ON SCALING LAWS FOR THE TRANSITION TO TURBULENCE IN UNIFORM-SHEAR FLOWS

Numerical and experimental results indicate that the critical amplitud e for non-linear growth of disturbances in a uniform shear flow follow s two scaling laws, depending on the shape of the initial disturbance: i) a Re-1 law for disturbances with zero streamwise dependence (strea ks) (Kreiss et al., submitted to J. Fluid Mech.); ii) a Re--0.4+/-0.1 law for disturbances with non-zero streamwise dependence (spots) (Dauc hot and Daviaud, submitted to Phys. Fluid A). It is shown that these l aws can be explained by the competition between non-linear growth and viscous dissipation and that the difference in exponent simply reflect s the difference in viscous-decay mechanism. Lower bounds for conditio ns for non-linear growth are derived analytically. They follow a Re-1 and Re-1/3 law for streamwise and spotwise initial perturbations. The transition to a self-sustained turbulent state is also discussed. Uppe r bounds for this transition are derived. They follow, respectively, a Re -1/2 and Re -1/6 law for streak or spot initial perturbations.