Salinity transfer in bounded double diffusive convection

Abstract

The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilised by the thermal field. Our simulations are directly compared to experiments by Hage and Tilgner (Phys. Fluids 22, 076603 (2010)) for several sets of parameters and reasonable agreement is found. This in particular holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have minor influence on salinity flux but affects the Reynolds number and the morphology of the flow. Next to the numerical calculation, we apply the Grossmann-Lohse theory for Rayleigh-Bénard flow to the current problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.

Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

“…Yang et al (2015) applied the GL theory to the salt-finger case and found a good agreement with observations. Given that the diffusive case of double-diffusive convection is in many ways more similar to Rayleigh-Bénard convection than the salt-finger case is, it seems likely that GL theory might prove useful also for the diffusive regime.…”

“…Nu } Ra Grossmann and Lohse (2001), and it is argued that these can be used also for double diffusion by Yang et al (2015).…”

“…These values suggest that (32) is close to (28) and that perhaps GL theory can be applied unmodified to the double-diffusive case. Yang et al (2015) applied the theory without modifications to the salt-finger case with a good result, and we shall start with that approach as well. Using our DNS, we can diagnose how the dissipation is partitioned between the mixed and boundary layers.…”

A Reduced Model for Salt-Finger Convection in the Small Diffusivity Ratio Limit

“…This result is to be compared with the asymptotic result Nu S ∼Ra 1/3 obtained by Yang et al [23] for a vertically-bounded domain.…”

“…In this paper, we therefore study the properties of this model at some length, albeit in two dimensions. To do so, we employ a doubly-periodic setting as appropriate for oceanic and astrophysical applications with distant boundaries, in contrast to earlier studies of salt-finger convection in vertically-bounded domains, e.g., [21][22][23][24][25]. In this formulation, elevator modes consisting of vertically-invariant upward and downward moving fingers are exact nonlinear solutions, and we believe that analogous modes are crucial even in vertically-bounded domains because of their efficiency in extracting energy from the salinity field.…”