Energetic Turbulence Research Articles

Observations of Turbulence in a Partially Stratified Estuary

The authors present a field study of estuarine turbulence in which profiles of Reynolds stresses were directly measured using an ADCP throughout a 25-h tidal day. The dataset that is discussed quantifies turbulent mixing for a water column in northern San Francisco Bay that experiences a sequence of states that includes a weak ebb and flood that are stratified, followed by a strong, and eventually unstratified, ebb and flood. These measurements show that energetic turbulence is confined to a bottom mixed layer by the overlying stratification. Examination of individual Reynolds stress profiles along with profiles of Richardson number and turbulent Froude number shows that the water column can be divided into regions based on the relative importance of buoyancy effects. Using the measured turbulence production rate P, the dissipation rate ϵ is estimated. The observed turbulence had values of ϵ/νN2 > 20 all of the time and ϵ/νN2 > 200 most of the time, suggesting that the observed motions were buoyancy affected turbulence rather than internal waves. However, at times, turbulent Froude numbers in much of the upper-water column were less than one, indicating important stratification effects. Taken as a whole, the data show that stratification affects the turbulent velocity variance q2 most severely; that is, observed reductions in u′w′ are largely associated with small values of q2 rather than with a dramatic reduction in the efficiency with which turbulent motions produce momentum fluxes. Finally, the dataset is compared to predictions made using the popular Mellor–Yamada level 2.5 closure. These comparisons show that the model tends to underestimate the turbulent kinetic energy in regions of strong stratification where the turbulence is strongly inhomogeneous and to overestimate the turbulent kinetic energy in weakly stratified regions. The length scale does not appear to compensate for these errors, and, as a result, similar errors are seen in the eddy viscosity predictions. It is hypothesized that the underestimation of q2 is due to an inaccurate parameterization of turbulence self-transport from the near-bed region to the overlying stratification.

Determination of 3-D Flow Fields in Agitated Vessels by Laser-Doppler Velocimetry: Use and Interpretation of RMS Velocities

Laser Doppler velocimetry measurements have been used to calculate the hydraulic and energetic efficiency and turbulence structure for three agitators, a Rushton turbine and two axial agitators: a Mixel TT and a Lightnin A310. The Mixel TT had the highest efficiencies, while in a viscous liquid (1% CMC solution) all three had comparably low efficiencies. Energy was dissipated mainly in the stream flowing out of the impeller region and in the main circulation loop. The turbulence length scale was estimated to be of the order of D/5 for the turbulent flow regime and of D/20 for the transitional flow regime. The mean and rms velocities were used to calculate the switching probability, used to simulate stochastically the flow in agitated vessels.

Energetics of grid turbulence in a stably stratified fluid

A biplane grid with a mesh spacing of 10.8 cm was towed horizontally in a towing tank to generate turbulence in a non-stratified fluid and in stratified fluids with different constant density gradients. Turbulence velocity components and density fluctuations were measured using an array of cross-film and conductivity probes. Based on the mesh size of the grid, the nominal values of the (internal) Froude numbers were ∞, 80 and 40, and the corresponding Reynolds number was 4.3 × 104. The decay rates of the (turbulence) kinetic, potential and total energies and the dissipation rates of the kinetic and potential energies were calculated from the experimental data. For each of these quantities, the decay may be represented as a function of the downstream distance raised to a given power. The kinetic energy and its dissipation rate are lower for the stratified cases than for the non-stratified case but are almost compensated for by the corresponding potential energy and its dissipation rate. Our results are consistent with those of direct numerical simulations and agree reasonably well with those obtained in stratified wind and water tunnels. However, the results differ from laboratory results obtained using an optical method to measure the turbulent motion of tracer particles in the wake of a vertically towed grid; these latter results show an abrupt reduction in the decay rate of the turbulence kinetic energy after one Brunt–Vaisala period. A similar trend is also observed in results obtained in facilities with fairly high background turbulence or internal waves. This discrepancy is discussed and an explanation is presented. Furthermore, it is demonstrated that strongly stratified thin sheets with density gradients larger than that of the undisturbed fluid may be generated by local but incomplete mixing. The persistence of such thin sheets is proportional to the Schmidt number (≈ 500) in stratified salt water or the Prandtl number (≈ 0.71) in thermally stratified air.

Phase averaged velocity field in an axisymmetric jet subject to a sudden velocity decrease

An unsteady transient axisymmetric turbulent jet was studied experimentally. The initial flow perturbation consisted of a sudden and large decrease in the ejection velocity. The temporal evolution of the mean and fluctuating unsteady velocity field was measured by using X hot-wire probes. In the jet far field, adaptation of the externally imposed unsteadiness to the local jet time scale is confirmed quantitatively. The main features of the phase averaged velocity field are presented and comments are made about the instantaneous state of the turbulence energetics. Transient mean radial velocities are deduced and an important increase of the instantaneous rate of entraining external fluid into the jet is found. Finally, we show that the pressure effect due to radial impusle terms plays an important role in the propagation of the mean perturbation. The longitudinal adaptation of the perturbation time scale driven by the local jet time scale provides a turbulent flow that is intermediate to quasi-static flows and rapidly distorted flows.

Turbulence Effects on the Vaporization of Monocomponent Single Droplets

Abstract An experimental facility has been developed to study the effects of turbulence on droplet vaporization. The facility allows lo generate a zero mean velocity, isotropic and homogeneous turbulence and to vary systematically the turbulence kinetic energy. The influence of turbulence on suspended single droplets of five n-alkane hydrocarbons is investigated, by determining the average vaporization rates by image analysis techniques. The experiments have been conducted under normal pressure and temperature conditions; for all cases, the length scales of energetic turbulence eddies are larger than the initial droplet diameter. For all the investigated cases, it is found that the presence of turbulent velocity fluctuations increases the average vaporization rates compared to the stagnant case. The linear regression rate of the projected droplet surface area versus time is observed under all turbulence conditions. It is observed that droplets of the five investigated fuels respond differently to the same...

Energetics of grid turbulence in a stably stratified fluid

A biplane grid with a mesh spacing of 10.8 cm was towed horizontally in a towing tank to generate turbulence in a non-stratified fluid and in stratified fluids with different constant density gradients. Turbulence velocity components and density fluctuations were measured using an array of cross-film and conductivity probes. Based on the mesh size of the grid, the nominal values of the (internal) Froude numbers were ∞, 80 and 40, and the corresponding Reynolds number was 4.3 × 104. The decay rates of the (turbulence) kinetic, potential and total energies and the dissipation rates of the kinetic and potential energies were calculated from the experimental data. For each of these quantities, the decay may be represented as a function of the downstream distance raised to a given power. The kinetic energy and its dissipation rate are lower for the stratified cases than for the non-stratified case but are almost compensated for by the corresponding potential energy and its dissipation rate. Our results are consistent with those of direct numerical simulations and agree reasonably well with those obtained in stratified wind and water tunnels. However, the results differ from laboratory results obtained using an optical method to measure the turbulent motion of tracer particles in the wake of a vertically towed grid; these latter results show an abrupt reduction in the decay rate of the turbulence kinetic energy after one Brunt–Väisälä period. A similar trend is also observed in results obtained in facilities with fairly high background turbulence or internal waves. This discrepancy is discussed and an explanation is presented. Furthermore, it is demonstrated that strongly stratified thin sheets with density gradients larger than that of the undisturbed fluid may be generated by local but incomplete mixing. The persistence of such thin sheets is proportional to the Schmidt number (≈ 500) in stratified salt water or the Prandtl number (≈ 0.71) in thermally stratified air.

Turbulent mixing and transport in a thermally stratified interfacial layer in decaying grid turbulence

A stably stratified mixing layer, sandwiched in between regions of neutral turbulence, was studied in decaying grid turbulence. The layer, which was shearless, was formed by heating the upper half of the flow by means of elements placed at the entrance to the plenum of a large, open circuit low speed wind tunnel 0.91×0.91 m2 in cross section and 9.14 m in length. The hot air above mixed with the cold below forming the stratified layer in between. As the flow evolved and the turbulence decayed, the buoyancy forces increased relative to the inertial forces (i.e., the Richardson number increased) causing the heat flux to collapse. This resulted in a thinning of the mixing layer with downstream distance (rather than growth which occurs for the passive case). Inside the layer the vertical velocity variance diminished and the vertical heat flux correlation coefficient was reduced to zero. Smoke wire photographs showed a wavylike damped region inside the layer, surrounded by the normal, more energetic turbulence outside. Second-order turbulence quantities scaled in the same way with the local Richardson number both along the layer and across it. The two stably stratified cases studied had centerline Froude numbers of 95 and 65 at 40 mesh lengths from the grid. The results are compared to a passive thermal mixing layer and are contrasted with recent experiments concerning a constant temperature gradient in grid turbulence.

Effects of heat release on the large-scale structure in turbulent mixing layers

The effects of chemical heat release on the large-scale structure in a chemically reacting, turbulent mixing layer are investigated using direct numerical simulations. Three-dimensional, time-dependent simulations are performed for a binary, single-step chemical reaction occurring across a temporally developing turbulent mixing layer. It is found that moderate heat release slows the development of the large-scale structures and shifts their wavelengths to larger scales. The resulting entrainment of reactants is reduced, decreasing the overall chemical product formation rate. The simulation results are interpreted in terms of turbulence energetics, vorticity dynamics, and stability theory. The baroclinic torque and thermal expansion in the mixing layer produce changes in the flame vortex structure that result in more diffuse vortices than in the constant-density case, resulting in lower rotation rates of the large-scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques.

Reinterpretation of cloud-topped mixed-layer entrainment closure

Mixed-layer models of convective boundary layers in the atmosphere and oceans are powerful and useful tools for including important physical processes in general-circulation models of the two media as well as for diagnostic and prognostic studies of air-sea interaction and pollution dispersion. Recently, the appropriate physical and mathematical interpretation of the entrainment closure in such models has come under discussion. In mixed-layer ocean models and models of the dry convective atmospheric mixed layer, the discussion is essentially moot because, when the closure is implemented, its mathematics are independent of the physical interpretation. However, in mixed-layer models of the cloud-topped boundary layer, different physical interpretations lead to quite different mathematical formulations of the closure that yield widely differing results. In this paper, a new interpretation of the turbulence energetics for the cloud-topped case is discussed. It retains the mathematical simplicity of an earlier approach while allowing consistency with recent numerical results concerning asymmetric diffusivities. Although the definitive study of the problem, by either theoretical, observational or numerical methods, remains for the future, the interpretation of turbulence energetics presented here is sufficiently flexible to be adaptable to new results. DOI: 10.1111/j.1600-0870.1987.tb00302.x

Anomalous Sounds from the Entry of Meteor Fireballs

A very bright fireball observed over New South Wales in 1978 produced anomalous sounds clearly audible to some of the observers. An investigation of the phenomenon indicates that bright fireballs radiate considerable electromagnetic energy in the very-low-frequency (VLF) region of the spectrum. A mechanism for the production of VLF emissions from the highly energetic wake turbulence of the fireball is proposed. Trials with human subjects revealed a very extended range of thresholds for the perception of electrically excited sounds among a sample population, particularly when the VLF electric field excites surface acoustic waves in surrounding objects. This fact, together with variable propagation effects and local conditions, can account for the sporadic distribution of reports of anomalous sounds from fireballs and auroras.

Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step

Incompressible flow over a backward-facing step is studied in order to investigate the flow characteristics in the separated shear-layer, the reattachment zone, and the redeveloping boundary layer after reattachment. Two different step-heights are used: h/δs = 2.2 and h/δs = 3.3. The boundary layer at separation is turbulent for both cases. Turbulent intensities and shear stress reach maxima in the reattachment zone, followed by rapid decay near the surface after reattachment. Downstream of reattachnent, the flow returns very slowly to the structure of an ordinary turbulent boundary layer. In the reattached layer the conventional normalization of outerlayer eddy viscosity by U∞ δ* does not collapse the data. However, it was found that normalization by U∞ (δ − δ*) does collapse the data to within ± 10% of a single curve as far downstream as x/xR ≈ 2, the last data station. This result illustrates the strong downstream persistence of the energetic turbulence structure created in the separated shear layer.

Fully developed turbulence and statistical mechanics

This paper gives a self contained review of some recent progress of the statistical theory of fully developed turbulence. The emphasis is on both analogies and differences with Hamiltonian statistical mechanics, in particular critical phenomena. The method of spectral equations, which plays to a certain extent the role of a mean field theory, is discussed in detail. It is here viewed as a reformulation of the Kolmogorov 1941 theory leading to quantitative insight into the energetics of turbulence (power-law spectra, direct and inverse energy cascades, energy dissipation in the limit of zero viscosity, etc.). In addition, it sheds light on the proven and conjectured properties of the Navier-Stokes and Euler equations which are reviewed in terms more accessible than those of the mathematical literature. There are strong experimental indications (intermittency) that the Kolmogorov 1941 theory is only approximate. Some of the current efforts to handle higher than second order statistics by formal methods inspired from quantum field theory or critical phenomena are also discussed.

Experimental study of the structure of isotropic turbulence with intermediate range of Reynolds number

The energetic isotropic turbulence generated by a waterfall of low head was found to be developed in part through the unstable two-phase flow of entrained air bubbles. The resulting turbulent field had a turbulent Reynolds number of ≳2×104 and maintained a self-similar structure throughout the decay period studied. The present study may provide some insight into the structure of turbulence produced by the breaking waves over the ocean.