Boundary Layer on an Inclined Flat Plate

Abstract

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 ( $$\beta _{H}$$ ) has been considered. The pressure gradient ( $${\text {d}}p/{\text {d}}x$$ ) in the flow direction is zero for $$\beta _{H} = 0$$ , favourable (negative) for $$\beta _H > 0$$ and adverse (positive) for $$\beta _H < 0$$ . The base flow is computed by the numerical solution of the Falkner-Skan equation. The displacement thickness ( $$\delta ^*$$ ) 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 $$\beta _H=0.022$$ , 0.044 and 0.066 for favourable and adverse pressure gradients. The temporal growth rate ( $$\omega _i$$ ) is negative for all the global modes. The $$\omega _i$$ is smaller for the favourable pressure gradient (FPG) than that of the adverse pressure gradient (APG) at the same Reynolds number ( $${\text {Re}} = 340$$ ). 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.