Abstract
The nonlinear rotating channel problem in the neighborhood of the instability to streamwise rolls is studied with particular attention to the spanwise structure of the solutions. A Newton algorithm is developed for the geometry of neutral surfaces and is used to find accurate values for the minimum point of the neutral paraboloid. A Ginzburg-Landau (GL) equation for spanwise modulated states is derived. The derivation is simplified by writing the Navier-Stokes equations as a spatial evolution equation. Accurate numerical values for the coefficients in the GL equation, for a family of basic states interpolating between rotating plane Poiseuille flow and Couette flow, are obtained using a Chebyshev spectral-collocation method with a staggered grid. Analysis of the GL equation points to the importance of spanwise quasiperiodic states and stationary solitary wave-like states for the rotating channel problem with large spanwise dimension
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