Kelvin-Helmholtz (KH)-like structures sheared in the direction of the mean shear and connecting both layers. For intermediate angles and density differences, an intermittent state (I state) is found, which exhibits a rich range of spatio-temporal behaviour and an interfacial region that contains features of KH-like structures and of the other two lower-dissipation states: thin interfaces and Holmboe-like structures. We map the state diagram of these flows in the Atwood number-θ plane and examine the force balances that determine each of these states. We find that the L and H states are hydraulically controlled at the ends of the duct and the flow is determined by the pressure difference associated with the density difference between the reservoirs. As the inclination increases, the along-slope component of the buoyancy force becomes more significant and the I and T states are associated with increasing dissipation within the duct. We replot the state space in the Grashof number-θ phase plane and find the transition to the T state is governed by a critical Grashof number. We find that the corresponding buoyancy Reynolds number of the transition to the T state is of the order of 100, and that this state is also found to be hydraulically controlled at the ends of the duct. In this state the dissipation balances the force associated with the along-slope component of buoyancy and the counterflow has a critical composite Froude number.

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Section: Qualitative Resultssupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Stratified shear flow: experiments in an inclined duct

Meyer

Linden

2014

J. Fluid Mech.

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“…We expect an analogous schematic to the one shown in Figure 8 should hold for the Holmboe problem. Similar effects should also be observed when smooth basic states [30][31][32][33][34][35] are considered in the non-Boussinesq regime. In terms of general applicability, since large-scale stratified flows tend to be dominated by buoyancy effects, non-Boussinesq effects are more likely to manifest for small-scale flows.…”

Section: Conclusion and Discussionsupporting

confidence: 69%

“…Normally there is a symmetric Holmboe mode arising from the interaction between a leftward Rossby wave with a rightward gravity wave, together with a rightward Rossby wave and a leftward gravity wave. NonBoussinesq effects will modify the gravity waves so that the interaction is no longer symmetric, and the instabilities should have non-zero c r , as in some previous works where the interaction was made asymmetric via other means (e.g., making the distance between the density and the vorticity defects asymmetric) [12][13][14]17,24,[30][31][32][33][34] . We expect an analogous schematic to the one shown in Figure 8 should hold for the Holmboe problem.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Stratified shear flow instabilities in the non-Boussinesq regime

Heifetz

Mak

2015

Physics of Fluids

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Effects of the baroclinic torque on wave propagation normally neglected under the Boussinesq approximation is investigated here, with a special focus on the associated consequences for the mechanistic interpretation of shear instability arising from the interaction between a pair of vorticity-propagating waves. To illustrate and elucidate the physical effects that modify wave propagation, we consider three examples of increasing complexity: wave propagation supported by a uniform background flow; wave propagation supported on a piecewise-linear basic state possessing one jump; and an instability problem of a piecewise-linear basic state possessing two jumps, which supports the possibility of shear instability. We find that the non-Boussinesq effects introduces a preference for the direction of wave propagation that depends on the sign of the shear in the region where waves are supported. This in turn affects phase-locking of waves that is crucial for the mechanistic interpretation for shear instability, and is seen here to have an inherent tendency for stabilisation. a)

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“…Holmboe instabilities have been reproduced in laboratory experiments [5][6][7][8][9][10][11] and have been numerically simulated [12][13][14][15][16][17][18][19]. At finite amplitude these Holmboe modes * Electronic address: navidcon@phys.uoa.gr † Electronic address: pjioannou@phys.uoa.gr equilibrate into propagating waves and they can induce mixing in highly stratified environments [12,17,20].…”

Section: Introductionmentioning

confidence: 99%

Optimal excitation of two dimensional Holmboe instabilities

Constantinou¹,

Ioannou²

2011

Physics of Fluids

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Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However these instabilities occur in limited bands in the parameter space. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that is obtained for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges as a persistent quasi-mode for parameter values for which the flow is stable.

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Symmetric Holmboe instabilities in a laboratory exchange flow

Cited by 36 publications

References 19 publications

Stratified shear flow: experiments in an inclined duct

Stratified shear flow: experiments in an inclined duct

Stratified shear flow instabilities in the non-Boussinesq regime

Optimal excitation of two dimensional Holmboe instabilities

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