The evolution of grid-generated turbulence in a stably stratified fluid

Abstract

The spatial decay and structural evolution of grid-generated turbulence under the effect of buoyancy was studied in a ten-layer, salt-stratified water channel. The various density gradients were chosen such that the initial overturning turbulent scale was slightly smaller than any of the respective buoyancy scales. The observed general evolution of the flow from homogeneous turbulence to a composite of fossil turbulence or quasi-two-dimensional turbulence and internal wavefield is in good agreement with the predictions of Gibson (1980) and the lengthscale model of Stillinger, Helland & Van Atta (1983). The effect of the initial size of the turbulent lengthscale compared with the buoyancy scale on the decay and evolution of the turbulence is investigated and the observed influence on the rate of decay of both longitudinal and vertical velocity fluctuations pointed out by Van Atta, Helland & Itsweire (1984) is shown to be related to the magnitude of the initial internal wavefield at the grid. An attempt is made to remove the wave-component kinetic energy from the vertical-velocity-fluctuation data of Stillinger, Helland & Van Atta (1983) in order to obtain the true decay of the turbulent fluctuations. The evolution of the resulting fluctuations is similar to that of the present large-grid data and several towed-grid experiments. The rate of destruction of the density fluctuations (active-scalar dissipation rate) is estimated from the evolution equation for the potential energy, and the deduced Cox numbers are compared with those obtained from oceanic microstructure measurements. The classical Kolmogorov and Batchelor scalings appear to collapse the velocity and density spectra better than the buoyancy scaling proposed by Gargett, Osborn & Nasmyth (1984). The rise of the velocity spectra at low wavenumbers found by Stillinger, Helland & Van Atta (1983) is shown to be related to internal waves.

Turbulent energy production and entrainment at a highly stratified estuarine front

“…Shaded region defines extent of data compiled by Barry et al [2001b, Figure 7] representing the results of laboratory experiments using grid-generated turbulence. Data represented by the shaded region are drawn from Stillenger et al [1983], Rohr [1985], Itsweire et al [1987], and Barry et al [2001b]. entrainment velocity on the order of 1 to 4 Â 10 À3 m s À1 .…”

Parameterizing individual effects of shear and stratification on mixing in stably stratified shear flows

“…First, it is known that l E /l d = l E ɛ/q 3 is approximately constant for active turbulence that is only weakly affected by stratification [Ivey and Imberger, 1991;Schumann and Gerz, 1995], and (10) implies a ∝ Fr d À2 for low Fr d À1 . Second, in stratified turbulence, l E is commonly considered to grow up to l O (within a factor of O (1)) from laboratory experiments [Stillinger et al, 1983;Itsweire et al, 1986;Rohr et al, 1988b] and numerical experiments [Smyth et al, 2001;Shih et al, 2005]. However, the data analyzed in this study suggests that l E grows up to l B (shown later).…”

“…For DNS experiments, nondimensional parameters are calculated and then averaged in time. For water channel experiments, only data points that satisfy the minimum ɛ/(nN 2 ) criteria used by Itsweire et al [1986] and Ivey and Imberger [1991] are retained. For wind tunnel experiments by Lienhard and van Atta [1990], data points corresponding to the 'stratification overshoot' are excluded.…”

The length scale equation in turbulence models

“…Clearly this ratio cannot exceed unity, since the frequency of internal waves is bounded by the buoyancy frequency. In practice, the turbulence frequency does not drop below about twice the buoyancy frequency, or equivalently the turbulence length scale does not exceed 1.4 times the Ozmidov length scale according to the observations of Stillinger et al (1983) and Itsweire et al (1986). Therefore, <1.4L O , where L O =(ε/N 3 ) 1/2 is the Ozmidov scale.…”

“…There exist a suite of experiments on the decay of gridgenerated turbulence in stably stratified fluids, starting from the pioneering experiments of Dickey and Mellor (1980), that show that there is an upper bound on the parameter τ =N /q, beyond which the decay of turbulence changes due to more efficient conversion of TKE into internal wave energy (Stillinger, Helland and Van Atta, 1983;Itsweire, Helland and Van Atta, 1986; see also Hopfinger, 1987;Browand, Guyomar and Yoon, 1987;and Rohr and Van Atta, 1987).…”