The near-field shape and stability of a porous plume

When a fluid is injected into porous medium saturated with an ambient of greater density, the forms plume that rises upwards due to buoyancy. In near field injection point, adjusts its speed match buoyancy velocity medium, either thinning or thickening conserve mass. These adjustments are dominant controls on near-field shape, rather than mixing fluid, which occurs over larger vertical distances. this study, we focus behaviour in field, demonstrating for moderate rates, will reach steady state, whereby it matches few width scales from point. However, very small instability breaks apart insurmountable density contrast surrounding fluid. The shape depends only single dimensionless parameter, ratio between inlet and velocity. A linear stability analysis performed, indicating ratios, infinitesimal perturbation can be constructed becomes unstable, whilst shown stable. Finally, comment application such flows context CO $_2$ sequestration geological reservoirs.