Supersonic Boundary Layer in Regions with Small Temperature Perturbations on the Wall

Local temperature perturbations of the boundary layer in the regime of free viscous–inviscid interaction

“…The size of the element is an important parameter of the problem and discussed below. We assume, unlike in Koroteev & Lipatov (2009), that thermal perturbations are not small T ∼ T ∼ O(1).…”

“…The sizes of these regions are proportional to powers of the parameter Re = −2 . For the problem under consideration the detailed analysis of equations corresponding to each region was fulfilled in Lipatov (2006) and Koroteev & Lipatov (2009) and therefore is not described here. Note that the effect of perturbations is defined by scales of terms in Navier-Stokes equations.…”

“…Stationary solutions which are described in terms of free interaction of the boundary layer with the inviscid flow for the supersonic case corresponding to small perturbations of temperature T T ∼ O(1) were found in Koroteev & Lipatov (2009) and were also obtained for the subsonic case in Koroteev & Lipatov (2011).…”

“…The present work continues the studies started in Lipatov (2006) and Koroteev & Lipatov (2009), which were devoted to the construction of asymptotic solutions of Navier-Stokes equations in the regions containing local heating elements which are situated on the surface of the body. In our previous work (Koroteev & Lipatov 2009), we demonstrated how this problem can be solved analytically for small temperature perturbations.…”

“…In our previous work (Koroteev & Lipatov 2009), we demonstrated how this problem can be solved analytically for small temperature perturbations. The idea lying behind this approach consists of the possibility to utilize small temperature perturbations to control separation of the boundary layer and influence the delay of laminar-turbulent transition.…”