On <i>g</i>-jitter effects on three-dimensional laminar thermal convection in low gravity

Abstract

We numerically study the forced-oscillation-frequency responses on the three-dimensional thermal convection in a cubic cavity heated from one wall and chilled from its opposite wall in the non-gravitational field at vibrational Rayleigh number (the Rayleigh number based on the cavity's acceleration amplitude instead of the gravitational acceleration) Ra η = 5.0×10 3 -1.1×10 5 , Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillation frequency ω = 1.0×10 0 -1.0×10 3 . The direction of the forced sinusoidal oscillation is parallel to the temperature gradient inside the cubic cavity. We especially focus upon the influences of both Ra η and ω. As a result, five kinds of structures S2 (with a single roll), S4 (with a toroidal roll), S5 (with four roll), S6 (with four roll) and S (with six roll) appear in the tested ranges of Ra η and ω. The S consists of a pair of trident currents, namely, three ascending streams and three matching descending streams in the cubic cavity. And, such flow structures are revealed in detail. Whenever it is not conductive but convective for ω < 5.0×10 2 , convective motion always starts with the S4 from the rest at each forcing cycle. We find out the optimum frequency where the amplitude of a spatially-averaged kinetic energy K , which is defined by the difference between the maximum K and the minimum K over one forcing cycle, attains the maximum at each Ra η . At ω = , the flow structure is characterised by the S4. So, this fact suggests that the optimum frequency can be related with the S4. In addition, we show the occurrence condition for convection as a function of Ra η and ω, and the boundary for the quasi-steady approximation which is permissible at ω ≲ 10 0 from a quantitative viewpoint.