Shear and nonlinear density effects in double-diffusive finger convection: Numerical investigations

Abstract

[Abstract] Double-diffusive convection in the form of salt-finger instability plays a fundamental role in scalar transport and mixing in stratified fluids. Extending previous investigations of shear-induced finger dynamics (https://doi.org/10.1063/5.0300705), the present study examines the combined effects of laminar shear flow, equation of state (EOS) nonlinearity, and buoyancy intensity on salt-finger convection. The governing two-dimensional Navier-Stokes equations are solved using a high-order finite volume method employing a fifth-order weighted essentially non-oscillatory (WENO) scheme for nonlinear advection, a fourth-order central discretization for viscous terms, and a third-order total variation diminishing (TVD) Runge-Kutta scheme for time integration. Simulations are performed for Reynolds numbers in the range 0-700 and thermal Rayleigh numbers varied from 7x104 to 7x108, considering both linear and nonlinear EOS, with density varying quadratically with temperature and linearly with salinity. The results reveal that the coupled effects of EOS nonlinearity, shear intensity, and thermal Rayleigh number strongly influence the morphology, dynamics, and transport properties of salt fingers. At low Rayleigh number 7x104, weak buoyancy forces render the flow highly susceptible to shear-induced deformation, leading to fewer and less coherent finger structures. The moderate Rayleigh number regime RaT=7x106 is characterized by a more balanced competition between buoyancy-driven convection and shear advection, resulting in well-developed salt fingers and enhanced scalar transport. In contrast, at high Rayleigh number 7x108, intensified buoyancy-driven transport promotes the formation of more numerous and finer-scale finger structures, accompanied by enhanced interfacial activity and mixing. Under nonlinear conditions, the flow exhibits a marked asymmetry with respect to the mid-plane of the domain, characterized by accelerated and narrowed descending fingers due to enhanced buoyancy forces, while ascending fingers are damped and increasingly tilted under shear. Furthermore, probability density function (PDF) analysis show that the mixing characteristics are strongly dependent on the combined effects of Rayleigh number, shear intensity, and EOS nonlinearity, significantly modifying scalar distributions, transport efficiency, and interfacial mixing.