Numerical simulations of turbulent spots in supersonic boundary layers: Effects of Mach number and wall temperature

The compressible Navier–Stokes equations are solved for turbulent spots in otherwise laminar boundary layers with external flow Mach numbers of 3 and 6. In each case two wall temperature conditions are simulated, one corresponding to an adiabatic wall and the other to a cooled wall where the wall temperature is equal to the free stream temperature. The simulations show that the main parameter determining the spot lateral growth rate is the Mach number. The wall temperature plays a secondary role, with the cooled wall cases having lower lateral growth rates. The lateral spreading near the wing tips of the spots is examined in detail, revealing two components of the lateral growth mechanism. Firstly, turbulent structures are shown to convect outwards from the core of the spot, accounting for half the lateral growth rate at Mach 3 and three quarters at Mach 6. Secondly, new structures are created, the origin of which is shown to be in the instability of lateral jets of fluid issuing from the spot.