E. Kit

Experimental investigation of the field of velocity gradients in turbulent flows

We present results of experiments on a turbulent grid flow and a few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was done by a twelve-wire hot-wire probe (3 arrays × 4 wires), produced for this purpose using specially made equipment (micromanipulators and some other auxiliary special equipment), calibration unit and calibration procedure. The probe had no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results. Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate-of-strain tensor, the positiveness of the total enstrophy-generating term ω i ω j s ij ( s ij = ½(∂ u i /∂ x j +∂ u j /∂ x i ), ω i = e ijk ∂ u j /∂ x k ) even for rather short records and the tendency for alignment in the strict sense between vorticity and the vortex stretching vector W i = ω j s ij . An emphasis is put on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference (e.g. s ij s ij and ω i ω j s ij ) as the most appropriate to describe physical processes. From the methodological point of view the main result is that the multi-hot-wire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least at moderate Reynolds numbers.

Large-scale structures in a forced turbulent mixing layer

The large-scale structures that occur in a forced turbulent mixing layer at moderately high Reynolds numbers have been modelled by linear inviscid stability theory incorporating first-order corrections for slow spatial variations of the mean flow. The perturbation stream function for a spatially growing time-periodic travelling wave has been numerically evaluated for the measured linearly diverging mean flow. In an accompanying experiment periodic oscillations were imposed on the turbulent mixing layer by the motion of a small flap at the trailing edge of the splitter plate that separated the two uniform streams of different velocity. The results of the numerical computations are compared with experimental measurements. When the comparison between experimental data and the computational model was made on a purely local basis, agreement in both the amplitude and phase distribution across the mixing layer was excellent. Comparisons on a global scale revealed, not unexpectedly, less good accuracy in predicting the overall amplification.

Pulsating flow in a pipe

Turbulent and laminar pulsating flows in a straight smooth pipe are compared at identical frequencies and Reynolds numbers. Most measurements were made at a mean Reynolds number of 4000, but the influence of Re was checked for 2900 < Re < 7500. The period of forcing ranged from 0.5 to 5 s, with corresponding change in the non-dimensional frequency parameter α = R √(ω/ν) from 4.5 to 15. The amplitude of the imposed oscillations did not exceed 35% of the mean in order to avoid flow reversal or relaminarization. Velocities at the exit plane of the pipe and pressure drop along the pipe were measured simultaneously; velocity measurements were made with arrays of normal hot wires. The introduction of the periodic surging had no significant effect on the time-averaged quantities, regardless of the flow regime (i.e. in both laminar and turbulent flows). The time-dependent components at the forcing frequency, represented by a radial distribution of amplitudes and phases, are qualitatively different in laminar and turbulent flows. The ensemble-averaged turbulent quantities may also be represented by an amplitude and a phase; however, the non-harmonic content of these intensities increases with increasing amplitude of the imposed oscillations. A normalization procedure is proposed which relates phase-locked turbulent flow parameters in unsteady flow to similar time-averaged quantities. An integral momentum equation in a time-dependent flow requires that a triad of forces (pressure, inertia and shear) will be in equilibrium at any instant of time. All the terms in the force-balance equation were measured independently, providing a good check of data. The analysis of the experimental results suggests that turbulence adjusts rather slowly to the local mean-flow conditions. A simple eddy-viscosity model described by a complex function can account for ‘memory’ of turbulence and explain the different phase distribution in laminar and turbulent flows.

Evolution of a nonlinear wave field along a tank: experiments and numerical simulations based on the spatial Zakharov equation

Evolution of a nonlinear wave eld along a laboratory tank is studied experimentally and numerically. The numerical study is based on the Zakharov nonlinear equation, which is modied to describe slow spatial evolution of unidirectional waves as they move along the tank. Groups with various initial shapes, amplitudes and spectral contents are studied. It is demonstrated that the applied theoretical model, which does not impose any constraints on the spectral width, is capable of describing accurately, both qualitatively and quantitatively, the slow spatial variation of the group envelopes. The theoretical model also describes accurately the variation along the tank of the spectral shapes, including free wave components and the bound waves.

An experimental and numerical study of the spatial evolution of unidirectional nonlinear water-wave groups

Spatial evolution of nonlinear narrow-spectrum deep-water wave groups is studied experimentally in a wave tank. The experimental results are compared with the computations based on the unidirectional Zakharov equation and the Dysthe model. The very good agreement between the computational results based on both models with the experiments prompted an attempt to perform simulations for a wider initial spectral width, that formally violate the assumptions adopted in the derivation of the Dysthe model. The accuracy of the results based on the Dysthe model is checked against the solutions of the Zakharov equation, which is free of restrictions on the spectral width. Conclusions regarding the domain of validity of the Dysthe model are drawn.

Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves

and does not have any restrictions on thespectral width. It was used in the same paper to derive the cubic Schr¨odingerequation which describes the temporal evolution of the wave envelope under theassumption of a narrow spectrum. The cubic Schr¨odinger equation was subsequentlyderived by a multiple-scale perturbation method and applied to studies of waterwaves by numerous investigators; for references see e.g. Mei (1989). Unsatis ed bythe unfavourable comparison of the solution of the cubic Schr¨odinger equationwith the exact computations, Dysthe (1979) extended the perturbation analysis tothe fourth-order in

Measurement of turbulence near shear-free density interfaces

The results of an experimental study carried out to investigate the structure of turbulence near a shear-free density interface are presented. The experimental configuration consisted of a two-layer fluid medium in which the lower layer was maintained in a turbulent state by an oscillating grid. The measurements included the root-mean-square (r.m.s.) turbulent velocities, wavenumber spectra, dissipation of turbulent kinetic energy and integral lengthscales. It was found that the introduction of a density interface to a turbulent flow can strongly distort the structure of turbulence near the interface wherein the horizontal velocity components are amplified and the vertical component is damped. The modification of r.m.s velocities is essentially limited to distances smaller than about an integral lengthscale. Inspection of spectra shows that these distortions are felt only at small wavenumbers of the order of the integral scale and a range of low-wavenumbers of the inertial subrange; the distortions become pronounced as the interface is approached. Comparison of the horizontal velocity data with the rapid distortion theory (RDT) analyses of Hunt & Graham (1978) and Hunt (1984) showed a qualitative agreement near the interface and a quantitative agreement away from the interface. On the other hand, the RDT predictions for the vertical component were in general agreement with the data. The near-interface horizontal velocity data, however, showed quantitative agreement with a model proposed by Hunt (1984) based on nonlinear vortex dynamics near the interface. The effects due to interfacial waves appear to be important for distances less than about 10% of the integral lengthscale. As a consequence of the non-zero energy flux divergence, the introduction of a density interface to oscillating grid turbulence increases the rate of dissipation in the turbulent layer except near the interface, where a sharp drop occurs. The present measurements provide useful information on the structure of turbulence in shear-free boundary layers, such as atmospheric and oceanic convective boundary layers, thus improving modelling capabilities for such flows.

An experimental study of helicity related properties of a turbulent flow past a grid

Results of direct measurements of helicity density and other velocity derivative related flow properties are reported for a turbulent flow past a grid at Reλ=75. The velocity and vorticity vectors exhibit a tendency to be aligned. The flow is found to lack reflectional symmetry, which is manifested by a nonzero correlation between the velocity and vorticity vector fluctuations and considerable asymmetry in the probability density function of the cosine of the angle between the velocity and vorticity vector fluctuations. This asymmetry, as well as the tendency for alignment, increases for larger values of ‖v‖ ‖ω‖.

Simulation of an interferometric synthetic aperture radar imagery of an ocean system consisting of a current and a monochromatic wave

A model which simulates azimuthal imaging of a monochromatic ocean wave and current by an interferometric synthetic aperture radar (INSAR) is developed. The model allows one to obtain simulation of a regular synthetic aperture radar (SAR) as a particular case. The effects of velocity bunching and scanning distortion, as well as the dependence of the output on wave propagation direction, are considered. SAR and INSAR imaging of a monochromatic wave is compared both qualitatively and quantitatively for a wide range of governing parameters. Analytical expressions for both SAR and INSAR outputs were obtained for small values of the velocity-bunching parameter. The accuracy of these analytical approximations was checked numerically.

EXPERIMENTAL AND THEORETICAL INVESTIGATION OF NONLINEAR SLOSHING WAVES IN A RECTANGULAR CHANNEL

Experimental and theoretical studies of sloshing waves in a rectangular channel in the vicinity of the second cutoff frequency are presented. The experiments were performed in a wave tank which is 1.2m wide, 18m long and 0.9m deep. Sloshing waves were generated by a computer-controlled segmented wavemaker consisting of four independent modules. A sharp transition between two wave patterns, which exhibited hysteresis-type behaviour, was observed. At lower forcing frequencies a steady wave regime was obtained, while at higher frequencies modulation on a long timescale appeared. At stronger forcing, solitons were generated periodically at the wavemaker and then propagated away with a seemingly constant velocity. Experimental results are compared with numerical solutions of the appropriate nonlinear Schrodinger equation, a derivation of which is also presented. The importance of dissipation on the physical processes of wave evolution is discussed, and a simple dissipative model is suggested and incorporated in the governing equations.