Micro-scale instability in a continuously stratified fluid

Experimental observations of small-scale structures caused by flow instabilities at layers of high density gradient in the wake behind a cylinder in a fluid with a continuous salt concentration stratification are reported. In the density wake it is possible to discern a number of structures such as wedge-like structures or cusps; small-scale instabilities (breakers) in the zones of interaction of attached internal waves and the high-gradient wake envelope; small-scale instability of the density boundary layer with a complicated density gradient pattern superimposed on a smooth velocity profile, and small-scale wake structures behind attached vortices in the case of a closed (central) wake envelope.Translated from Izvestiya RossiiskoiAkademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–10, May–June, 1995.     

Features of the dynamics of hydrothermodynamic perturbations in a stably stratified fluid

The evolution of a certain class of arbitrary-amplitude perturbations in a stratified binary mixture is investigated analytically and numerically. The radical differences between the process in question and the process of hydrostatic adaptation in an ordinary single-component medium are demonstrated. In particular, a long-life “wake“ with nonzero temperature and admixture concentration perturbations that compensate one another in the density field may be formed when the process is completed. The slow process of dissipation of this wake, associated with heat and mass transfer, is investigated.     

Associated disturbances around a vortex ring in a stratified fluid

A motion of a vortex ring in a stratified fluid is accompanied by associated disturbances which, in the schlieren visualization in the field of a horizontal density gradient, have the shape of a symmetric four-petal configuration. The criterion of the existence of the disturbances is the Froude number Fr based on the motion velocity and the vertical vortex size. On the range Fr > 1, the disturbances are stable with respect to the variation of themotion regime and the distortion of the vortex shape. For Fr < 1 the disturbances disappear. Computer processing of the schlieren photographs showed that the experimental spatial dependences of the disturbance amplitude are close to the functions describing the distribution of the vertical velocity component in the inviscid flow past a sphere.     

Coherent motion of turbulent thermal plume in stably stratified fluid

The purpose of this study is to clarify the existence of an ordered and large scale coherent motion in a turbulent plane thermal plume in a thermally-stable stratified fluid inside a comparatively large enclosure. First, the upper part of the thermal plume was carefully observed by a flow visualization. Secondly, a wave form of plume temperature variation was measured. Thirdly, a spectrum analysis was carried out on time series data of the thermal plume. Finally, physical characteristics were investigated on vortices in the thermal plume based on results of the wave form and the spectrum analysis of the plume temperature. As a result, the main conclusions are obtained as follows. (1) An existence of vortices near the upper part of the thermal plume was firstly found by careful flow visualization. (2) From the wave form of temperature variation and the spectrum analysis of the thermal plume, it was clarified that the vortices are generated in the transition state and are transported to the turbulent state. (3) The vortices are ordered and they behave as a large scale coherent motion in the turbulent thermal plume.     

Suppression of forced and convective flows of a stably stratified fluid in vertical channels

In order to improve certain technological processes, for example, single-crystal growing, it is desirable to be able to control the flow rate in order to influence the heat and mass transfer processes. For this purpose it is usual to employ rotation, an electromagnetic field or reduced gravity [1]. Here, with reference to simple solutions of the system of equations of free convection in infinite vertical channels, it is shown that the problem of reducing the intensity of the flow can be solved given a suitable relation between the degree of stable stratification (with respect to density) and the factors responsible for the flow. The possibility of using temperature stratification is considered, but all the conclusions are also fully applicable to concentration stratification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 172–174, March–April, 1987.The authors wish to thank B. Ya. Martuzan for his useful comments and interest in the work.     

Experimental study of the initial growth of a localized turbulent patch in a stably stratified fluid

We present a laboratory experiment of the initial growth of a turbulent patch in a stably stratified fluid. The patch is created due to a localized source of turbulence, generated by a horizontally oriented and vertically oscillating grid much smaller than the tank size and far from solid boundaries. Synchronized and overlapping particle image velocimetry(PIV) and planar laser induced fluorescence (PLIF) measurements capture the evolution of the patch through its initial growth until it reached a maximum size. The simultaneous measurements of density and velocity fields allow for a direct quantification of the distribution of kinetic energy, buoyancy and degree of mixing within the patch. We can also relate the propagation speed of the turbulent/non-turbulent interface and its thickness to the properties of the turbulent fluid inside the evolving patch. The velocity measurements in this setup indicate significant transient effects inside the patch during its growth. A local analysis of the turbulent/non-turbulent interface provides direct measurements of the entrainment velocity w_e as compared to the local vertical velocity and turbulent intensity at the proximity of the interface. The detailed information about the growth of localized sources of turbulence in stratified environment might be of use in stealth design of autonomous underwater vehicles.     

A multiple-source wind tunnel design for producing turbulent shear flows in a stably stratified fluid

The design and construction of a thermally stratified, multiple source wind tunnel for producing linear vertical temperature and velocity profiles is discussed. The tunnel utilizes 10 initially independent layers to produce continuous velocity and temperature profiles for which the turbulence in nominally homogeneous in the lateral direction. The tunnel is capable of producing uniform vertical velocity shears of up to 5 s^-1 and vertical temperature gradients of up to 200 °C/m. This stably stratified, uniform mean shear grid turbulence was found by means of a flow mapping to depart from homogeneity by roughly ±15% in the test section.also Scripps Institution of Oceanography, La Jolla, CA92093, USAThis work was supported by NSF Grant OCE92-17213 and ONR Grant N00014-94-0233. The authors would like to thank Dr. Michael Head of Precision Measurement Engineering and Jack Yampolsky for their crucial contributions to the design and construction of this facility.     

Experimental and numerical investigation of the dynamics of uniform turbulence of a stably stratified fluid

The results of experimental and numerical studies of the dynamics of the parameters of uniform turbulence of a stably stratified fluid for different molecular Prandtl-Schmidt numbers over a wide range of buoyancy times Nτ are given. The tank, the measurement apparatus used, and the experimental procedure are briefly described. The numerical modeling used a second-order model of uniform turbulence of a stratified medium. The influence of fluctuations of the turbulent mass (heat) flux q(Nτ) on the evolution of the statistical parameters of the velocity and temperature fields is analyzed, and an invariant equation is found for the parameters of the strong turbulence of the stratified fluid. It is shown that the statistical parameters of the turbulence, being smoothed with respect to the amplitude of the fluctuations, vary self-similarly with time after the collapse point. Donetsk State University, Donetsk 340055.¹Institute of Heat and Mas Transfer, National Academy of Sciences of Belarusia, Minsk 220072. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 64–75, July–August, 1998.     

Vortex collapse and turbulence

Recent calculations related to the self-induced collapse of large-scale vortex structures into fine scale, possibly singular, structures in the Euler and Navier–Stokes equations are described. The practical importance of these intense events is their possible role in turbulence through the effects of strong intermittency and how that will direct turbulence modelling. Despite a concerted international effort to simulate these events over a decade ago, their dynamical origin remains largely unknown. A new international collaboration designed to push our understanding of the Euler singularity problem is described. These events are closely related to one of the outstanding mathematical questions of our time: whether solutions of the three-dimensional incompressible Navier–Stokes equations, lying in a bounded domain with finite energy and no external forcing, remain regular for arbitrarily long times (www.claymath.org/Millennium_Prize_Problems).     

Shear instability of flows of a stratified ideal fluid of finite depth

A linear analysis is made of the stability of flows, stratified with respect to depth, of an ideal liquid of finite depth with a Helmholtz velocity profile. Apart from a Kelvin-Helmholtz wave, additional unstable modes are also discovered. Analytical expressions are obtained for the neutral curve of these modes. Their nature is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–179, November–December, 1988.The author is grateful to V. I. Klyatskin and L. Ya. Lyubavin for their interest in the study and for fruitful discussions.     

Vortex motions in stratified wake flows

The vortex wakes of obstacles (circular cylinder and sphere) moving through a linearly stratified fluid have been investigated, by means of flow visualization, at Reynolds numbers smaller than 800 and non-dimensional buoyancy frequencies smaller than 6. Vortex shedding from a horizontally suspended circular cylinder is suppressed when the fluid is stratified. The wake of a sphere is affected by lee waves when the Reynolds number exceeds about 200.     

Vortex systems in the stratified wake of a sphere

The fine structure of the flow and the characteristics of the principal types of vortex structures in the wake of a sphere moving uniformly and horizontally in an exponentially stratified fluid have been experimentally investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–90, July–August, 1991.The authors are grateful to G. Yu. Stepanov for his careful analysis of the first version of this article and his valuable comments.     

Kinematic simulation for stably stratified and rotating turbulence

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory (RDT) to a kinematic simulation (KS) of the Boussinesq equation with a Coriolis term.Scalings for one- and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.     

Wave/vortex decompositions in stably stratified flows

The slowly evolving vortex part of stably stratified flows, both homogeneous and of shear-layer type, is extracted using a diagnostic decomposition of the velocity field based upon the potential vorticity. Comparisons with a decomposition theoretically valid for the linear regime are also made. For the homogeneous flows considered here, the vortex part apparently strongly interacts with the wave field, whatever the decomposition in use. A numerical wave filtering process is applied to simulate the flow dynamics driven by the vortex part only. The resulting vortex flow is the same for each decomposition. In the shear layers, by contrast, only the decomposition based upon the potential vorticity is able to extract the vortex part of the flow, whether the shear layer is moderately or strongly stratified. We propose an argument to account for the fact that a highly energetic vortex part is more likely to be found in a strongly stratified shear layer.This work has been supported by EDF (Direction des Etudes et Recherches, Laboratoire National d'Hydraulique) under Contract No. 2J6773.     

Mixing in a stably stratified shear layer: two- and three-dimensional numerical experiments

A direct method for analyzing diapycnal mixing in a stably stratified fluid (Winters et al., 1995) has been applied to the stably stratified shear layer. The diapycnal flux and mixing efficiency are computed as functions of time, whatever the turbulent activity in the fluid. The mixing properties of two- and three-dimensional numerical simulations of the Boussinesq equations are analyzed and compared. The interest of the former simulations is to emphasize the fundamental role of three-dimensional effects in fluid mixing and to quantify it. We focus on the influence of stratification (measured by the minimum Richardson number J) and changes in Prandtl number on the overall mixing that occurs as the computed flows evolve from unstable initial conditions.

In three dimensions, the flow dynamics exhibit three successive stages, each with different mixing properties. During the first stage, a primarily two-dimensional Kelvin–Helmholtz instability develops and the mixing efficiency is high (the flux Richardson number Rf_b ranges between 0.37 and 0.68, decreasing as J increases). The second stage is characterized by the development of small-scale three-dimensional instabilities. These motions result in significantly higher diapycnal flux than during the first stage but in only moderate mixing efficiency (Rf_b0.32), as the rate of kinetic energy dissipation is also high during this stage. Finally, the turbulent activity is progressively expulsed toward the outer regions of the shear layer and decays in time while the central region relaminarizes. During this final stage, Rf_b approaches an asymptotic value close to 0.25 and the diapycnal diffusivity displays a clear functional dependence on a gradient Richardson number Ri_b of the form Ri_b⁻².

As expected, the two-dimensional flows are unable to reproduce the mixing properties of the flow, except during the first stage. During the subsequent turbulent regime, both the diapycnal flux and the dissipation rate of kinetic energy are too small (because, for the latter quantity, of the nonlinear enstrophy conservation constraint). The final stage consists in a quasi-stationary weakly turbulent regime, for which the diapycnal diffusivity behaves as Ri_b⁻¹. It should be noted that, despite these differences, Rf_b relaxes toward the 0.25 value found in three dimensions.     

Vortex shedding from a ring in shear flow

Vortex shedding from a bluff ring in a linear shear flow has been investigated experimentally. The shedding frequency, measured using a hot wire in various positions within the near wake of the ring, was found to be remarkably insensitive to a mean flow shear parameter, , defined by (d/U _o).U/y, where d is the mean ring diameter and U _o is the undisturbed upstream velocity on the ring axis; even for = 0.41, corresponding to a velocity variation of about ±24% across the outer ring diameter, the Strouhal number was only about 5% lower than in uniform flow. However, the strong axisymmetric shedding which dominates the flow for = 0 is significantly affected by shear. Indeed, spatial correlation measurements demonstrated that the shedding actually becomes anti-symmetric at the highest values of . The implication of these results is that vortex flowmeters constructed using a ring as the shedding body would be relatively unaffected by changes in the upstream mean flow profile.