Double-diffusive convection in rotating fluids under gravity modulation

Abstract

This study employs the method of normal modes and linear stability analysis to investigate double-diffusive convection in a horizontally layered, rotating fluid, specifically focusing on its application to oceanic dynamics. Double diffusive convection arises when opposing gradients of salinity and temperature interact within a fluid, a phenomenon known as thermohaline convection, and it is crucial for the understanding of ocean circulation and its role in climate change. With the increasing mass of water due to glaciers melting, fluid pressure variations occur, leading to slight fluctuations in gravity. We conduct both stationary and oscillatory stability analyses to determine the onset of double-diffusive convection under gravity modulation. Our analysis reveals that time-dependent periodic modulation of gravitational fields can stabilize or destabilize thermohaline convection for both stationary and oscillatory convection, with amplitude stabilizing and frequency destabilizing. The wavenumber in the y- direction also affects convection in the equatorial regions. This wavenumber exhibits destabilizing effects for large values and stabilizing effects for small values for both stationary and oscillatory convection. Rotation along with gravity modulation tends to destabilize the system for both stationary and oscillatory convection. The key difference between stationary and oscillatory convection is that oscillatory convection exhibits large values of the Rayleigh number, thus susceptible to overstability while stationary convection tends to have relatively smaller Rayleigh numbers and thus more stable. This research provides insights into the complex interplay between gravity modulation and thermohaline convection, contributing to our understanding of ocean dynamics and their implications for climate change.