Vertical structure in stratified wakes with high initial Froude number

Abstract

Initially turbulent bluff body wakes decay in the presence of a stable background density gradient to form chains of comparatively stable and long-lived vortex structures, most of the late-time properties of which have been shown to be independent of the initial generating Froude number (for a sphere of diameter, D, moving at speed, U, F = 2U/ND, where N is the buoyancy frequency). Results of experiments with vertical interrogation planes are described, where any anticipated F-dependence might be most evident, as the competing effects of horizontal inertial forcing and the restoring buoyancy force can be measured directly by simultaneous measurement of horizontal and vertical velocity components. Experiments were conducted at sufficiently large values of Re [ges ] 3 × 103 and F [ges ] 4 that turbulence can occur over many scales in the near wake, and the scaling properties might then extrapolate to ocean engineering applications.When F [ges ] 4, the fluid motions in the intermediate, non-equilibrium régime always occur in coherent patches whose vertical extent is smaller than the total wake height. The patches of vorticity have longer horizontal than vertical coherence lengths, and may be termed layers, even though they are far from uniform in the horizontal. The degree to which the complex vertical structure is later dominated by the mean wake defect depends strongly on F.The total wake height, LV, depends on the initial value of F so that LV/D ∼ F0.6. LV is established early and remains almost unchanged up to Nt ≈ 30. At later times, the non-equilibrium wake exchanges potential with kinetic energy and re-adjusts according to local dynamical constraints, so that, within each layer, the quasi-two-dimensional flow proceeds without any further dependence on, or memory of, the initial value of F. The flow is everywhere stable to overturning Kelvin–Helmholtz instabilities and local length and velocity scales evolve so that the local horizontal and vertical Froude numbers, FH, FV, are both of order 0.1.Although Osmidov-length arguments for vertical scale selection appear to be physically appropriate, they do not correctly predict the measured F-dependence in either LV, or in the layer height, lV. Thus the physical mechanism responsible remains elusive, as the alternative laminar instability mechanisms are not presented with the appropriate, scale-free initial conditions over the parameter range in which they have been shown to operate.Ultimately, the measurements support the application of low FH and FV scaling theories to the late wake flow. The preceding non-equilibrium stage, when the vertical structure of the late wake is determined, does not yield so readily to assumptions involving the smallness of the vertical velocity component.