Mahinder S. Uberoi

Equipartition of Energy and Local Isotropy in Turbulent Flows

Homogeneous turbulence in which 〈v2〉 = 〈w2〉 ≠ 〈u2〉 was produced experimentally, where 〈u2〉, 〈v2〉, and 〈w2〉 are the mean‐square turbulent velocities in x, y, and z direction, respectively. The decay of turbulence and the energy transfer between 〈u2〉 and (〈v2〉+〈w2〉) were measured, and it was found that the larger components (〈v2〉 and 〈w2〉) are losing more energy due to viscosity than by transfer to the smaller component (〈u2〉). However, 〈u2〉 is receiving enough energy by transfer to compensate for its decay and is in fact slowly increasing. The measurement of mean‐square vorticity components shows that the turbulence is becoming locally isotropic at a faster rate than the equipartition of energy is taking place.In another set of experiments it was found that when approximately isotropic turbulence is subjected to deformation, the three components of turbulent energy become widely different in magnitude and that the turbulence is not locally isotropic. This indicates that even at high Reynolds number the def...

Experiments on vortex stability

The tip vortex of a laminar flow wing was studied at a sectional lift‐to‐drag ratio of 60. The vortex Reynolds number was Γ0/ν=7.8×104, where Γ0 is the total circulation and ν is the kinematic viscosity. At and near the wing the vortex core was turbulent with an axial jet. Downstream of the wing the jet rapidly dissipated and a wake developed in the core and intensity of turbulent velocities decreased. From 13 to 40 chord length periodic oscillations dominated the velocity fluctuations with little background turbulence. These instabilities had a symmetric and a helical mode with wavelength of the same order as the core diameter. In this range of distances along the vortex core the maximum axial, swirl, and fluctuating velocities vary slowly. At 40 chord lengths behind the wing there is a rapid change in these velocities. This change of state of the vortex core is accompanied by change of velocity fluctuations from periodic to turbulent. The core showed spatial excursions. Measurements up to 80 chord lengt...

Energy Transfer in Isotropic Turbulence

Energy transfer from large to small eddies at three stations in turbulence behind a square mesh is determined by measuring the rates of change and viscous dissipation of the spectrum and the results are compared with a theoretical prediction. Large eddies for which viscous dissipation is negligible satisfy a similarity relation which agrees with the fact that the total energy decays as some negative power of time. Small eddies which are in approximate statistical equilibrium satisfy local similarity according to Kolmogoroff. Various terms in the vorticity equation are also determined and the quantities representative of small scale motion are universal constants when expressed in terms of Kolmogoroff parameters.

Turbulent Energy Balance and Spectra of the Axisymmetric Wake

Axisymmetric turbulent wake behind a sphere in an incompressible fluid has been experimentally investigated from 50 to 300 diam downstream from the sphere at Reynolds numbers from 4000 to 150 000. Mean and turbulent velocity measurements show that the region of self‐preservation starts 50 sphere diam downstream, and the virtual origin of the wake is 12 sphere diam downstream. Detailed measurements were made in the self‐preserving region of the wake. The three components of the turbulent velocity, turbulent shear, and the mean velocity defect were measured across the wake using the hot‐wire anemometer. From the measurements the turbulent energy production, dissipation, convection, and diffusion across the wake were determined. The one‐dimensional energy spectra of the three components of the turbulent velocity, their dependence on distance along and across the wake and on Reynolds number have been measured. The large scale motion (low wavenumbers) is dynamically similar and the small scale motion (large wavenumbers) exhibits Kolmogoroffs universal equilibrium. The present spectral measurements are compared with other published measurements of the universal equilibrium spectra in various turbulent flows.

Structure of Temperature Fluctuations in the Turbulent Wake behind a Heated Cylinder

Convection, production, diffusion, and dissipation of temperature fluctuations have been measured in the dynamically similar turbulent wake behind a headed circular cylinder 1140 diameters downstream from the cylinder at a Reynolds number of 960. The measurements show strong production and dissipation and moderate convection and diffusion. In addition, the dependence of one‐dimensional spectra of temperature fluctuations on wake parameters and the skewness of the temperature derivative have been measured for the Reynolds number range 440‐69 000. All measurements are consistent with the assumption of local isotropy except for the skewness of the temperature derivative.

Experiments on turbulent structure and heat transfer in a two‐dimensional jet

Turbulence and heat transfer were measured in a heated jet of air and development of self‐similarity was determined. Temperature fluctuation balance was measured across the jet. Turbulent velocity and temperature spectra and their dependence on jet Reynolds number and location across the jet were measured. The jet nozzles with length to width ratios of 20, 40, and 140 were used and the effect of aspect ratio on turbulent structure was determined.

Spectra of Turbulence in Wakes behind Circular Cylinders

One‐dimensional spectra of turbulent wakes behind circular cylinders are measured in the range of 50‐800 diam downstream of the cylinders and for a Reynolds number range of 320‐95 000. The spectra of large‐scale (low‐wavenumber) turbulence are anisotropic and dynamically similar. The small‐scale turbulence is locally isotropic and an inertial subrange was found for large Reynolds numbers. A proposed formula describes the spectra over the entire wavenumber range and for all Reynolds numbers.

Temperature fluctuations in the turbulent wake behind an optically heated sphere

Convection, production, diffusion, and dissipation of temperature fluctuations have been measured in the dynamically similar turbulent wake behind an optically heated sphere 136 sphere diameters downstream and at a Reynolds number 4300. The measurements show strong convection and dissipation and moderate diffusion and production. In addition, the dependence of one‐dimensional spectra of temperature fluctuations on wake parameters, intermittency, and the skewness of temperature and velocity derivatives have been measured in a Reynolds number range 1000‐38 000. The skewness of temperature derivative exhibits locally nonisotropic behavior especially at low Reynolds numbers.

Effect of Grid Geometry on Turbulence Decay

Longitudinal and lateral turbulence intensities u2¯ and v2¯ are measured behind homogeneous grids of various geometries. For all grids used, the ratio u2¯/v2¯ is essentially constant during decay and lies between 1.2 and 1.35, depending on the grid geometry. The turbulence intensity u2¯∼t−n where n is constant during decay but depends on the grid geometry and varies from 1.22 to 1.48. This implies that the rate of decay depends on the initial energy spectrum and the energy‐containing (large) eddies maintain a similarity during decay.

Turbulent mixing in a two‐dimensional jet

An ensemble of instantaneous temperature profiles across a two‐dimensional heated jet was obtained by shooting a fine platinum resistance thermometer across the jet at speeds much higher than the local velocity of the jet. Each recording of the ensemble was shifted to have a common center, and ensemble averages were obtained counting only the profiles for which the spatial location in question was inside the jet. This conditional averaging produced mean and mean‐square fluctuations which are quite flat across the jet, indicating that the fluid inside the jet is well‐mixed. Visual inspection of instantaneous records showed no cold spots in the jet. Ensemble averages were also measured by aligning the edge or beginning of the instantaneous profiles. This led to a sharper rise in the mean temperature profile and an overshoot in the mean‐square temperature fluctuations. This indicates that mixing across the turbulent‐nonturbulent interface is stronger than in the main body of the jet.