Boundary Layer on an Inclined Flat Plate

This chapter presents a global stability analysis of the two-dimensional incompressible boundary layer with the effect of streamwise pressure gradients. A symmetric wedge flow with different non-dimensional pressure gradient parameters (β<inf>H</inf> ) has been considered. The pressure gradient (d p/ d x ) in the flow direction is zero for β<inf>H</inf>= 0, favourable (negative) for β<inf>H</inf>> 0 and adverse (positive) for β<inf>H</inf>< 0. The base flow is computed by the numerical solution of the Falkner-Skan equation. The displacement thickness (δ^∗ ) at the inflow boundary is considered for computing the Reynolds number. The governing stability equations for perturbed flow quantities are derived in the body-fitted coordinates. The stability equations are discretized using Chebyshev spectral collocation method. The discretized equations and boundary conditions form a general eigenvalues problem and are solved using Arnoldi’s algorithm. The global temporal modes have been computed for β<inf>H</inf>= 0.022, 0.044 and 0.066 for favourable and adverse pressure gradients. The temporal growth rate (ω<inf>i</inf> ) is negative for all the global modes. The ω<inf>i</inf> is smaller for the favourable pressure gradient (FPG) than that of the adverse pressure gradient (APG) at the same Reynolds number (Re = 340 ). Thus, FPG has a stabilization effect on the boundary layer. Comparing the spatial eigenmodes and spatial amplification rate for FPG and APG show that FPG has a stabilization effect while APG has a destabilization effect on the disturbances.