Jet formation in salt-finger convection: amodified Rayleigh-Benard problem

摘要

Large-scale coherent structures such as jets in Rayleigh-Benard convection and related systems are receiving increasing attention. This paper studies, both numerically and theoretically, the process of jet formation in two-dimensional salt-finger convection. The approach utilizes an asymptotically derived system of equations referred to as the modified Rayleigh-Benard convection (MRBC) model, valid in the geophysically and astrophysically relevant limit in which the solute diffuses much more slowly than heat. In these equations, convection is driven by a destabilizing salinity gradient while the effects of the stabilizing temperature gradient manifest themselves as an additional anisotropic dissipation acting on large scales. The MRBC system is specified by two external parameters: the Schmidt number Sc (ratio of viscosity to solutal diffusivity) and the Rayleigh ratio Ra (ratio between the Rayleigh numbers of the destabilizing solutal stratification and the stabilizing thermal stratification). Two distinct Ra regimes are explored for fixed Sc = 1. In all cases studied the system develops a horizontal jet structure that is maintained self-consistently by turbulent fluctuations, but coarsens over time. For intermediate Rayleigh ratios (e.g. Ra = 6), the MRBC model captures the relaxation oscillations superposed on the jet structure observed at similar parameter values in direct numerical simulations of the primitive equations. For smaller Rayleigh ratios (e.g. Ra = 2), a regime for which direct numerical simulation of the primitive equations is difficult because of the presence of fast gravity waves, the MRBC model reveals the existence of statistically steady jets whose properties are studied in detail. Three hierarchical models, the MRBC and further reductions in the form of quasilinear and single-mode approximations, are used to confirm that jets form and are sustained as a result of the interaction between fluctuations (salt fingers) and large-scale horizontally