Velocity gradient

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

Three-dimensional shape of a drop under simple shear flow

Abstract: The three-dimensional deformation of an isolated drop in an immiscible liquid phase undergoing simple shear flow was investigated by using a parallel-plate apparatus. The drop was observed by video-enhanced contrast optical microscopy, either along the vorticity direction or along the velocity gradient direction of the shear flow. An experimental methodology based on image analysis was especially developed to study in a quantitative way the three-dimensional shape of the deformed drop, both under steady-state flow and during transients. Up to moderate deformations, the steady-state drop shape was well described within experimental error by an ellipsoid having three different axes. The deviation of drop shape from an ellipsoid at higher deformations was also characterized in a quantitative way. Good agreement was found between the experimental results of this work and numerical simulations reported in the literature.

The stability of a sheared density interface

Abstract: This study investigates the stability of stratified shear flows when the density interface is much thinner than, and displaced with respect to, the velocity interface. Theoretical results obtained from the Taylor–Goldstein equation are compared with experiments performed in mixing layer channels. In these experiments a row of spanwise vortex tubes forms at the level of maximum velocity gradient which, because of the profile asymmetry, is displaced from the mean interface level. As the bulk Richardson number is lowered from a high positive value the effects of these vortex tubes become more pronounced. Initially the interface cusps under their influence, then thin wisps of fluid are drawn from the cusps into asymmetric Kelvin–Helmholtz billows. At lower Richardson numbers increasingly more fluid is drawn into these billows. The inherent asymmetry of flows generated in mixing layer channels is shown to preclude an effective study of the Holmboe instability. Statically unstable flows (negative Richardson numbers) are subject to the Rayleigh–Taylor instability. However, if the absolute value of the Richardson number is sufficiently small the Kelvin–Helmholtz instability dominates initially.

Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments

Abstract: A linear theory of wave propagation in saturated, unconsolidated granular materials, including marine sediments, is developed in this article. Since the grains are unbonded, it is assumed that the shear rigidity modulus of the medium is zero, implying the absence of a skeletal elastic frame. The analysis is based on two types of shearing, translational and radial, which occur at grain contacts during the passage of a wave. These shearing processes act as stress-relaxation mechanisms, which tend to return the material to equilibrium after the application of a dynamic strain. The stress arising from shearing is represented as a random stick-slip process, consisting of a random succession of deterministic stress pulses. Each pulse is produced when micro-asperities on opposite surfaces of a contact slide against each other. The quantity relevant to wave propagation is the average stress from all the micro-sliding events, which is shown to be a temporal convolution between the deterministic stress, h(t), from a single event and the probability, q(t), of an event occurring between times t and t+dt. This probability is proportional to the velocity gradient normal to the tangent plane of contact between grains. The pulse shape function, h(t), is derived by treating the micro-sliding as a strain-hardening process, which yields an inverse-fractional-power-law dependence on time. Based on two convolutions, one for the stress relaxation from translational and the other from radial shearing, the Navier–Stokes equation for the granular medium is derived. In a standard way, it is split into two equations representing compressional and shear wave propagation. From these wave equations, algebraic expressions are derived for the wave speeds and attenuations as functions of the porosity and frequency. Both wave speeds exhibit weak, near-logarithmic dispersion, and the attenuations scale essentially as the first power of frequency. A test of the theory shows that it is consistent with wave speed and attenuation data acquired recently from a sandy sediment in the Gulf of Mexico during the SAX99 experiment. If dispersion is neglected, the predicted expressions for the wave speeds reduce to forms which are exactly the same as those in the empirical elastic model of a sediment proposed by Hamilton. On this basis, the concept of a “skeletal elastic frame” is interpreted as an approximate, but not equivalent, representation of the rigidity introduced by grain-to-grain interactions.