Velocity gradient

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

Velocity characteristics of the flow in the near wake of a disk

Abstract: Measurements of the velocity characteristics of near-wake flows were obtained with a direction-sensitive laser-Doppler anemometer The wakes were formed downstream of central disks of diameters 8·9, 12·5 and 14·2 mm which were located on the centreline of a 20·0 mm jet Detailed measurements were obtained with initial annular-jet velocities of from 9·4 to 39·5 m/s and include values of the axial and radial components of the mean velocity, the three normal stresses and the shear stress Probability density distributions and energy spectra were also measuredThe results show, for example, that the curvature of the annular jet increases with disk diameter and that the ratios of the maximum positive and negative centre-line velocities to the exit velocity increase with decreasing disk diameter and are essentially independent of the initial velocity The turbulent field is substantially anisotropic with a minimum turbulence intensity of around 30% in the recirculation region; the locations of zero shear stress and zero mean velocity gradient are not coincident The measured spectra reveal predominant frequencies in a small region of the outer-shear layer and in the vicinity of the jet exit; these discrete frequencies did not propagate downstream nor into the recirculation region

P and S waves diffracted around the core and the velocity structure at the base of the mantle

Abstract: Summary. Decay spectra and dT/dΔ on 13 great circle paths for P and seven for SH, are used in a joint interpretation of P and SH diffraction data, in terms of a transition zone with linear velocity profile above the core—mantle boundary (CMB). Error analysis reveals that the effect of large-scale lateral variations at the base of the mantle can be significant, and this effect is accounted for in the standard errors as associated with the data and used in the inversion procedure. Employing a full wave theoretical approach discussed previously, synthetic decay spectra and dT/dΔ are calculated for every individual path, to be compared to the real data. Following recommendations of a previous paper, it is illustrated here by examples that thickness zt and velocity gradients dα/dz, dβ/dz of the transition zone have a characteristic effect on the decay spectra of P and SH, and these effects are taken into account in searching the model space for the best fitting model (in the least-squares sense). Subject to the constraint of a linear velocity profile, the combined P and SH data set allows a thickness zt of 50–100 km and the P and S velocities both decrease with depth. The preferred model, PEMC-L01, has zt= 75 km and dα/dz=dβ/dz 2–0.0019; the S velocity gradient is close to critical and the ‘index of inhomogeneities’η∼ 4.5. There is a suggestion of an additional low-Q at the base of the mantle, but this is not absolutely required due to the large standard errors associated with the relevant data. The models are determined primarily from the decay spectra. They also fit the dT/dA data reasonably well, but these data do not discriminate between several different models considered here. Allowing for the possibility of lateral variations, previously published data can be reconciled with the present model, possibly with some modifications warranted by short-period information. The physical implications are an anomalous density gradient and/or superadiabatic temperature gradient above CMB. The numerical results with regard to density and/or temperature must be treated with caution, since the seismic parameters dφ/u'z and η are very sensitive to apparently small changes in the model.

Inertial effects on the transfer of heat or mass from neutrally buoyant spheres in a steady linear velocity field

Abstract: Microscale inertia is found to break the degenerate closed-streamline configuration that occurs in a shearing flow past a neutrally buoyant torque-free spherical particle in the inertialess limit. The broken symmetry at small but finite Re allows heat or mass to be convected away in an efficient manner in sharp contrast to the inertialess diffusion-limited scenario. Inertial forces scale with the particle Reynolds number, defined as Re=γa2∕ν, where a is the radius of the particle, γ is the characteristic magnitude of the velocity gradient, and ν is the kinematic viscosity of the suspending fluid. The dimensionless heat or mass transfer rate is then given by Nu=C(RePe)1∕3+O(1) when Re≪1 and RePe≫1, the constant C being a function of the flow in the vicinity of the particle. Here, Nu is the Nusselt number defined as Q∕(4πkaΔF), where Q is the dimensional heat/mass flux, k the appropriate transport coefficient, and ΔF the driving force viz. the temperature or concentration difference between the particle a...

On steady flows of fluids with pressure– and shear–dependent viscosities

Abstract: There are many technologically important problems such as elastohydrodynamics which involve the flows of a fluid over a wide range of pressures. While the density of the fluid remains essentially constant during these flows whereby the fluid can be approximated as being incompressible, the viscosity varies significantly by several orders of magnitude. It is also possible that the viscosity of such fluids depends on the shear rate. Here we consider the flows of a class of incompressible fluids with viscosity that depends on the pressure and shear rate. We establish the existence of weak solutions for the steady flows of such fluids subjected to homogeneous Dirichlet boundary conditions and to specific body forces that are not necessarily assumed to be small. A novel aspect of the study is the manner in which we treat the pressure that allows us to establish its compactness, as well as that of the velocity gradient. The method draws upon the physics of the problem, namely that the notion of incompressibility is an idealization that is attained by letting the compressibility of the fluid to tend to zero.

Changes in velocity profiles at roughness transitions in coarse grained channels

Abstract: Heterogeneous coarse grained channels are often characterized by local transitions in bed surface roughness. Distinct spatial zones in terms of grain size have been reported, for example sand ribbons and bedload sheets. The transition from areas of finer to coarser grained surface sediment is often abrupt. However, the effects of these transitions on the shape of the velocity profile and associated shear velocity and roughness length estimates have not been investigated in detail in coarse grained channels. This paper therefore examines the combined effects of a sudden change in surface roughness and of superimposed scales of resistance on the structure of the turbulent boundary layer. Measurements along roughness transitions from smooth to rough beds were conducted in a flume using artificial roughness features and in a natural gravel bed river. Immediately at the transition from a zone of close packed roughness to a rougher section dominated by obstacles superimposed on the more or less uniform roughness surface, boundary shear stress and roughness length increase considerably. Downstream from this transition, velocity profiles become concave upwards. Downstream and upstream sections show significant differences in terms of near bed velocities (deceleration downstream of the transition), velocity gradient and turbulence intensity of the streamwise velocity component. Comparing the mean velocity profiles corresponding to these two different roughness surfaces gives some indication of the proportion of total shear velocity (or shear stress) associated with the pressure drag produced by large and isolated obstacles.