Turbulence and mixing in a stratified shear flow

Stephenson, Philip; Fernando, H. J. S.

doi:10.1080/03091929108227777

Cited by 15 publications

(9 citation statements)

References 20 publications

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“…These empirical relationships are consistent with those in Strang (1997), who found u/DU 5 0.12 6 0.03 and '/h r 5 0.18 6 0.05 over a much larger range of Richardson number than presently tested. Similar relationships are reported in Narimousa et al (1986), Narimousa and Fernando (1987), Moore and Long (1971), and Stephenson and Fernando (1991). The turbulent Froude and Reynolds numbers were therefore estimated as…”

Section: Processingsupporting

confidence: 49%

“…A 5-mm-thick Plexiglas splitter plate placed just below the bottom disk prevented fluid below the disk stacks from being pumped toward the rotating disks. The splitter plate decreased turbulence significantly near the pump in previous experiments (Stephenson and Fernando 1991). The thermal isolation of the test fluid from the motor driving the pump allowed the tank to be run for long times with no significant change in the test fluid temperature (García et al 2006).…”

Section: Experiments a Mixing Facilitymentioning

confidence: 93%

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Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow

Jackson

Rehmann

2014

Journal of Physical Oceanography

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Laboratory experiments were performed to measure differential diffusion of temperature and salinity across a sheared density interface. The eddy diffusivity of temperature K T exceeded the eddy diffusivity of salinity K S by as much as 1.5 orders of magnitude at low «/nN 2 , where « is the rate of dissipation of turbulent kinetic energy, n is the kinematic viscosity, and N is the buoyancy frequency in the pycnocline. The diffusivity ratio d 5 K S /K T increased from about 0.05 to 1 over the range 0.1 , «/nN 2 , 40. These differences made the eddy diffusivity of density depend on the density ratio. The trend of d with «/nN 2 was consistent with trends found in other experiments, simulations, and theory, and the collapse of several datasets allowed the diffusivity ratio to be expressed as a function of «/nN 2 . However, shear decreased differential diffusion less in the experiments than predicted by theory for homogeneous turbulence subjected to constant shear and stratification. No strong effect of the density ratio on the diffusivity ratio was apparent. Because many flows in oceanography and limnology have values of «/nN 2 low enough to exhibit significant differential diffusion, accounting for differential diffusion in interpreting measurements and modeling stratified water bodies is recommended.

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Section: Processingsupporting

confidence: 49%

Section: Experiments a Mixing Facilitymentioning

confidence: 93%

Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow

Jackson

Rehmann

2014

Journal of Physical Oceanography

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“…l/z m increased from nearly zero just above the bottom to 0.2-0.3 at z/z m = 0.1, kept its value for 0.1 < z/z m < 0.8, and decreased to 0.1-0.2 near z/z m = 1.0 (figure 8b). This result agrees with the laboratory experiments in the stratified fluid, showing l/z m ∼ 0.2 (Stephenson & Fernando 1991).…”

Section: Turbulent Properties In the Mixed And Interfacial Layerssupporting

confidence: 92%

The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

Sakamoto

Akitomo

2009

J. Fluid Mech.

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To investigate turbulent properties and the developing mechanisms of the tidally induced bottom boundary layer in the linearly stratified ocean, numerical experiments have been executed with a non-hydrostatic three-dimensional model in the rotating frame, changing the temporal Rossby number Rot = |σ/f|, i.e. the ratio of the tidal frequency σ to the Coriolis parameter f. After the flow transitions to turbulence, the entire water column can be characterized by three layers: the mixed layer where density is homogenized and the flow is turbulent (z < zm); the stratified layer where the initial stratification remains and the flow is laminar (z > zt); and the interfacial layer between them where the flow is turbulent but the stratification remains (zm < z < zt). Turbulence is scaled by the frictional velocity uτ and the mixed-layer thickness zm (uτ and uτ/N where N is the buoyancy frequency) in the mixed (interfacial) layer, and has similarity. The mixed layer is thickened by the process where light water of the upper stratified layer is mixed with the lower unstratified layer water through the interfacial layer. As Rot approaches unity, i.e. near the critical latitude, the mixed layer develops more rapidly according to the following mechanism. As becomes Rot closer to unity, the current shear in the interfacial layer is intensified, since the difference of velocity becomes larger between the lower turbulent mixed and upper laminar stratified layers, and this leads to thickening of the interfacial layer. As a result, density deviation of the water entrained from above becomes larger, and this causes more rapid development of the mixed layer. In terms of the energy conversion from the eddy kinetic energy (EKE) to the potential energy (PE), the efficiency factor β which is the ratio of the conversion rate from EKE to PE to that from the tidal shear to EKE increased from 0.25% for Rot = 0.5 to 3.5% for Rot = 1.05 on average. When the time is normalized by the period required for the mixed layer to be thickened to the unstratified turbulent boundary layer δ = uτ/|f+σ|, the mixed layer development occurred in a similar manner in all cases. This similarity suggests the possibility of universal formulation for the turbulent tidal mixing under stratification.

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“…At this concentration, the intensity of the fluorescent light is proportional to the concentration of the dye; the attenuation of the beam intensity over the 8 cm horizontal dimension of the field of view was less than 8%, and could be easily accounted for in the data analysis. Extensive discussions on the use of fluorescent dyes for monitoring concentration, the response of dyes to light intensity at different concentrations and corrections for beam attenuation are given in Liu et al (1977), Koochesfahani (1984), Koochesfahani & Dimotakis (1986), , Papantoniou & List (1989) and Stephenson & Fernando (1991).…”

Section: Experimental Methodsmentioning

confidence: 99%

Turbulence, waves and mixing at shear-free density interfaces. Part 2. Laboratory experiments

1997

Self Cite

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A laboratory experimental study was performed to investigate turbulence, waves and mixing at a sharp density interface (with a jump in buoyancy Δb), subjected to shear-free turbulence induced by oscillating grids with typical velocity and length scales of uH and LH, respectively. The cases where turbulence is present on one side (single-sided stirring) or on both sides (double-sided stirring) of the interface were considered. Extensive flow visualization studies and quantitative measurements were performed on the motion field and mixing characteristics at the interface. It was found that, rather than any one mechanism controlling the mixing process, different mechanisms (namely engulfment, generation of waves and their breaking, eddy impingement and Kelvin–Helmholtz billows) play dominant roles over different ranges of the bulk Richardson number Ri(Ri =ΔbLH/u2H). For the Ri range where wave generation is significant, certain hypotheses and predictions of the companion paper by Fernando & Hunt (1997) were tested in detail, by flow visualization studies of the qualitative properties of interfacial motions and quantitative measurements of the r.m.s. fluctuations of interfacial velocity and displacement, the local gradient Richardson number within the stratified layer, the frequency spectra and the related fractal properties of the interface. The results are consistent with the hypothesis that, at high values of Ri(>35), the density interface consists of linear internal waves driven by turbulence at high frequencies and breaking waves with sharp horizontal gradients of density at low frequencies.

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Turbulence and mixing in a stratified shear flow

Cited by 15 publications

References 20 publications

Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow

Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow

The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

Turbulence, waves and mixing at shear-free density interfaces. Part 2. Laboratory experiments

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