Forced Plumes in Uniformly Stratified Environment

Abstract

This research investigates radially spreading intrusion created from a forced plume, when fluid continuously injected vertically from a nozzle entrains uniformly stratified ambient as it falls back upon itself. The flow evolution is determined as it depends upon the ambient buoyancy frequency, $N$, the source momentum and buoyancy fluxes, $M_0$ and $F_0$, respectively. A turbulent forced plume falls to maximum depth, $\Zm$, rises back upon itself as a fountain to its neutral buoyancy depth, $\Zs$, then spreads radially outwards. Through theory and experiments we determine that $\Zs=f(\sigma) \Hp$, in which $\Hp= M0^(3/4) F0^(-1/2)$, $\sigma = (M0 N/F0)^2$, and $(sigma) propto \sigma^(-3/8)$ for $\sigma \lesssim 50$ and $f(\sigma) \propto \sigma^{-1/4}$ for $\sigma \gtrsim 50$ respectively. In the inertia-buoyancy regime the intrusion front advances in time as $\Rs \propto t^(3/4)$,consistent with models assuming a constant buoyancy flux into the intrusion where the intrusion first forms at radius, $R_1$, with thickness, $h_1$, constant in time. The intrusion thickness, $h(r,t)$, adopted a self-similar shape of the form $h/h_1 \simeq [(\Rs-r)/(\Rs-R_1)]^p$, with $p\simeq 0.55\ \pm 0.03$. From dense descending plumes in uniformly stratified ambient, we conveniently applied our results to supervolcanoes penetrating and spreading in the stratosphere.