On the competition between centrifugal and shear instability in spiral Couette flow

Abstract

The linear stability of a fluid confined between two coaxial cylinders rotating independently and with axial sliding (spiral Couette flow) is examined. A wide range of experimental parameters has been explored, including two different radius ratios. Zeroth-order discontinuities are found in the critical surface; they are explained as a result of the competition between the centrifugal and shear instability mechanisms, which appears only in the co-rotating case, close to the rigid-body rotation region. In the counter-rotating case, the centrifugal instability is dominant. Due to the competition, the neutral stability curves develop islands of instability, which considerably lower the instability threshold. Specific and robust numerical methods to handle these geometrical complexities are developed. The results are in very good agreement with the experimental data available, and with previous computations.

Stability of flow between rotating cylinders with axial buoyancy effect

“…A zeroth-order discontinuity in Re ic is found in the co-rotating case Re o > 0. Although this behavior has been found by other authors [4][5][6] , this specific example shows that such kind of discontinuity is universal in the flow under the condition of competition between two instability mechanisms.…”

“…2(b) and 2(c)). Meseguer and Marques [4] have discussed this phenomenon and pointed out that it is caused by the competition between centrifugal and shear instability leading to islands of instability appearing in the neutral stability curves. Similar islands of instability have also been found by Meseguer and Marques [5] , Peng and Zhu [6] .…”

“…Examples include the competitions between buoyancy and shear in inclined natural convection [1] , between rotation and buoyancy in binary mixtures [2] , between rotation and shear in Hagen-Poiseuille flow [3] , between rotation and axial sliding in Taylor-Couette flow [4] , and between rotation and axial pressure gradient in spiral Poiseuille flow [5] . Peng & Zhu [6] studied the problem in their most recent work on Bingham-plastic fluid flow in spiral Couette flow with axial sliding and found inhibiting effects on the competition.…”

Parametric instability in oscillatory shear flows

“…There have been other related studies of Taylor-Couette flows where each cylinder rotates azimuthally at a fixed rate but the inner cylinder oscillates in the radial direction (Marques & Lopez 1997Meseguer & Marques 2000). They conclude that the oscillation in the axial direction always has a stabilizing effect.…”

Spatial and temporal resonances in a periodically forced hydrodynamic system

“…When more than one forcing mechanism is present, multiple minima may occur in the marginal stability curves due to competition between the various forces (e.g. [15,17]). In our problem, the two competing mechanisms are the centrifugal instability of the circular Couette flow (which results in a cellular structure periodic in z of alternating sign of azimuthal vorticity) and the annular Stokes flow (which sends waves, independent of z, of alternating sign of azimuthal vorticity into the annular region from both the inner and outer cylinder walls).…”