Stability analysis of axisymmetric supersonic wakes using various basic states

Abstract

Two-dimensional stability analyses are conducted of turbulent axisymmetric supersonic wakes at M = 2.46. The aim is to investigate which azimuthal modes are dominant and how the stability behaviour is influenced by the choice of basic state. To that end, axisymmetric (two dimensional) and three dimensional direct numerical simulations (DNS) with either laminar or turbulent inflow conditions were conducted of supersonic wakes to provide the respective basic states for the stability analysis. The global stability analyses were then performed by computing the temporal pulse response using forced Navier-Stokes simulations for each basic state. Using the time- and azimuthally-averaged data from the 3D DNS with turbulent inflow as basic state, an absolute instability of the axisymmetric mode at a Reynolds number, based on wake-generating body diameter and freestream velocity, ReD = 100,000 was found. This is in contrast to results obtained earlier using an axisymmetric flow solution as the basic state. The linear stability analysis for all basic states is presented showing the temporal growth of various azimuthal modes and the respective radial mode shapes. The results are also contrasted to those obtained from nonlinear DNS.