Weak time-scale separation at the onset of oscillatory magnetoconvection in rapidly rotating fluids

Abstract

Convective instabilities are one of the integral parts of the dynamics of flows driven by thermal buoyancy. Naturally, physical phenomena exhibit a wide disparity in the length and timescales of the field variables in numerical simulations and experimental observations. Such variations are not represented in the traditional normal mode stability analysis attempting to understand the onset of convection. This study attempts to incorporate different time constants for different perturbation variables in the linear stability analysis with the help of a Taylor series expansion. The infinite horizontal layer model is chosen for simplicity. Apart from the classical Rayleigh-Bénard system, additional physical effects such as background rotation and magnetic field have been considered with plausible implications for geophysical flow applications. The time scale separation is implemented by considering a slight change in the frequency of temperature perturbation compared to that for other physical quantities. Both analytical and numerical methods have been utilised for the investigation. The threshold buoyancy force is reduced when the temperature perturbation has a smaller frequency than the frequencies of other variables. Besides that, the onset wavenumber and frequency of the oscillatory modes are modified due to weak scale separation from the onset characteristics of the reference case. In particular, enhanced frequency of temperature perturbations leads to smaller-scaled magnetically controlled convective rolls and larger-scaled viscously controlled instabilities at the onset. A robust dependence of the onset characteristics with the parameter quantifying the timescale separation is obtained. Additionally, two transitions in the convective onset modes with scale separation have been identified.