Velocity gradient

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

Single Polymer Dynamics in an Elongational Flow

Abstract: The stretching of individual polymers in a spatially homogeneous velocity gradient was observed through use of fluorescently labeled DNA molecules. The probability distribution of molecular extension was determined as a function of time and strain rate. Although some molecules reached steady state, the average extension did not, even after a ∼300-fold distortion of the underlying fluid element. At the highest strain rates, distinct conformational shapes with differing dynamics were observed. There was considerable variation in the onset of stretching, and chains with a dumbbell shape stretched more rapidly than folded ones. As the strain rate was increased, chains did not deform with the fluid element. The steady-state extension can be described by a model consisting of two beads connected by a spring representing the entropic elasticity of a worm-like chain, but the average dynamics cannot.

Analysis and interpretation of instantaneous turbulent velocity fields

Abstract: Methods of analyzing and interpreting velocity-field data (both two- and three-dimensional) to understand the kinematics, dynamics, and scales of turbulence are discussed. Reynolds decomposition and vorticity are traditionally used; however, several other methods, including Galilean (constant convection velocity) and LES decompositions (low-pass filtering), in conjunction with critical-point analysis of the local velocity gradient tensor, reveal more about the structure of turbulence. Once the small-scale structures have been identified, it is necessary to assess their importance to the overall dynamics of the turbulence by visualizing the motions they induce and the stresses they impose both on other small-scale vortices and on the larger-scale field.

A geodetic plate motion and Global Strain Rate Model

Abstract: We present a new global model of plate motions and strain rates in plate boundary zones constrained by horizontal geodetic velocities. This Global Strain Rate Model (GSRM v.2.1) is a vast improvement over its predecessor both in terms of amount of data input as in an increase in spatial model resolution by factor of ∼2.5 in areas with dense data coverage. We determined 6739 velocities from time series of (mostly) continuous GPS measurements; i.e., by far the largest global velocity solution to date. We transformed 15,772 velocities from 233 (mostly) published studies onto our core solution to obtain 22,511 velocities in the same reference frame. Care is taken to not use velocities from stations (or time periods) that are affected by transient phenomena; i.e., this data set consists of velocities best representing the interseismic plate velocity. About 14% of the Earth is allowed to deform in 145,086 deforming grid cells (0.25° longitude by 0.2° latitude in dimension). The remainder of the Earth's surface is modeled as rigid spherical caps representing 50 tectonic plates. For 36 plates we present new GPS-derived angular velocities. For all the plates that can be compared with the most recent geologic plate motion model, we find that the difference in angular velocity is significant. The rigid-body rotations are used as boundary conditions in the strain rate calculations. The strain rate field is modeled using the Haines and Holt method, which uses splines to obtain an self-consistent interpolated velocity gradient tensor field, from which strain rates, vorticity rates, and expected velocities are derived. We also present expected faulting orientations in areas with significant vorticity, and update the no-net rotation reference frame associated with our global velocity gradient field. Finally, we present a global map of recurrence times for Mw=7.5 characteristic earthquakes.

The structure of the turbulent pressure field in boundary-layer flows

Abstract: The paper is discussion of measurements of the statistical properties of the pressure field at the wall of turbulent attached shear flows. These measurements have been made only in part by the author. A preliminary discussion is given of the important limitations imposed by the imperfect space resolution of contemporary pressure transducers. There follows a discussion of the appropriate scales of the pressure field. It is shown that measurements of the longitudinal cross-spectral densities lead to similarity variables for the space-time covariance of the pressure and for the corresponding spectra. The existence of these similarity variables may be due to the dispersion of the sources of pressure by the mean velocity gradient. Such a mechanism is illustrated by a simple model. Lateral cross-spectral densities also lead approximately to similarity variables.Computations based directly upon detailed pressure-velocity correlation measurements by Wooldridge & Willmarth reveal that an important part of the pressure at the wall of a boundary layer is contributed by source terms which are quadratic in the turbulent velocity fluctuations; the interaction of the mean strain rate with normal velocity fluctuations, being in effect limited to a region very near the wall, supplies a dominant contribution only at high frequencies and its scales, downstream convective speed and convective memory are markedly smaller than those of the observed wall pressure.The inner part of the Law of the Wall region (y* [les ] 100) seems to be substantially free of pressure sources and within that region (a) the pressure can be given in terms of its boundary value, and (b) the local velocity field is dependent upon but unbale to affect appreciably the turbulent pressures.

Wall Slip Corrections for Couette and Parallel Disk Viscometers

Abstract: Often for slurries, gels, emulsions, and foams inhomogeneous fluid properties at solid boundaries create “apparent wall slip.” The reduced fluid viscosity at the boundary creates a thin layer of fluid having a large velocity gradient that can be treated as a “slipping layer”. In measurements of fluid viscosity it is necessary to correct for wall slip to determine the true deformation experienced by the bulk of the sample and the true viscosity. The classic earlier techniques for capillaries and Couette geometries were first presented by Mooney. We present a new analysis of the Couette geometry that requires only two measurements rather than the three used by Mooney. We also present a new analysis for flow between rotating parallel disks. The parallel disk geometry has several experimental advantages for measuring fluid viscosities in the presence of wall slip. The analysis of experimental data on a clay suspension and oil‐in‐water emulsion are presented to demonstrate these new techniques.