A reduced model for salt-finger convection in the small diffusivity ratio limit

Abstract

A simple model of nonlinear salt-finger convection in two dimensions is derived and studied. The model is valid in the limit of small solute to heat diffusivity ratio and large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modified Rayleigh-Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute field and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identified for the second model: The weakly driven regime is characterized by a large-scale flow associated with a balance between advection and linear instability, while the strongly driven regime produces multiscale structures, resulting in a balance between the energy input through linear instability and the energy transfer between scales. For both regimes, we analytically predict and numerically confirm the dependence of the kinetic energy and salinity fluxes on the ratio between solute and heat Rayleigh numbers. The spectra and probability density functions are also computed.

arXiv comment25 pages, 16 figures

References in corpus (13)

• Numerically determined transport laws for fingering ("thermohaline") convection in astrophysics
• Chemical Transport and Spontaneous Layer Formation in Fingering Convection in Astrophysics
• Numerical Simulations of Thermohaline Convection: Implications for Extra-Mixing in Low-Mass RGB Stars
• Dynamics of fingering convection I: Small-scale fluxes and large-scale instabilities
• Dynamics of fingering convection II: The formation of thermohaline staircases
• Exponentially growing solutions in homogeneous Rayleigh-Benard convection
• Scaling and universality in turbulent convection
• Excitation of gravity waves by fingering convection, and the formation of compositional staircases in stellar interiors
• Scaling laws and flow structures of double diffusive convection in the finger regime
• Salinity transfer in bounded double diffusive convection
• 2D or not 2D: the effect of dimensionality on the dynamics of fingering convection at low Prandtl number
• Vertically bounded double diffusive convection in the fingering regime: comparing no-slip vs free-slip boundary conditions
• Non-Gaussian buoyancy statistics in fingering convection

Cited by in corpus (5)

• Fingering convection in the stably-stratified layers of planetary cores
• Equatorially Trapped Convection in a Rapidly Rotating Shallow Shell
• Staircase solutions and stability in vertically confined salt-finger convection
• Spontaneous generation of helical flows by salt fingers
• Growth of helicity in salt-finger convection in the two-dimensional three-component limit