THE EFFECT OF 3-DIMENSIONAL FREESTREAM DISTURBANCES ON THE SUPERSONIC-FLOW PAST A WEDGE

The interaction between a shock wave (attached to a wedge) and small a mplitude, three-dimensional disturbances of a uniform, supersonic, fre estream flow are investigated. The paper extends the two-dimensional s tudy of Duck et al. [P W. Duck, D. G. Lasseigne, and M. Y. Hussaini, ' 'On the interaction between the shock wave attached to a wedge and fre estream disturbances,'' Theor. Comput. Fluid Dyn. 7, 119 (1995) (also ICASE Report No. 93-61)] through the use of vector potentials, which r ender the problem tractable by the same techniques as in the two-dimen sional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results ar e presented for specific classes of freestream disturbances, and the s tudy shows conclusively that the shock is stable to all classes of dis turbances (i.e., time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic ( loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-B essel series, valid far downstream of the shock. (C) 1997 American Ins titute of Physics.