Caulfield C. P.

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Caulfield
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C. P.
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  • Preprint
    Laboratory experiments on two coalescing axisymmetric turbulent plumes in a rotating fluid
    ( 2011-04-07) Yamamoto, H. ; Cenedese, Claudia ; Caulfield, C. P.
    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)x0tr, 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.
  • Preprint
    Entrainment and mixed layer dynamics of a surface-stress-driven stratiified fluid
    ( 2014-12) Manucharyan, Georgy E. ; Caulfield, C. P.
    We consider experimentally an initially quiescent and linearly stratified fluid with buoyancy frequency NQ in a cylinder subject to surface-stress forcing from a disc of radius R spinning at a constant angular velocity Ω. We observe the growth of the disc-adjacent turbulent mixed layer bounded by a sharp primary interface with a constant characteristic thickness lI. To a good approximation the depth of the forced mixed layer scales as hF/R∼(NQ/Ω)−2/3(Ωt)2/9. Generalising the previous arguments and observations of Shravat, Cenedese & Caulfield. (2012), we show that such a deepening rate is consistent with three central assumptions that allow us to develop a phenomenological energy balance model for the entrainment dynamics. First, the total kinetic energy of the deepening mixed layer EKF∝hFu2F, where uF is a characteristic velocity scale of the turbulent motions within the forced layer, is essentially independent of time and the buoyancy frequency NQ. Second, the scaled entrainment parameter E=h˙F/uF depends only on the local interfacial Richardson number RiI=(N2QhFlI)/(2u2F). Third, the potential energy increase (due to entrainment, mixing and homogenisation throughout the deepening mixed layer) is driven by the local energy input at the interface, and hence is proportional to the third power of the characteristic velocity uF. We establish that internal consistency between these assumptions implies that the rate of increase of the potential energy (and hence the local mass flux across the primary interface) decreases with RiI. This observation suggests, as originally argued by Phillips (1972), that the mixing in the vicinity of the primary interface leads to the spontaneous appearance of secondary partially mixed layers, and we observe experimentally such secondary layers below the primary interface.
  • Article
    The relationship between flux coefficient and entrainment ratio in density currents
    (American Meteorological Society, 2010-12) Wells, Mathew ; Cenedese, Claudia ; Caulfield, C. P.
    The authors explore the theoretical and empirical relationship between the nonlocal quantities of the entrainment ratio E, the appropriately depth- and time-averaged flux coefficient Γ, and the bulk Froude number Fro in density currents. The main theoretical result is that E = 0.125 Γ Fro2(CU3/CL)/cosθ, where θ is the angle of the slope over which the density current flows, CL is the ratio the turbulent length scale to the depth of the density current, and CU is the ratio of the turbulent velocity scale to the mean velocity of the density current. In the case of high bulk Froude numbers Γ Fro−2 and (CU3/CL) = Cϵ 1, so E 0.1, consistent with observations of a constant entrainment ratio in unstratified jets and weakly stratified plumes. For bulk Froude numbers close to one, Γ is constant and has a value in the range of 0.1–0.3, which means that E Fro2, again in agreement with observations and previous experiments. For bulk Froude numbers less than one, Γ decreases rapidly with bulk Froude number, explaining the sudden decrease in entrainment ratios that has been observed in all field and experimental observations.