Stability of thermal convection in a salinity gradient due to lateral heating

Chen, C.F; Briggs, David; Wirtz, R. A.

doi:10.1016/0017-9310(71)90140-2

Cited by 171 publications

(104 citation statements)

References 7 publications

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“…A situation similar to the stratified Boycott effect arises in salt-stratified systems with heated vertical sidewalls (Thorpe et al 1969;Chen et al 1971), wherein buoyant up-welling is driven by the sidewalls. Once fluid from the base of the tank reaches its neutral buoyancy height, a primary intrusion develops.…”

Section: Discussionmentioning

confidence: 97%

The stratified Boycott effect

2005

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We present the results of an experimental investigation of the flows generated by monodisperse particles settling at low Reynolds number in a stably stratified ambient with an inclined sidewall. In this configuration, upwelling beneath the inclined wall associated with the Boycott effect is opposed by the ambient density stratification. The evolution of the system is determined by the relative magnitudes of the container depth, h, and the neutral buoyancy height, h n = c 0 (ρ p − ρ f )/|dρ/dz|, where c 0 is the particle concentration, ρ p the particle density, ρ f the mean fluid density and dρ/dz < 0 the stable ambient stratification. For sufficiently weak stratification, h < h n , the Boycott layer transports dense fluid from the bottom to the top of the system; subsequently, the upper clear layer of dense saline fluid is mixed by convection. For sufficiently strong stratification, h > h n , layering occurs. The lowermost layer is created by clear fluid transported from the base to its neutral buoyancy height, and has a vertical extent h n ; subsequently, smaller overlying layers develop. Within each layer, convection erodes the initially linear density gradient, generating a step-like density profile throughout the system that persists after all the particles have settled. Particles are transported across the discrete density jumps between layers by plumes of particle-laden fluid.

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Section: Discussionmentioning

confidence: 97%

The stratified Boycott effect

2005

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“…Some aspects of heating a stable salinity gradient from the side have been considered previously by Thorpe, Hutt & Soulsby (1969), Chen, Briggs & Wirtz (1971), Wirtz, Briggs & Chen (1972) and Chen (1 974).t These investigations were primarily concerned with the onset of motion at low Rayleigh numbers. The work of Thorpe et al was further restricted in that most of the experiments and all of the theory were carried out for the case when the fluid is confined by a narrow slot.…”

Section: Horizontal Temperature Differencesmentioning

confidence: 96%

Ice blocks melting into a salinity gradient

1980

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I n our previous qualitative paper, it was shown that when a vertical ice surface melts into a stable salinity gradient, the melt water spreads out into the interior in a series of nearly horizontal layers. The experiments reported here are aimed a t quantifying this effect, which could be of some importance in the application to melting icebergs. Experiments have also been carried out with heated and cooled vertical walls a t larger Rayleigh numbers R than those of previous experiments.The main result is that for most of our experiments there is no significant difference between these three cases when properly scaled. The layer thickness over a wide range of R is described to within the experimental accuracy by where the term in brackets is the horizontal buoyancy difference evaluated a t the mean salinity and dpldz is the vertical density gradient due to salinity. I n the case of ice melting into warm water the effective wall temperature T, is approximately 0 "C, whereas in colder water the freezing point depression must be taken explicitly into account. A detailed examination of the vertically flowing inner melt water layer in both homogeneous and salinity stratified cases has been made. This layer and the melt water which is mixed outwards from it into the turbulent horizontal layers have little effect on the outer flow. At high R and large external salinity, however, mixing can reduce the effective salinity a t the inner edge of the horizontal layers, and thus the layer scale. A puzzling feature is the relatively weak dependence of layer scale on local salinity, though the vigour of convection and the rate of melting are greater where the salinity is high.The direct application of our results to oceanographic situations predicts layer scales under typical summer conditions of order tens of metres in the Antarctic and of order metres in the Arctic. More measurements will be needed, especially close to icebergs, before the application of these ideas to polar regions can be properly evaluated.

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“…For example, in the experiments of Chen, Briggs & Wirtz (1971), water with a vertical salinity gradient was heated from a vertical boundary. In one example, shown in their figure 8(b), instabilities are observed to start forming in the middle of the wall around 8 minutes after the wall temperature was raised.…”

Section: Introductionmentioning

confidence: 99%

Thermal instability in a time-dependent base state due to sudden heating

Kerr

Gumm

2017

J. Fluid Mech.

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link City Research OnlineUnder consideration for publication in J. Fluid Mech. 1Thermal instability in a time-dependent base state due to sudden heatingDepartment of Mathematics, City, University of London, Northampton Square, London EC1V 0HB, U.K. (Received 31 May 2017)When a large body of fluid is heated from below at a horizontal surface the heat diffuses into the fluid, giving rise to a gravitationally unstable layer adjacent to the boundary. A consideration of the instantaneous Rayleigh number using the thickness of this buoyant layer as a length scale would lead one to expect that the heated fluid is initially stable, and only becomes unstable after a finite time. This transition would also apply to other situations, such as heating a large body of fluid from the side, where a buoyant upward flow develops near the boundary. In such cases when the evolving thermal boundary layer first becomes unstable the time-scale for the growth of the instabilities may be comparable to the time-scale of the evolution of the background temperature profile, and so analytical approximations such as the quasi-static approximation, where the time-evolution of the background state is ignored, are not strictly appropriate.We develop a numerical scheme where we find the optimal growth of linear perturbations to the background flow over a given time interval. Part of this problem is to determine an appropriate measure of the amplitude to the disturbances, as inappropriate choices can lead to apparent growth of disturbances over finite time intervals even when the fluid is stable. By considering the Rayleigh-Bénard problem, we show these problems can be avoided by choosing a measure of the amplitude that uses both the velocity and temperature perturbations, and which minimizes the maximum growth.We apply our analysis to the problems of heating a semi-infinite body of fluid from horizontal and vertical boundaries. We will show that for heating from a vertical boundary there are large and small Prandtl number modes. For some Prandtl numbers both modes may play a role in the growth of instabilities. In some cases there is transition during the evolution of the most unstable instabilities in fluids such as water, where initially the instabilities are large Prandtl number modes and then morph into small Prandtl number modes part of the way through their evolution.

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Stability of thermal convection in a salinity gradient due to lateral heating

Cited by 171 publications

References 7 publications

The stratified Boycott effect

The stratified Boycott effect

Ice blocks melting into a salinity gradient

Thermal instability in a time-dependent base state due to sudden heating

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