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Decay of stratified turbulent wakes behind a bluff body


The dissertation investigates buoyancy effects in turbulent bluff-body wakes that evolve in stratified fluids. The investigation utilizes high-resolution numerical simulations and employs a body-inclusive approach to describe the flow from the body into the far wake unlike the usual temporal-model approximation of most prior stratified-wake simulations. The dissertation is composed of three main parts. The first part focuses on the dynamics of vorticity that accounts for the unexpected regeneration and increase of turbulence in the near-to-intermediate wake when stratification increases in the regime of low body Froude numbers. The second part characterizes buoyancy effects on the evolution of turbulent kinetic energy in a sphere wake at moderate Froude number and an intermediate Reynolds number. The third part concerns the decay of a disk wake at relatively high Reynolds number and a wide range of Froude numbers, constitutes the major contribution of this thesis, and is summarized below.

Large-eddy simulations (LES) of flow past a disk are performed at Re = UbLb/ν = 50,000 and at Fr = Ub/NLb = ∞,50,10,2; Ub is the free-stream velocity, Lb is the disk diameter, ν is the fluid kinematic viscosity, and N is the buoyancy frequency.

In the axisymmetric wake in a homogeneous fluid, it is found that the mean streamwise velocity deficit (U0) decays in two stages; U0 ∝ x−0.9 during 10 < x/Lb < 65 followed by U0 ∝∼ x−2/3. Consequently, none of the simulated stratified wakes is able to exhibit the classical 2/3 decay exponent of U0 in the interval before buoyancy effects set in. The turbulent characteristic velocity, taken as K1/2 with K the turbulent kinetic energy (TKE), satisfies K1/2 ∝∼ x−2/3 after x/Lb ≈ 10. Turbulent wakes are affected by stratification within approximately one buoyancy time scale (Ntb ≈ 1) after which, provided that RehFrh2 ≥ 1, we find 3 regimes: weakly stratified turbulence (WST), intermediately stratified turbulence (IST), and strongly stratified turbulence (SST). The regime boundaries are delineated by the turbulent horizontal Froude number Frh = u′h/NLHk; here, u′h and LHk are r.m.s horizontal velocity and TKE- based horizontal wake width. WST begins when Frh decreases to O(1), spans 1 < Ntb < 5 and, while the mean flow is strongly affected by buoyancy in WST, turbulence is not. Thus, while the mean flow transitions into the so-called non-equilibrium (NEQ) regime, turbulence remains approximately isotropic in WST. The next stage of IST, identified by progressively increasing turbulence anisotropy, commences at N tb ≈ 5 once F rh decreases to O(0.1). During IST, the mean flow has arrived into the NEQ regime with a constant decay exponent, U0 ∝ x−0.18, but turbulence is still in transition. The exponent of 0.18 for the disk wake is smaller than the approximately 0.25 exponent found for the stratified sphere wake. When F rh decreases by another order of magnitude to F rh ∼ O(0.01), the wake transitions into the third regime of SST that is identified based on the asymptote of turbulent vertical Froude number (Frv = u′h/Nlv) to a O(1) constant. During SST that commences at Ntb ≈ 20, turbulence is strongly anisotropic (u′z ≪ u′h), and, both u′h and U0 satisfy x−0.18 decay signifying the arrival of the NEQ regime for both turbulence and mean flow. Turbulence is patchy and temporal spectra are broadband in the SST wake.

Energy budgets reveal that stratification has a direct and positive influence on the prolongation of wake life. During the WST/early-IST stage, energy budgets show that the mean buoyancy flux acts to augment the MKE before the additional augmentation by reduced turbulent production. On the other hand, during WST/early-IST, the decay of TKE is faster than the unstratified case because of negative buoyancy flux (a sink that serves to increase turbulent potential energy) and increased dissipation and, additionally, also by the reduced production. In the late-IST/early-SST stages, production is enhanced and, additionally, there is injection from turbulent potential energy so that the TKE decay slows down. Only in the SST stage, when NEQ is realized for both the mean and turbulence, the turbulent buoyancy flux becomes negative again, acting as a sink of TKE.

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