Effect of density gradients in confined supersonic shear layers. Part 2: 3-D modes

The effect of basic flow density gradients on the supersonic wall modes were investigated in Part 1 of this analysis. In that investigation only the 2-D modes were studied. Tam and Hu investigated the 3-D modes in a confined vortex sheet and reported that the first 2-D Class A mode (A01) had the highest growth rate compared to all other 2-D and 3-D modes present in the vortex sheet for that particular set of flow patterns. They also showed that this result also held true for finite thickness shear layers with delta(sub w) less than 0.125. For free shear layers, Sandham and Reynolds showed that the 3-D K-H mode became the dominant mode for M(sub c) greater than 0.6. Jackson and Grosch investigated the effect of crossflow and obliqueness on the slow and fast odes present in a M(sub c) greater than 1 environment and showed that for certain combination of crossflow and wave angles the growth rates could be increased by up to a factor of 2 with respect to the 2-D case. The case studied here is a confined shear layer shown in Part 1. All solution procedures and basic low profiles are the same as in Part 1. The effect of density gradients on the 3-D modes present in the density ratios considered in Part 1 are investigated.