On the evolution of layer dynamics and critical power laws in double-diffusive finger convection at neutral buoyancy

Abstract

In this paper, we aim to explore the dynamics of the evolution of the thermohaline layer and estimate critical power-law time scales in a double-diffusive salt finger system at neutral buoyancy. To achieve this, we employ a high-resolution numerical model that simulates a two-layer finger system similar to a laboratory setup. Our model allows the system to naturally evolve by selecting its own length scale and no finger length scales were imposed. Our investigation reveals that the finger system inherently exhibits characteristics of salinity and density inversion. However, this tendency gradually diminishes at higher Rayleigh numbers (RaT). We accurately derive the critical power-law time scales for salinity and density inversion, maximum velocity, and the onset time of convection over a wide range of Rayleigh numbers (103 to 109). Notably, we observe an interesting relationship between the power-law time scale of the density inversion ratio (tρi) -the time scale when both layers become neutrally stable and the ratio Φ, which is approximately equal to 1.618. Specifically, we find the functional form as tρi ∼ RaT/RaTΦ for a significant range of Rayleigh numbers.