Stability effects of a base cavity on the wake of axisymmetric bluff bodies

We extend our previous research on the instability properties of the laminar incompressible flow around a cylindrical body with a rounded nose and length-to-diameter ratio $L/D=2$, at zero angle of attack, by analyzing the effects of a cylindrical base cavity of length $h$ and diameter $D_c$. We combine experiments, three-dimensional direct numerical simulations and a global linear stability analysis. The direct numerical simulations and the global stability results accurately predict the stabilizing effect of the cavity on the stationary, three-dimensional bifurcation in the wake as $h/D$ increases. In fact, it is shown that, for a given value of $D_c/D$, the critical Reynolds number for the steady bifurcation, $Re_ {cs}$, increases monotonically as $h/D$ increases, reaching an asymptotic value, that depends on $D_c/D$, at $h/D\approx$ 0.7. On the other hand, for a fixed value of $h/D$, $Re_{cs}$ exhibits a maximum at $D_c/D\approx$ 0.8. Similar behavior has been observed experimentally and numerically for the second, oscillatory bifurcation, and its associated critical Reynolds number, $Re_ {co}$.