Global stability of flow in symmetric wavy channels

Abstract

AbstractA two-dimensional global stability analysis is numerically conducted for the basic fully developed steady flow inside symmetric wavy channels. The relative amplitude of channel modulation, defined as ratio of wall modulation amplitude to mean hydraulic diameter, is fixed via the analysis at a large value of 0.15. The relative channel wavelength, defined as the ratio of wall modulation wavelength to mean hydraulic diameter, is varied between 1 and 5. An important feature of the present approach is the detailed consideration of the streamwise conditions imposed on the flow, which allows a tailored restriction of the possible disturbances by modifying the number of channel sections that set the periodicity. Stability of the base flow is determined on the basis of the spectral structure analysis conducted, possible after calculation of the complete eigenvalue spectrum and facilitated by the spectral method employed. Two different destabilization mechanisms have been identified for the geometry studied. For small relative channel wavelengths, with values below approximately 2.7, the flow is destabilized via a Hopf bifurcation produced by a Tollmien–Schlichting wave at Reynolds numbers in the approximated range from 265 to 324. For large relative channel wavelengths, with values above approximately 2.5, a pitchfork bifurcation (or a Hopf bifurcation with very small oscillation frequency), not previously reported in the literature and produced by a symmetric stationary disturbance, is found at Reynolds numbers in the approximated range from 146 to 230.