ARTICLE:

• Double-diffusive Finger Convection near Neutral Buoyancy  download article

Om Prakash Singh
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India

K.R. Sreenivas
Enginering Mechanics Unit, Jawaharlal Nehru Center for Advanced Scientific Research, Bangalore 560064, India

J. Srinivasan
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India

ABSTRACT

This is a numerical study of double-diffusive finger convection at a density interface in the thermo-haline system for which the ratio of salt to heat diffusivity is 1/100. The initial configuration of the system is such that a uniformly salty and warm fluid lies above a reservoir of cold and fresh fluid. Specifically, the issue concerning the value of the heat-to-salt flux ratio is addressed. We systematically decreased the solute concentration and thus the Salinity Rayleigh number while keeping the density stability ratio, R_ρ, fixed to 1.001 (line corresponding to R_ρ = 1 is neutral buoyancy line). Four cases were calculated for the thermal Rayleigh numbers, Ra_T, of 10⁶, 10⁵, 10⁴ and 10³ all at fixed R_ρ and aspect ratio. Across the 4 runs conducted, the convective motion shows considerable variation in both structure and time scale. In the range of parameters used, the ratio of the flux of density due to heat to that salt, R_f, varies from 0.82 to 0.27 as the Rayleigh number is decreased from 10⁶ to 10³ at constant R_ρ. Finger system never reaches equilibrium in any of the four cases. High Ra_T system exhibits strong convection due to high driving force amassed in the salinity field. Fingers transport substantial amount of heat and salinity across the reservoir resulting in high R_f. Low Ra_T system exhibits strong diffusion of heat due to sluggish penetration of fingers into the opposite reservoir and the consequence is low R_f. Value of flux ratio reported here shows that the disagreement can be traced to the hypothesis of maximum flux and growth rate as the R_ρ approaches 1.

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