Decay of turbulent wakes behind a disk in homogeneous and stratified fluids

Body-inclusive large-eddy simulations of disk wakes are performed for a homogeneous fluid and for different levels of stratification. The Reynolds number is 5 104 and the Froude number (Fr) takes the values of 1, 50, 10 and 2. In the axisymmetric wake of a disk with diameter Lb 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 and, subsequently, 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. Stratification affects the wake within approximately one buoyancy time scale, after which, we find three regimes: weakly stratified turbulence (WST), intermediately stratified turbulence (IST) and strongly stratified turbulence (SST). WST begins when the turbulent Froude number (Frh) decreases to O.1 /, spans 1. Ntb. 5 and, while the mean flow is strongly affected by buoyancy in WST, turbulence is not. During IST, which commences at Ntb 5 when Frh D O.0 :1 /, the mean flow has arrived into the non-equilibrium (NEQ) regime with U0 / x 0 :18, but the turbulence state is still in transition, as indicated by progressively increasing turbulence anisotropy. When Frh O.0 :01 / at Ntb 20, the wake transitions into SST, where the turbulent vertical Froude number (Fr v) asymptotes to a O.1 / constant. There is strong anisotropy (u 0 z u 0h), and both u 0 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. The wake height decreases as LV O.U0 =N / in IST/SST. Energy budgets reveal that stratification prolongs wake life during WST/early-IST by both an energy transfer from mean potential energy to mean kinetic energy and reduction of turbulent production. In the late-IST/early-SST stages, production is enhanced and, additionally, there is injection from turbulent potential energy slowing down turbulent kinetic energy (TKE) decay. Only in the SST stage, when NEQ is realized for both the mean and turbulence, does the turbulent buoyancy flux become negative again, acting as a sink of TKE.