The nonlinear stability of spatially inhomogeneous shear flows, including the effect of feedback
Abstract
The stability of spatially developing free shear flows which are taken to be weakly diverging is studied. An attempt is made to find twodimensional timeperiodic perturbations of such flows, which vanish at infinity in all space directions and are termed global modes. Of particular interest are flow conditions at which the first of these global modes becomes linearly unstable, i.e., selfexcited. Assuming that the Hopf bifurcation at this point is supercritical and that the weak nonparallel and nonlinear effects are of equal importance, the spatiotemporal evolution of the globalmode amplitude is found to be governed by a GinzburgLandau equation with variable coefficients.
 Publication:

European Journal of Mechanics B Fluids
 Pub Date:
 1991
 Bibcode:
 1991EJMF...10..295M
 Keywords:

 Flow Stability;
 Free Flow;
 Nonlinear Equations;
 Nonuniform Flow;
 Shear Flow;
 Flow Velocity;
 LandauGinzburg Equations;
 Self Excitation;
 Fluid Mechanics and Heat Transfer