Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid

Abstract

The evolution of unsheared grid-generated turbulence in a stably stratified fluid was investigated in a closed-loop salt-stratified water channel. Simultaneous single-point measurements of the horizontal and vertical velocity and density fluctuations were obtained, including turbulent mass fluxes central in understanding the energetics of the fluctuating motion. When the buoyancy lengthscale was initially substantially larger than the largest turbulent scales, the initial behaviour of the velocity and density fields was similar to that in the non-stratified case. With further downstream development, the buoyancy lengthscale decreased while the turbulence scale grew. Deviations from neutral behaviour occurred when these two lengthscales became of the same order, after the initially larger inertial forces associated with the initial kinetic energy had become weaker and buoyancy forces became important.Buoyancy forces produced anisotropy in the largest scales first, preventing them from overturning, while smaller-scale isotropic turbulent motions remained embedded within the larger-scale wave motions. These small-scale motions exhibited classical turbulent behaviour and scaled universally with Kolmogorov length and velocity scales. Eventually even the smallest scales of the decaying turbulence were affected by buoyancy, all isotropic motions disappeared, and Kolmogorov scaling failed. The turbulent vertical mass flux decreased to zero for this condition, indicating that the original turbulent field had been completely converted to random internal wave motions.The transition from a fully turbulent state to one of internal waves occurred rapidly in a time less than the characteristic time of the turbulence based on the largest-scale eddies found in the flow at transition. The dissipation rate for complete transition to a wave field was found to be of the order of εt = 24.5νN2, where ν is the kinematic viscosity and N the Brunt-Väisälä frequency. This is in fairly good agreement with the value 30νN2 predicted by Gibson (1980, 1981).The present experiments have determined quantitative limits on the range of active turbulent scales in homogeneous stratified turbulence, in terms of an upper limit near the buoyancy lengthscale and a lower limit determined by viscosity in the usual way. This description has been used here to help explain and assimilate the results from the earlier stratified grid-turbulence experiments of Lin & Veenhuizen (1975) and Dickey & Mellor (1980). While some of the features of the present observations may be qualitatively seen in the numerical simulations of the problem of Riley, Metcalfe & Weissman (1981), there are fundamental differences, probably due in part to large differences in initial lengthscale ratios and in the limited range of scales attainable in numerical simulations. The present experiments may serve as a useful test case for future modelling and interpretation of the behaviour of turbulence in stratified flows observed in the oceans and atmosphere.

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

“…They agree well, except that the parameterizations underestimate l E /l d and a from Stillinger [1981]. This is caused by the lack of G d from Stillinger [1981] in the fitting process. However, it is also likely that the data points from Stillinger [1981] …”

“…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).…”

“…This is caused by the lack of G d from Stillinger [1981] in the fitting process. However, it is also likely that the data points from Stillinger [1981] …”

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).…”