INSTABILITY OF A ROTATING SHEAR-LAYER IN THE TRANSONIC REGIME

We have studied numerically the stability of a two-dimensional Couette flow in a polytropic fluid subjected to a localized shear, using a ps eudo-spectral method (Fourier-Chebyshev). The polytropic index has bee n chosen equal to 2 and a radial force (pseudo-gravity) is introduced in order to perform comparisons with the shallow water experimental re sults. When the Reynolds number is not too low, the initial flow which is purely azimuthal becomes unstable and a stable rotating pattern is formed, with a number of azimuthal modes which decreases when the Mac h number increases. A qualitative agreement is found with the experime ntal results, although the spatial resolution constraint strongly limi ts the numerical Reynolds and Mach numbers. From the variation of the linear growth rate of the unstable modes with the Mach number, we are able to show the transition between a flow subjected to Kelvin-Helmhol tz instability towards one essentially driven by a centrifugal instabi lity, which is efficient for rotating supersonic flows if the angular momentum decreases outwards. The latter situation may occur for some f lows in astrophysical disks.