Velocity gradient

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

Myocardial velocity gradients detected by Doppler imaging.

Abstract: Using a scanner whose colour Doppler mode has been adapted to display tissue motion (instead of blood flow), velocity gradients have been detected across the myocardium. A velocity gradient is a gradual spatial change in the value of velocity estimates. Velocity gradients have potential for assessing regional myocardial contractility. 28 M-mode scans were performed on nine normal volunteers at different locations in the left-ventricle posterior wall. In each case simultaneous Doppler M-mode and pulse-echo M-mode images were obtained. Doppler velocity gradient (DVG) was calculated from Doppler M-mode images and rate of change of wall thickness (RCWT) was calculated from pulse-echo M-mode images. In all Doppler M-mode images statistically significant velocity gradients were observed. In all but one scan, cyclically consistent peaks in DVG occur relative to the electrocardiogram waveform. 99% of systolic and 89% of early diastolic peaks in RCWT have a corresponding peak in DVG. Velocity gradients are consistent with wall thickness changes, suggesting that they have potential for assessment of myocardial contractility.

Large-scale velocity structures in turbulent thermal convection.

Abstract: A systematic study of large-scale velocity structures in turbulent thermal convection is carried out in three different aspect-ratio cells filled with water. Laser Doppler velocimetry is used to measure the velocity profiles and statistics over varying Rayleigh numbers Ra and at various spatial positions across the whole convection cell. Large velocity fluctuations are found both in the central region and near the cell boundary. Despite the large velocity fluctuations, the flow field still maintains a large-scale quasi-two-dimensional structure, which rotates in a coherent manner. This coherent single-roll structure scales with Ra and can be divided into three regions in the rotation plane: (1) a thin viscous boundary layer, (2) a fully mixed central core region with a constant mean velocity gradient, and (3) an intermediate plume-dominated buffer region. The experiment reveals a unique driving mechanism for the large-scale coherent rotation in turbulent convection.

Shear-induced isotropic-to-lamellar transition.

Abstract: Reciprocating shear is found to increase the isotropic-to-lamellar transition temperature in a symmetric diblock copolymer melt. The temperature at which the isotropic state becomes unstable rapidly approaches the ordering transition as the shear rate increases. Shear-induced ordering results in lamellae orientation with wave vectors directed normal to the shear and velocity gradient directions. These results are anticipated by a recent theory that accounts for the suppression of fluctuations by a symmetry breaking field in this class of weakly first-order phase transitions.

Analysis of HDG Methods for Stokes Flow

Abstract: In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically solving the Stokes equations. The method uses polynomials of degree k for all the components of the approximate solution of the gradient-velocity-pressure formulation. The novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method. It renders the analysis of the projection of the errors very concise and allows us to see that the projection of the error in the velocity superconverges. As a consequence, we prove that the approximations of the velocity gradient, the velocity and the pressure converge with the optimal order of convergence of k+1 in L 2 for any k > 0. Moreover, taking advantage of the superconvergence properties of the velocity, we introduce a new element-by-element postprocessing to obtain a new velocity approximation which is exactly divergence-free, H(div)-conforming, and converges with order k+2 for k > 1 and with order 1 for k = 0. Numerical experiments are presented which validate the theoretical results.

Further experiments in nearly homogeneous turbulent shear flow

Abstract: The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.