Salt-Finger Instability Generated by Surface-Tension and Buoyancy-Driven Convection in a Stratified Fluid Layer

Abstract

Consider a shallow layer of fluid stratified by a solute gradient with a free surface being heated differentially across the two side walls. Convection due to surface-tension and buoyancy effects will be generated. The cooler, solute-poor fluid sinks along the cold wall and flows toward the hot wall along the bottom of the tank. The warmer, solute-rich fluid returns along the free surface of the layer. The resulting vertical distributions of temperature and solute are conducive to the onset of salt-finger instability, thus generating secondary motion in the primary convection cell. Our recent experiments confirm the existence of such secondary motion. Experiments were conducted in a stratified fluid layer contained in a shallow tank 5 cm wide × 1 cm high × 10 cm long. One side wall (1 × 10 cm) was made of chrome-plated copper and can be maintained at a constant temperature. The opposite side wall was made of Plexiglas for visualization purposes. The fluid was an ethanol-water solution, initially stratified from 96% ethanol at the bottom to 100% ethanol at the top free surface. Experiments were carried out with the copper wall maintained at a temperature lower than the ambient. Secondary motion was first noted at an 0.8°C temperature difference. At a 1.7°C temperature difference, the secondary motion became fully developed. Flow visualization in a longitudinal plane perpendicular to the initial temperature gradient showed that the motion consisted of vortices with axes aligned with the direction of the primary motion. A discussion of the instability mechanism based on a parallel flow model of the actual flow is presented following the presentation of the experimental investigation.