Bifurcation of developed flow in rectangular channels rotating about the transverse axis

Abstract

The linear problem of the stability of Poiseuille flow between two infinite plates rotating about an axis parallel to the plates and normal to the flow direction was studied in [1, 2]. It was established that the flow is least stable with respect to disturbances in the form of standing waves known as Taylor eddies. The experimental data of [1, 3] and the results [4] of a numerical integration of the Navier-Stokes equations for channels with cross sections highly elongated in the direction of the axis of rotation are in good agreement with the conclusions of the linear theory. In the case of channels with a side ratio of the order of unity, which is of greater practical interest, the primary flow becomes essentially three-dimensional and evolves with variation of the governing criteria: the Reynolds and Rossby numbers. Obviously, this seriously complicates the use of the methods of the linear theory. The effect of the ratio of the sides of the cross section on the stability of the primary flow regime was studied experimentally in [3]. The present article describes the results of an investigation of the problem based on a numerical method of integrating the nonlinear Navier-Stokes equations. Moreover, an asymptotic estimate of the stability limit of the primary regime, based on a local condition of inviscid instability of rotating flows, is presented.