Velocity gradient

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

On the velocity of P in the upper mantle

Abstract: The travel times of P in the upper mantle are considered. Usually the phases are more clearly recorded at epicentral distances beyond 15° and here the time-distance curves have appreciable curvature. At smaller distances the time-curves are nearly straight lines, that sometimes are cut off at distances less than 15°. Travel times have been calculated on various velocity assumptions so as to agree with the empirically determined travel times. For the uppermost mantle the velocity has been taken either to be constant or slightly increasing down to a depth sufficiently great for the phases to be recorded, though with small amplitudes, at least to distances of 15°, or a low velocity layer has been inserted that cuts off the time-curve at smaller distances. The bending branch of the time-curve from about 15° onwards can be produced by a slow, gradual increase of velocity downwards from about 100 km depth, or by a somewhat faster increase causing a reversal of the time-curve and a cusp at about 15°, or else by an abrupt increase of velocity and velocity gradient at a depth somewhat greater than 200 km. In this last case reflections and refractions emerge at distances smaller than 15°.

Fluid kinematics on a deformable surface

Abstract: An expression for the rate-of-strain tensor on a rigid surface due to Caswell is generalized to an arbitrarily moving and continuously deforming surface or interface between two immiscible fluids. Corresponding expressions for the velocity gradient and vorticity tensors are derived in an inertial frame of reference. A noteworthy feature of the expression for the rate-of-strain tensor is the presence of a tangent-tangent component, which is absent in the case of a rigid surface. Kinematic applications based on numerical solutions of the Navier-Stokes equation for laminar and turbulent flow demonstrate the significance and implications of the derived expressions.

Excitation wave breaking in excitable media with linear shear flow

Abstract: If an excitable medium is moving with relative shear, the waves of excitation may be broken by the motion. We consider such breaks for the case of a constant linear shear flow. The mechanisms and conditions for the breaking of solitary waves and wave trains are essentially different: the solitary waves require the velocity gradient to exceed a certain threshold, while the breaking of repetitive wave trains happens for arbitrarily small velocity gradients.