Experiments on buoyant plumes in a rotating channel

The influence of bounding geometry and rotation on the discharge of buoyant fluid from a turbulent axisymmetric plume in an open-ended channel is examined through an experimental study. Both homogenous and stratified ambients are considered. In the non-rotating channel, the plume rises and spreads as a pair of counterflowing gravity currents at either the free surface tin a homogenous ambient) or at the plume's level of neutral buoyancy tin a stratified fluid). Scaling laws and accompanying experiments indicate that in a homogeneous environment, the surface gravity currents emerging from a channel of width W and depth H have a depth h which is independent of plume source conditions: h = (0.13 +/- 0.02) H-5/3 W-2/3 When the ambient is stratified and characterised by a constant Brunt-Vaisala frequency N, the current intruding at its neutral height Z(n) has a uniform thickness h = (1.1 +/- 0.2) B-3/8 N-9/8 W-1/2, where B is the plume buoyancy flux. These results were found to be robust for high Reynolds number gravity currents, but broke down for Re < 100 when viscous effects became important. Moreover, when the channel was sufficiently narrow, W<(H/3, Z(N)/3) the results broke down in a manner consistent with the channel walls acting to suppress entrainment into the plume. When the system is rotating, the mode of discharge is characterized in terms of the relative magnitudes of the channel width and the maximum radius attainable by the anticyclonic plume vortex before the onset of instability. In the homogeneous environment, the plume Vortex takes a columnar form, which may attain a radius, R-max = 8L(f), where L-f = B-1/4/f(3/4) is the rotational lengthscale and f is twice the rotation rate of the system. In the stratified environment, with N much greater than f, the plume vortex takes a lenticular form which may attain a radius of R-max = NZ(n/f) before going unstable. For W>R-max, the flow is unsteady, characterised by the pulsatile shedding of discrete vortices from the central plume. For W < R-max, the now is steady, characterised by a pair of counterflowing geostrophic gravity currents. Particular attention is given to the steady geostrophic regime in the homogeneous environment, from which it is possible to infer the volume flux of the fluid exiting the channel from the shape of the boundary currents, and so to infer the influence of rotation on the rate of entrainment into a turbulent plume. The experiments indicate that the volume flux exiting in the form of gravity currents, Q(g), is related to that which would emerge at the free surface in the absence of rotation, Q(0), through Q(g)/Q(0) = (5.0 +/- 1.0) (L-f/H) (5/3). This scaling result is consistent with the simple physical model of the plume entraining as it would in the absence of rotation up to a distance 2.6L(f) above the source, above which rotation serves to entirely suppress entrainment into the plume.