(a) Taylor vortices are run first at and then at . Using the Landau result that the…

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Instability, transition and turbulence

Fluid Dynamics, Ch Transition to turbulence

Problem

(a) Taylor vortices are run first at Ta/Tac=1.02Ta/Ta_c=1.02 and then at Ta/Tac=1.10Ta/Ta_c=1.10. Using the Landau result that the saturated amplitude scales as Ta−Tac\sqrt{Ta-Ta_c}, find the ratio of the amplitude measured at Ta/Tac=1.10Ta/Ta_c=1.10 to that at Ta/Tac=1.02Ta/Ta_c=1.02. (b) A flat plate is towed through still water (ν=1.00×10−6 m2 s−1\nu=1.00\times10^{-6}\,\mathrm{m^2\,s^{-1}}) at 0.60 m s−10.60\,\mathrm{m\,s^{-1}}. Using the Blasius-layer critical value Reδ1=520Re_{\delta_1}=520 together with Reδ1=1.721RexRe_{\delta_1}=1.721\sqrt{Re_x}, find the distance from the leading edge at which Tollmien-Schlichting waves first become possible.

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