Laboratory experiments on two coalescing axisymmetric turbulent plumes in a rotating fluid

Abstract

We investigate the early-time coalescence of two co-flowing axisymmetric turbulent plumes and the later-time flow of the induced vortices in a rotating, homogeneous fluid using laboratory experiments. The experiments demonstrate the critical importance of the rotation period Tf = 2π/f, where f is the Coriolis parameter of the background rotation. We find that if the plumes’ sources are sufficiently “close” for the plumes to merge initially at an “early time” tm≲tr = 3Tf/4, the experimentally observed merging height zme agrees well with the non-rotating theoretical relationship of zmt ≈ (0.44/α)x0<zr = 5.5F01/4f-3/4, where α is the entrainment “constant” of the turbulent plumes, x0 is the separation distance between the two plume sources, F0 is the source buoyancy flux of each plume, and zr is the distance that the plume rises in the time tr before rotational effects become significant. Therefore, rotation does not affect the initial time to merger or the initial merger height of such “close” plumes. For “late” times t>tr, however, the flow dynamics are substantially more complicated, as the flow becomes significantly affected by rotation. The propagation and entrainment of the plumes becomes strongly affected by the vortices induced by the entrainment flow in a rotating environment. Also, the plume fluid itself starts to interact with these vortices. If the plumes have already initially merged by the time t = tr, a single vortex (initially located at the midpoint of the line connecting the two plume sources) develops, which both advects and modifies the geometry of the merging plumes. Coupled with the various suppressing effects of rotation on the radial plume entrainment, the “apparent” observed height of merger can vary substantially from its initial value. Conversely, for more widely separated “distant” plumes, where x0>xc = (25α/2)F01/4f-3/4, the plumes do not merge before the critical time tr when rotation becomes significant in the flow dynamics and two vortices are observed, each located over a plume source. The combined effect of these vortices with the associated suppression of entrainment by rotation thus significantly further delays the merger of the two plumes, which apparently becomes possible only through the merger of the induced vortices.