No abstract

Linear stability of a laminar boundary-layer flow in a streamwise corner can only be treated with an ansatz that considers two-dimensional eigenfunctions with inhomogeneous boundary conditions in cross-flow directions. It is common practice to use Sommerfeld’s radiation condition with a certain wavenumber $\unicode[STIX]{x1D6FD}$ at the lateral domains of the integration domain which are at the same time the far-field domains for each wall. So far, this radiation condition has been exclusively used in a ‘symmetrical’ way, i.e. with the same $\unicode[STIX]{x1D6FD}$ on either far-field boundary plane. This has led to wave patterns that either enter or leave the corner region from the lateral sides for $\unicode[STIX]{x1D6FD}<0$ or $\unicode[STIX]{x1D6FD}>0$ respectively. Here, an ‘asymmetric’ use of Sommerfeld’s radiation condition is suggested, i.e. $\unicode[STIX]{x1D6FD}<0$ on one far side of the corner and $\unicode[STIX]{x1D6FD}>0$ on the other. With this modification, waves enter the corner area from one side and leave it through the other, i.e. they travel obliquely through the corner. In contrast to before, their amplification rate is always symmetric with respect to $\unicode[STIX]{x1D6FD}=0$ and there is no amplification-rate increase or decrease due to information that either continuously enters the corner from both sides or continuously leaves it through the far sides. The present analysis also shows that the inviscid corner modes are unaffected by the parameters of the far-field radiation boundary conditions. Nevertheless, superposition of two oppositely running single waves obtained by the modified application of the radiation condition leads to a similar wave pattern to that in the case with $\unicode[STIX]{x1D6FD}<0$ on both sides; however, with a slightly smaller amplification rate and a strictly streamwise propagation direction.

No abstract

The influence of constant wall temperatures on the compressible flow along a right-angled corner and its stability behaviour is investigated by temporal local linear stability analysis. Wall-cooling up to 90 % of the adiabatic wall-temperature for a subsonic flow (M a = 0.95) is considered. The maximum cross-flow velocity along the corner bi-sector for the base flow with adiabatic wall boundary condition is higher than for the base flow with constant adabatic wall-temperature. For increasing wall temperature, the amplification rate of the viscous modes decreases to a lesser extent than that of the corner mode, therefore the critical Reynolds-number is further on defined by the first viscous mode. The spatial behaviour is displayed using N-factors computed from Gaster-transformed modes.

No abstract