Spatially decaying turbulence and its relation to mixing across density interfaces

Abstract

The turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally. Measurements were carried out in a homogeneous layer of fluid as well as a two-layered fluid, which permitted us to determine the decay law of this turbulence and the way in which the structure of the turbulence depends on the mesh size and on the frequency and amplitude of the grid oscillation. It was found that the turbulent kinetic energy decays with distance from the grid according to a power law$\overline{q^2}\propto z^{-n}$, withnclose to 2, and that the turbulent Reynolds number remains approximately constant during decay. The linear dependence of the r.m.s. turbulent velocity on the grid oscillation frequency found by Thompson & Turner (1975) in the case of a square-bar grid has been confirmed. It is shown here that this linear relation remains valid when an interface is present and consequently the dependence of the entrainment velocity on the local Richardson number is of the form$u_e/u \propto Ri^{-\frac{3}{2}}$, the Péclet number being high. While the bearing of these results on the problem of the thermocline or an inversion is clear we wish to emphasize that the spatial decay of turbulence is interesting in itself.

Effect of background turbulence on an axisymmetric turbulent jet

“…In the homogeneous region, the RMS velocities in the downstream and transverse directions decay as power law with distance from the grid with the exponents of -1. Consequently the turbulent kinetic energy power law decay exponent is -2 (Hopfinger and Toly, 1976). The ratio of vertical to horizontal RMS velocities, have been measured to be in the range 1.1-1.2 (De Silva and Fernando, 1994).…”

“…The results in Table 5.2 indicate that the flow is close to being isotropic at the measurement locations (especially in the transverse plane), though not perfectly isotropic. The flow generated by oscillating grids is typically characterized by anisotropy ratios between 1.1 and 1.2 (Hopfinger and Toly, 1976).…”

Evaluation of oscillating grids and orbital shakers as means to generate isotropic and homogeneous small‐scale turbulence in laboratory enclosures commonly used in plankton studies

“…There are different ways to overcome this problem. For example, the probe can be moved at a large and constant velocity to have a significant relative mean flow (e.g., Thompson andTurner 1975, Hopfinger andToly 1976). In this study, we used the linear regression method developed by Stiansen and Sundby (2001), which is based on the inertial-advective subrange theory from Tennekes (1975).…”

“…Couette cylinders are used as viscosimeters and for the study of particle aggregation under shear flow (e.g., Serra et al 1997). Oscillating grids, a favorite of fluid dynamics experiments, have been extensively used in the study of sediment dynamics and mixing in stratified fluids (e.g., Rouse and Dodu 1955, Thompson and Turner 1975, Hopfinger and Toly 1976. To try to meet ecologically realistic conditions, these devices are often used in biological experiments using settings outside the ranges defined in their original application without a previous examination of hydrodynamics.…”

The length scale equation in turbulence models

“…Turbulence generated by an oscillating grid has been studied extensively in the laboratory both in neutrally and stably stratified fluids by turbulence researchers (Thompson and Turner, 1975;Hopfinger and Toly, 1976;Turner, 1981;E and Hopfinger, 1986;Nokes, 1988;Hannoun et al, 1988). These experiments provide considerable empirical knowledge on the behavior of turbulence in a particularly unique situation, when the only source of turbulence in regions far away from the grid is the turbulent diffusion.…”