Interaction of a turbulent boundary layer with a shock wave at transonic flow velocities
The authors develop an asymptotic theory of the interaction of a turbulent boundary layer on a flat plate with a normal shock wave, assuming that the velocity in the undisturbed boundary layer satisfies a power law with an exponent depending on the Reynolds number, instead of a logarithmic law. The plate is situated in a gas flow with \(M_{\infty}>1\), and the shock wave impinges on it at a distance L from the tip. Some estimates for the basic averaged parameters are firstly obtained, then three different regions are distinguished in the flow field. In the first region a boundary value problem is obtaind, i.e.: \((1+\phi_{\xi})\phi_{\xi \xi}-\phi_{\eta \eta}=0\), \(\phi_{\eta}(\xi,0)=-\phi_{\xi \xi}(\xi,0), \phi \to 0 (\xi^ 2+\eta^ 2\to \infty\), \(\xi<0)\), \(\phi_{\xi}\to -2 (\xi^ 2+\eta^ 2\to \infty\), \(\xi>0)\). A solution of the problem is constructed numerically, and compared with experimental results.
scientific article; zbMATH DE number 3860715