Effect of thermal diffusion on instabilities of stratified shear flows

  • Park, Junho (Coventry University)
  • Mathis, Stéphane (CEA Saclay)

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In many naturally-occurring and engineering systems where fluid flow is coupled with heat transfer, it is important to understand the role of thermal diffusion. The thermal diffusion is characterised by the Prandtl number $Pr=\nu/\kappa$, which is the ratio between fluid kinematic viscosity $\nu$ and thermal diffusivity $\kappa$. Depending on situations, $Pr$ varies significantly; for instance, the value of $Pr$ is $Pr\sim O(10^{-6})$ in stellar interior, $Pr\sim O(10^{-2})$ in the liquid metal core of the Earth, $Pr\sim O(1)$ for the air, or $Pr\gg 1$ for oils. At low $Pr$, high thermal diffusivity tends to suppress the effect of stable stratification, as revealed in the study of shear instability where both the stratification and shear are along the vertical direction (Lignières et al. 1999). Our study aims to explore further the effect of thermal diffusion in other configurations. For instance, we investigate as a first problem the horizontal shear instabilities with stratification in the vertical direction. The topic has relevance to the configuration in stellar radiation zones where the thermal diffusivity is high (i.e. a very small $Pr$ as $Pr\sim O(10^{-6})$). We conduct linear stability analysis for a base flow in the hyperbolic tangent profile, which has two types of instability: the inflection-point and inertial instabilities. In the presentation, it will be discussed how these two instabilities are affected by the high thermal diffusivity (see e.g., Park et al. 2020). The second topic to be considered is Taylor-Couette (TC) flow with stable stratification in the axial direction. Centrifugal instability of the TC flow is known to be suppressed by the stratification (Boubnov et al. 1995). For stratified TC flow, another instability known as the strato-rotational instability (SRI) also exists when the stratification is strong enough and perturbation is axisymmetric. In the presentation, it will be discussed how the centrifugal instability of stratified TC flow is destabilised while the SRI is suppressed as $Pr$ decreases.