Finite-amplitude salt fingers in a vertically bounded layer

We compute numerically the amplitude of long thin fingers that form in a li quid stratified with sugar S-* and salt T-* (measured in buoyancy units), f or which tau = k(S)/k(T) = 1/3 is the ratio of the two diffusivities and th e Prandtl number is Pr = v/k(T) similar to 10(3), where v is the viscosity. The finger layer in our model is bounded by rigid and slippery horizontal surfaces with constant T-*, S-* (the setup is similar to the classical Rayl eigh convection problem). The numerically computed steady fluxes compare we ll with laboratory experiments in which the fingers are sandwiched between two deep (convectively mixed) reservoirs with given concentration differenc es DeltaT(*), DeltaS(*). The model results, discussed in terms of a combina tion of asymptotic analysis and numerical simulations over a range of densi ty ratio R = DeltaT(*)/DeltaS(*), are consistent with the (DeltaS(*))(4/3) similarity law for the fluxes. The dimensional interfacial height (H-*) in the reservoir experiments (unlike that in our rigid lid model) is not an in dependent parameter, but it adjusts to a statistically steady value proport ional to (DeltaS(*))(-1/3). This similarity law is also explained by our mo del when it is supplemented by a consideration of the stability of the very thin horizontal boundary layers with large gradients (partial derivativeS( *)/partial derivativez) which form near the rigid surfaces. The preference for three-dimensional salt fingers is also explained by a combination of an alytical and numerical considerations.