Non-equilibrium turbulence generated by a fractal grid in density-stratified fluids

Turbulence generated by a towed space-filling square fractal grid was investigated in non-stratified, linearly stratified, and two-layer stratified fluids. Six cases were considered, with initial Reynolds numbers ReL0=U0L0/ν of 43 200 and 54 700. For the stratified cases, initial Froude numbers FrL0=U0/(NL0) ranged from 0.93 to 2.36, where U0, L0, N, and ν denote the initial characteristic velocity, the largest mesh size, buoyancy frequency, and kinematic viscosity, respectively. Velocity fields are measured using a two-dimensional, two-component particle image velocimetry system. Under stratification, the horizontal kinetic energy decays faster than in the non-stratified case. Dissipation reconstructed from the two planes, and the resulting Cε=εLu/urms3 (ε: total dissipation rate; Lu: longitudinal integral length scale; and urms: the root-mean-square (r.m.s.) streamwise velocity fluctuations) displays trends consistent with non-equilibrium behavior. The transition from non-stratified to weakly stratified turbulence, identified by the Froude number FrH=urms/NLu and the Reynolds number ReH=urmsLu/ν, occurs near the onset of Lu growth. The energy spectra initially exhibit a clear k−5/3 inertial range and only later steepen toward a −2 slope, indicating a delayed transition to quasi-two-dimensional turbulence. The coupled roles of different initial conditions and stratification in non-equilibrium dissipation mechanism are discussed.