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

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