The Influence of Gravity Modulation on a Stability of Plane-Parallel Convective Flow in a Vertical Fluid Layer with Heat Sources

Abstract

This paper is devoted to the investigation of the stability of plane-parallel flow in a vertical fluid layer with uniformly distributed heat sources in modulated gravity field. The layer boundaries are rigid and maintained at equal constant temperatures. Gravity is assumed to be vertical and consisting of both mean and sinusoidal modulation (‘jitter’). Specific feature of this problem is that in the absence of modulation, at zero Prandtl number, the decrements of normal-mode perturbations of the base state are complex-valued and hydrodynamic instability mode is caused by travelling perturbations (travelling vortices at the boundaries of counter flows). With the increase in Prandtl number the instability mode changes from hydrodynamic instability of the counter flows to growing thermal waves. In the presence of gravity modulation, the base flow is the superposition of the same stationary flow as in the absence of modulation and time-periodic flow. The linear stability of this base state is studied by the numerical solution of the linearized equations of small perturbations. Numerical data on temporal evolution of perturbations are used to determine the decrements of perturbations and instability boundaries at different values of the Prandtl number. The calculations confirm that all perturbations are quasi-periodic. Parameter ranges where modulation makes stabilizing or destabilizing effect are defined. Sharp stabilization of the base flow in low-frequency range is discovered and explained by transformation of the neutral curves with the decrease of frequency which incleds formation of a bottleneck, break into two instability regions (the isolated region of hydrodynamic instability at lower Grashof number values and bag-shaped region of thermal wave instability at higher Gr), decrease in the size of the hydrodynamic instability region and shift upward of the thermal wave instability region and vanishing the isolated region of hydrodynamic instability.