D. Harris et al., An inhomogeneous Landau equation with application to spherical Couette flow in the narrow gap limit, PHYSICA D, 137(3-4), 2000, pp. 260-276
A nonlinear evolution equation is derived which governs the amplitude modul
ation of Taylor vortices between two rapidly rotating concentric spheres wh
ich bound a narrow gap and almost co-rotate about a common axis of symmetry
. In this weakly nonlinear regime the latitudinal vortex width is comparabl
e to the gap between the shells. The vortices are located close to the equa
tor and are modulated on a latitudinal length scale large compared to the g
ap width but small compared to the shell radius. The tendency for vortices
off the equator to oscillate introduces the phenomenon of phase mixing, Ste
ady finite amplitude solutions of the model equation are determined both nu
merically and analytically. The linear eigensolutions are identified by an
ascending sequence of eigenvalues lambda = lambda(n) (n = 0, 1,...). Each e
igensolution has its own finite amplitude continuation under variation of l
ambda which is a measure of the excess Taylor number. Without phase mixing
each vortex amplitude increases monotonically with growing lambda and does
so indefinitely,In contrast, with phase mixing each pair of linear modes (n
= 0, 1), (n = 2, 3), etc. are connected under the finite amplitude continu
ation; both the mode amplitude and lambda remain bounded. Though the small
phase mixing results agree with the non-phase mixed ones up to moderately l
arge lambda, this range is of Limited extent. As phase mixing is increased
the solution space shrinks and the amplitude of the remaining solutions is
strongly suppressed. (C) 2000 Elsevier Science B.V. All rights reserved.