Velocity gradient

About: Velocity gradient is a research topic. Over the lifetime, 3013 publications have been published within this topic receiving 77120 citations.

Turbulence structure in free‐surface channel flows

Abstract: A turbulence structure in horizontal liquid streams bounded by a free surface and a wall has been investigated using 10–25 μm oxygen bubbles as tracers. High speed video movies indicate that the dominant flow structure is caused by the periodic ejection of intensely turbulent fluid with low streamwise momentum from the wall region into the relatively quiescent bulk fluid which it displaces and mixes with slowly. The motion of these bursts is constrained by the free interface. Between bursts and the interface a high speed region with a steep velocity gradient develops as a consequence. This in turn causes progress of the burst fluid toward the interface to slow down and eventually to turn back toward the wall, giving rise to characteristic rolling structures, which rotate clockwise if the flow is viewed as going from left to right. To complement the video studies, quantitative data were obtained by analyzing bubble streak lines generated by photography of optically chopped flashes. These data show that in the vicinity of the interface the velocity fluctuations normal to it are damped whereas those parallel to it are enhanced. Analysis of conditional samples of the data indicate that fluid with relatively low streamwise momentum tends to move toward the interface while fluid with high momentum moves away giving rise to rotating structures that roll along with the flow in agreement with the video studies. A high degree of correlation between ejection events near the wall and the fluid motion near the interface also confirm that the bursts extend across the flow stream. This has important implications for surface renewal theories of turbulent transport at fluid–fluid interfaces.

Study of turbulent structure with hot wires smaller than the viscous length

Abstract: The small-scale structure of the streamwise velocity fluctuations in the wall region of a turbulent boundary layer is examined in a new wind-tunnel facility using hot-wires smaller than any previously constructed (typical dimensions: l = 25 μm, d = 0.5 μm). In the boundary layer in which the measurements were made, the ratio of the hot-wire length to the viscous length is 0.3. The turbulent intensity measured with the small hot wires is larger than that measured with longer wires owing to the better spatial resolution of the small wires. The velocity fluctuations measured by the small hot wires are also analysed to determine the burst frequency at two Reynolds numbers and at various distances from the wall. The dimensionless burst frequency does not depend on the Reynolds number when scaled with wall parameters. However, it increases with Reynolds number when scaled with outer variables. Velocity fluctuations measured by two hot wires, less than two viscous lengths apart, are analysed to reveal the small-scale features present during a burst and in the absence of a burst. The main conclusions are: (1) intermittent small-scale shear layers occur most frequently when bursts are present, less frequently just after a burst, and even less frequently just before a burst; and (2) on occasion the velocity gradient of the small-scale shear layers is as large as the mean-velocity gradient at the wall.

Redshift-space distortion of the 21-cm background from the epoch of reionization – I. Methodology re-examined

Abstract: The peculiar velocity of the intergalactic gas responsible for the cosmic 21cm background from the epoch of reionization and beyond introduces an anisotropy in the three-dimensional power spectrum of brightness temperature fluctuations. Measurement of this anisotropy by future 21cm surveys is a promising tool for separating cosmology from 21cm astrophysics. However, previous attempts to model the signal have often neglected peculiar velocity or only approximated it crudely. This paper presents a detailed treatment of the effects of peculiar velocity on the 21cm signal. (1) We show that properly accounting for finite optical depth eliminates the unphysical divergence of 21cm brightness temperature in the IGM overdense regions found in previous work that employed the usual optically-thin approximation. (2) We show that previous attempts to circumvent this divergence by capping the velocity gradient result in significant errors in the power spectrum on all scales. (3) We further show that the observed power spectrum in redshift-space remains finite even in the optically-thin approximation if one properly accounts for the redshift-space distortion. However, results that take full account of finite optical depth show that this approximation is only accurate in the limit of high spin temperature. (4) We also show that the linear theory for redshift-space distortion results in a ~30% error in the power spectrum at the observationally relevant wavenumber range, at the 50% ionized epoch. (5) We describe and test two numerical schemes to calculate the 21cm signal from reionization simulations which accurately incorporate peculiar velocity in the optically-thin approximation. One is particle-based, the other grid-based, and while the former is most accurate, we demonstrate that the latter is computationally more efficient and can achieve sufficient accuracy. [Abridged]

Velocity and Concentration Distributions in Sheet Flow above Plane Beds

Abstract: This paper reports the results of experiments on particle-water flow over plane-topped stationary beds. The particles used were silica sands having d50 of 0.30 and 0.56 mm and Bakelite particles having d50 of 1.05 mm. The facility was a recirculating loop with pipe of 105-mm internal diameter. Data comprised measurements of hydraulic gradient, volumetric discharge, temperature, concentration profiles, velocity profiles, and delivered concentrations. The thickness of the sheet-flow layer is found to vary in proportion to the shear stress. The velocity at the top of the layer is found to be ∼9.4 times the shear velocity, and a simple relation expresses the velocity gradient at this height. The Richardson number at the top of the sheet flow averages ∼0.035, decreasing with increasing ratio of particle fall velocity to shear velocity.

Spectral modelling of homogeneous non-isotropic turbulence

Abstract: The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.