The dynamics and structure of double-diffusive layers in sidewall-heating experiments

Abstract

The dynamics and structure of double-diffusive layers were studied experimentally by heating a linear stable solute gradient from a sidewall in a wide tank. The formation and subsequent development of the layers were investigated by various flow-visualization techniques, namely fluorescent dye, fluorescent particles and shadowgraph. Experiments were performed in order to determine the stability diagram of the flow, following in each experiment the phase trajectory of the system in the phase plane of thermal and solute Rayleigh numbers. The experimentally obtained stability diagram appears to be similar to that obtained numerically by Thangam et al. (1981) and by Hart (1971) for a vertical narrow slot and a steady basic flow. It is shown that if the temperature of the sidewall rises slowly to its prescribed value, the thickness of the initial layers, formed at the onset of instability, is a function of the ambient density gradient and fluid properties only. On the other hand, if the wall temperature rises quickly (almost impulsive heating), the thickness of the initial layers is proportional to the imposed temperature difference, provided that the Rayleigh number, based on this difference, is larger than some critical value which is associated with the first merging of the layers. A criterion for the first merging of the initial layers is obtained, and it is suggested that this merging is due to subsequent instability of the system. The subsequent merging process, following the first merging, is not a simple successive doubling of the layer thickness and in each of five nearly identical experiments a different dependence of the average layer thickness on the instantaneous Rayleigh number is obtained. This indicates that the system of layers behaves chaotically after the first merging. The final thickness of the layers depends on the prescribed lateral temperature difference, and the ratio between the final and the initial thickness of the layers is a linear function of the final Rayleigh number. Flow-visualization experiments indicate that the layers consist of vortices with vertical scale of the layer thickness and various horizontal scales.

Double-diffusive processes : 1996 Summer Study Program in Geophysical Fluid Dynamics

“…In particular, when assumptions of such a type were made by Tanny & Tsinober (1988), for the interpretation of their experimental data, and by Kerr (1989), theoretically, the critical values of the Rayleigh numbers obtained in both these works showed reasonable agreement with the marginal stability curve computed for an infinite vertical slot by Hart (1971) and Thangam et ale (1980). Moreover, a weakly nonlinear analysis by Kerr (1990), where the quasi static assumption was also made, demonstrated that, like in the results obtained by Hart (1973) for the slot, it is the subcritical bifurcation that is responsible for the onset of the layers in the single-side-wall heating problem.…”

“…These include Thorpe, H utt & Soulsby (1969), , Narusawa & Suzukawa (1981), Tanny & Tsinober (1988) and Schladow, Thomas & Koseff (1992). The first of these concentrated on the onset of convection in a vertical slot, while the last focussed on the effects of having a vertical temperature stratification in addition to the salt stratification.…”

“…Although the earlier studies have determined some general characteristics of the layer behavior (such as, for example, the Chen scale, "successive" and "simultaneous" modes of layer formation; see , specific features of the behavior of the layers, namely as to under what circumstances they merge and what the thickness of the resulting layer is, turned out to be hardly susceptible of description in terms of any simple mechanism (such as the doubling of the layer height initially suggested by Wirtz & Reddy 1979, for example), but were found likely to be associated with some rather complex scenarios (Tanny & Tsinober 1988.…”

The diffusive regime of double-diffusive convection

“…First, there are lateral intrusions at depths of & % 2 % # " % 2 % m, linked to the descending plume of Mediterranean waters cascading down the slope (Özsoy et al, 1993;Özsoy and Beşiktepe, 1995). The DL-susceptible interior may favor DL convection over SF convection (Turner, 1978), in the context of side-wall buoyancy source (heat and salt) introduced into the stratified environment (Tsinober et al, 1983;Tanny and Tsinober, 1988). Boundary mixing driven by the doublediffusive convection (Özsoy et al, 1993;Özsoy and Beşiktepe, 1995), may be the dominant ventilation mechanism across the permanent halocline of the Black Sea, given the inferred transport of shelf-derived materials, including dissolved nutrients, Chernobyl tracers and inorganic particulates between surface and deep layers (Buesseler et al, 1991;Codispoti et al, 1991;Özsoy et al, 1991Buesseler and Livingston, 1997).…”

Double diffusion natural convection in open lid enclosure filled with binary fluids

“…The subject of natural convection for single fluid flow and double diffusion has been studied extensively [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Yet, most work done considers flow inside closed enclosures.…”