Modeling salt-finger convection in the oceanic parameter regimes*

Re-scaled incompressible Navier-Stokes Equations (RiNSE) are formulated to simulate salt-finger convection in the parameter regime of τ → 0, relevant in the oceanic regime, with τ being the ratio of the salinity diffusion to the temperature diffusion. The equations are re-scaled with anisotropy in the z direction ∂_z ∼ τ▽_⊥, so τ serves as a control parameter for spatial anisotropy. These preconditioned equations are exact and alleviate the stiffness issues at a small τ. The two-dimensional RiNSE setup is used to simulate the salt finger convection for τ =0.01, which shows the patchiness of fingers at the large scales, confirming the presence of multiscale phenomena. Spontaneous emergence of mean horizontal shear is also observed, causing the tilt of salt fingers. Taking a further lead from RiNSE, we propose an asymptotically reduced model permitting an eddy flux feedback on the temperature flux. This reduced model is an extension of the previously proposed model: Inertia-Free Salt Finger Convection (IFSC) (Xie et al., 2017). Both RiNSE and the reduced model simulations are compared for the salt finger convection in the limit τ → 0.