Multiple states and transport properties of double-diffusive convection turbulence

Significance When two different scalars which simultaneously affect the fluid density experience appropriate vertical gradients, double-diffusive turbulence occurs and greatly enhances the mixing. Such process is ubiquitous in nature. In the ocean, DDC has profound influences on the vertical mixing and causes the intriguing thermohaline staircases, namely, a stack of well-mixed convection layers separated by sharp interfaces with very high gradients of mean temperature and salinity. Here we conduct large-scale numerical simulations for such flows in the fingering regime, which is commonly found in the (sub)tropic region. We show that multiple equilibrium states exist in fingering thermohaline staircases with exactly the same background condition and develop scaling laws to describe the fluxes of finger interfaces. When fluid stratification is induced by the vertical gradients of two scalars with different diffusivities, double-diffusive convection (DDC) may occur and play a crucial role in mixing. Such a process exists in many natural and engineering environments. Especially in the ocean, DDC is omnipresent since the seawater density is affected by temperature and salinity. The most intriguing phenomenon caused by DDC is the thermohaline staircase, i.e., a stack of alternating well-mixed convection layers and sharp interfaces with very large gradients in both temperature and salinity. Here we investigate DDC and thermohaline staircases in the salt finger regime, which happens when warm saltier water lies above cold fresher water and is commonly observed in the (sub)tropic regions. By conducting direct numerical simulations over a large range of parameters, we reveal that multiple equilibrium states exist in fingering DDC and staircases even for the same control parameters. Different states can be established from different initial scalar distributions or different evolution histories of the flow parameters. Hysteresis appears during the transition from a staircase to a single salt finger interface. For the same local density ratio, salt finger interfaces in the single-layer state generate very different fluxes compared to those within staircases. However, the salinity flux for all salt finger interfaces follows the same dependence on the salinity Rayleigh number of the layer and can be described by an effective power law scaling. Our findings have direct applications to oceanic thermohaline staircases.