Penetration of a salinity front into a rotating basin : laboratory experiments and a simple theory

Abstract

Freshwater is released along a wall of a basin containing salt water and rotating anticlockwise. The freshwater source is located near the surface between the center of the cylindrical basin and a corner along the wall. Experiments are performed with different discharge rates and the same rotation rate. The freshwater initially forms a bulge near the source, and then a buoyant gravity current bends to the right and flows along the wall toward the periphery of the basin. Separation of the current at the corner is never observed. The salinity front along the wall moves persistently away from the wall with a time scale greatly exceeding the rotation period. Its movement is compared to numerical solutions of a two-layer theory, where friction in the Ekman layer straddling the layer interface is the sole ageostrophic effect. The theory shows that the depth of the interface (h) satisfies a nonlinear diffusion equation. The symmetric part of the diffusion tensor causes light fluid to move down the gradient of h and represents the effect of vertical friction. The associated diffusivity reaches a maximum at h/δ = π/2, where δ is the Ekman layer depth. The antisymmetric part of the diffusion tensor causes light fluid to move perpendicularly to ∇h and represents the effect of geostrophic motion. The associated diffusivity increases monotonically with h/δ and greatly exceeds the diffusivity of the symmetric part if h/δ is of order of one or more. Comparison of numerical solutions with experimental data supports the theory.