Energetics of grid turbulence in a stably stratified fluid

Abstract

A biplane grid with a mesh spacing of 10.8 cm was towed horizontally in a towing tank to generate turbulence in a non-stratified fluid and in stratified fluids with different constant density gradients. Turbulence velocity components and density fluctuations were measured using an array of cross-film and conductivity probes. Based on the mesh size of the grid, the nominal values of the (internal) Froude numbers were ∞, 80 and 40, and the corresponding Reynolds number was 4.3 × 104. The decay rates of the (turbulence) kinetic, potential and total energies and the dissipation rates of the kinetic and potential energies were calculated from the experimental data. For each of these quantities, the decay may be represented as a function of the downstream distance raised to a given power. The kinetic energy and its dissipation rate are lower for the stratified cases than for the non-stratified case but are almost compensated for by the corresponding potential energy and its dissipation rate. Our results are consistent with those of direct numerical simulations and agree reasonably well with those obtained in stratified wind and water tunnels. However, the results differ from laboratory results obtained using an optical method to measure the turbulent motion of tracer particles in the wake of a vertically towed grid; these latter results show an abrupt reduction in the decay rate of the turbulence kinetic energy after one Brunt–Väisälä period. A similar trend is also observed in results obtained in facilities with fairly high background turbulence or internal waves. This discrepancy is discussed and an explanation is presented. Furthermore, it is demonstrated that strongly stratified thin sheets with density gradients larger than that of the undisturbed fluid may be generated by local but incomplete mixing. The persistence of such thin sheets is proportional to the Schmidt number (≈ 500) in stratified salt water or the Prandtl number (≈ 0.71) in thermally stratified air.

An intercomparison study using 3-dimensional electromagnet turbulent velocity probes, a hot-film anemometer, and an airfoil probe

“…In general, spectra of all three components have similar spectral features expected from grid-generated turbulence: the energycontaining region at low wavenumbers, the inertial subrange region with a -513 slope, and a drop off in energy at high wavenumbers. Within the wavenumber range where the -513 slope is satisfied, spectra from all 3 components are similar, with u 0 slightly higher than VU and W O , consistent with the higher along-flow fluctuating velocities often observed in gridgenerated turbulence in a water-filled tank [7]. The spectral energy drops off at a wavenumber of about 2 cm-', independent of the mean flow speed.…”

Grid Turbulence Measurements with an Acoustic Doppler Current Profiler

“…Ref. [26] obtained the same power law and coefficient m in a water tank, where the towing speed U was the equivalent to the fluid speed.…”

“…The ADCP was mounted with the transducers submerged a couple of centimeters below the surface with the horizontal components of b 1 − b 4 pointing in the x, y, −x and −y-direction, respectively, and b 5 pointing downwards. The ADV beams were aligned with the tank axes and the measurement volume was located at z = −0.5 m. The carriage was accelerated at 0.5 m/s 2 until a constant towing speed of U = 0.2 or 0.4 m/s (also used in [26]) was reached, which yielded a mesh Reynolds number Re M = MU/ν [23], where ν = 10 −6 m 2 s −1 is the kinematic viscosity of water, in the range 20,000-100,000. The mean and start/stop movement of the grid set up a seiche motion in the tank that was damped out after a couple of minutes.…”

“…The present study is an extension of the previous work where the ability of an ADCP to measure grid-generated turbulence properties is investigated and comparisons are made with a Nortek Vectrino ADV. Grid-induced turbulence is a phenomenon that has been studied in wind tunnels [19][20][21][22][23][24][25], as well as in water tanks and flumes [26,27]. In wind tunnels and water flumes, the grid is fixed in space and the fluid flows past it.…”

“…In wind tunnels and water flumes, the grid is fixed in space and the fluid flows past it. In water tanks, the grid and instruments are usually towed along the longitudinal direction of the tank, which puts a constraint on the duration of each repetition [26]. Most studies related to grid-induced turbulence focus on the decay of turbulent properties, such as velocity variance and TKE, as function of the normalized downstream distance to the grid x/M, where x is the downstream distance and M is the mesh size.…”