Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

Abstract

We present the results of direct numerical simulations of flow patterns in a lowPrandtl-number (P r = 0.1) fluid above the onset of oscillatory convection in a Rayleigh-Bénard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box (L x ×L y ×1) and a wide range of Taylor numbers (750 ≤ T a ≤ 5000) for the purpose. The horizontal aspect ratio η = L y /L x of the box was varied from 0.5 to 10. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes (0.5 ≤ η < 1 and 1 < η < 2).The flow patterns observed in boxes with η = 1 and η = 2 were different from those with η < 1 and 1 < η < 2. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell (η = 1) for T a < 2700, but observed a set of parallel rolls in the form of standing waves for T a ≥ 2700. The three-dimensional convection was quasiperiodic or chaotic for 750 ≤ T a < 2700, and then bifurcated into a two-dimensional periodic flow for T a ≥ 2700. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle φ = π 2 − arctan (η −1 ) with the straight rolls.

Transitions in overstable rotating magnetoconvection

“…The transitions to convection including the bifurcation structure and pattern dynamics for such weaker rotation rate (0 < Ta ≤ 500), where stationary convection occurs, have been discussed in detail in a recent study [25]. The results of the investigation reported in the present study are mostly on low Prandtl number fluids (liquid metals) since they exhibit a very rich bifurcation structure near the onset of stationary as well as overstable convection in the absence or presence of magnetic field or rotation [13,[25][26][27][28][29][30][31][32][33][34].…”

“…Overstable convection or overstability has drawn considerable attention of the researchers over the years due to its appearance in various astrophysical applications like the convective motion in sunspot and stellar interiors [1][2][3][4][5][6][7][8]. To understand the basic properties of overstable convection, researchers often consider simplified convection models like Rayleigh-Bénard convection (RBC) [9][10][11][12][13] in the presence of rotation and/or magnetic field. The overstable convection occurs in RBC as the 'principle of exchange of stability' becomes invalid and the instability is manifested as a time dependent, oscillatory convective motion.…”

Zero Prandtl-number rotating magnetoconvection

“…Moreover, as argued in 56 , the modes of the form W 00n in the vertical velocity are also not excited as there is no horizontal mean flow. Now from the linearized equation (12) it is seen that the linear growth rate of the vertical velocity mode W 101 will first become positive as the value of Ra is increased from conduction state and hence this mode must be excited at the onset.…”

“…The effects of rotation and external magnetic field on the instabilities and bifurcation structures near the onset of convection when acted separately have recently been investigated in [55][56][57][58][59][60][61][62] and reported very rich dynamics including chaos at the onset of convection. However, instabilities and the associated bifurcation structures near the onset of RBC of electrically conducting fluids in presence of both rotation and uniform external magnetic field have not been studied so far.…”

Zero-Prandtl-number convection with slow rotation

“…Rotation about a vertical axis 16,[20][21][22][23][24][25][26][27][28][29][30][31][32] introduces the centrifugal force and the Coriolis force. Both the forces act along the horizontal plane.…”