A numerical study of layer formation due to fingers in double-diffusive convection in a vertically-bounded domain

Abstract

The evolution of ngers in a double-diffusivesystem is investigatedusing numerical integration of two-dimensional equations of motion for an incompressible, Boussinesq uid. The computational domain is periodic in the horizontal direction and is closed with no-ux boundary conditions in the vertical direction. The main result of this study is the evolution of the system from initially linear pro les for both fast and slow diffusing components to a layered state characterized by a nger zone sandwiched between two mixed layers. The horizontal boundaries in this system play an important role in the development of the layered state. At the top and bottom boundaries, light and heavy nger uxes accumulate leading to the formation of mixed layers exhibiting larger-scale eddies. In the quasi-equilibrium state, the nger zone is characterized by broken wiggly ngers which do not extend across the entire interface. The salinity ux at the mid-depth of the domain is approximately proportional to the 4 3 power of the salinity difference between the mixed layers, except for the initial phase and for the run-down phase.

Asymmetric salt fingers induced by a nonlinear equation of state

“…18 These blobs also play an important role in fingers reaching a finite amplitude, when blobs regularly detach from the tips of the fingers, keeping the extent of the finger zone at a statistically steady state. 3,9 The present simulations have not reached an equilibrium state ͑e.g., Fig. 4͒ and do not display any blob-shedding during the simulation period.…”

“…We have only focused on the initial evolution of the fingers, with special emphasis on the structure of the individual fingers. The investigation of the finite amplitude behavior of the system consisting of mixed layers and finger interfaces requires a significantly larger domain and a longer integration period ͑e.g., Ö zgökmen et al 9 ͒.…”

“…Salt fingers obtained in laboratory experiments 2,3 are symmetric, i.e., sinking and rising columns have the same horizontal and vertical structure, the same wave number and the same growth rate. Analytical studies of salt fingers ͑e.g., Stern, 1 Schmitt, 4 Kunze 5 ͒ as well as numerical simulations ͑Piacsek and Toomre, 6 Shen,7,8 Ö zgökmen et al 9 ͒ have employed a linear equation of state, leading to a symmetric array of salt fingers. The impact of the nonlinearity in the equation of state on the finger interface was explored by McDougall, 10,11 who found in laboratory experiments that the nonlinearity causes the salt finger interfaces between mixed layers to migrate upward, an effect also observed by Schmitt.…”

Fingering Convection: the Interplay of Small and Large Scales

“…For fingering convection there is not enough experimental evidence to give a clear‐cut answer. The numerical simulations of Shen [20] and Özgökmen et al [22] suggest that the “four‐thirds” law is valid, but it fails if applied to the oceanic observations of the C‐SALT campaign [26], [12].…”

“…While their fingers grow all the way across the small computational domain, they also induce larger scale recirculation cells in the streamfunction field. Finally, Özgökmen et al [22] have shown a simulation that initially uses linear profiles of temperature and salinity. They report the emergence of convective cells close to the upper and lower boundary that eventually grow, sandwiching a high gradient zone between them.…”