Inertially driven buckling and overturning of jets in a Hele-Shaw cell

We study a fluid jet descending through stratified surroundings at low Reynolds number in Hele-Shaw flow. The jet buckles and overturns inside a conduit of entrained fluid which supports smooth or unstable traveling waves. A model of the recirculating flow within the conduit shows that buckling and waves arise from Kelvin-Helmholtz instabilities and quantitatively accounts for the main experimental observations. Beyond the onset of the instability, a damped, forced Burgers' equation obtained from corrections to Darcy's law for small Reynolds number governs the interface dynamics and supports singularities corresponding to the observed jet overturning and unstable waves.