From thin plates to Ahmed bodies: linear and weakly nonlinear stability of rectangular prisms

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$ , while length-to-height $1/6< L/H<3$ covers a wide range geometries from thin plates elongated Ahmed bodies. First, global linear analysis yields series pitchfork and Hopf bifurcations: (i) at lower Reynolds numbers $Re$ two stationary modes, $A$ $B$ become unstable, breaking top/bottom left/right planar symmetries, respectively; (ii) larger oscillatory modes unstable and, again, each mode breaks one symmetries. critical values these four increase with $L/H$ reproducing qualitatively trend bifurcations in axisymmetric (e.g. disk, sphere bullet-shaped bodies). Next, weakly nonlinear based on coupled amplitude equations. For bodies, as increases, state $(A,0)$ appears first, followed by $(0,B)$ . While there bistability those states, only remains stable similar static wake deflection (across base dimension) observed turbulent regime. bifurcation sequence, including hysteresis, validated fully direct numerical simulations, shown be robust variations $W$ $L$ common