Velocity gradient

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

Variational approach to dynamic analysis of third-order shear deformable plates within gradient elasticity

Abstract: A variational approach based on Hamilton’s principle is used to develop the governing equations for the dynamic analysis of plates using the Reddy third-order shear deformable plate theory with strain gradient and velocity gradient. The plate is made of homogeneous and isotropic elastic material. The stain energy, kinetic energy, and the external work are generalized to capture the gradient elasticity (i.e., size effect) in plates modeled using the third-order shear deformation theory. In this framework, both strain and velocity gradients are included in the strain energy and kinetic energy expressions, respectively. The equations of motion are derived, along with the consistent boundary equations. Finally, the resulting third-order shear deformation (strain and velocity) gradient plate theory is specialized to the first-order and classical strain gradient plate theories.

Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence

Abstract: We show by direct numerical simulation (DNS) that the Lagrangian cross correlation of velocity gradients in homogeneous isotropic turbulence increases at short times, whereas its auto-correlation decreases. Kinematic considerations allow to show that two invariants of the turbulent velocity field determine the short-time velocity gradient correlations. In order to get a more intuitive understanding of the dynamics for longer times, heuristic models are proposed involving the combined action of local shear and rotation. These models quantitatively reproduce the effects and disentangle the different physical mechanisms leading to the observations in the DNS.

Axially symmetric stagnation-point flow of an electrically conducting fluid under transverse magnetic field

Abstract: This paper deals with the axially symmetric stagnation-point flow of an incompressible, viscous and electrically conducting fluid in the presence of a transverse magnetic field with small magnetic Reynolds numbers. The velocity distribution modified by the magnetic field is calculated for several values of N (= S R m , S : the pressure number, R m : the magnetic Reynolds number). The shear stress on the wall is expressed in terms of b and φ''(0), where b is a characteristic parameter of the asymptotic inviscid flow and φ''(0) is the non-dimensional velocity gradient on the wall. The flow of this type may be considered as a simple model of the circumstance in the neighbourhood of the nose of a body of revolution moving through an ionized atmosphere at hypersonic speed. In this context, it may be convenient to use Bush's results for estimating b . The ratio of the shear stresses with and without the magnetic field thus calculated is shown graphically as a function of N . It is found that the shear stress at...

Non-newtonian viscosity and normal pressure associated with the flow alignment in macromolecular liquids

Abstract: Non-linear constitutive laws previously obtained within the framework of irreversible thermodynamics are applied to the calculation of the flow alignment and the friction pressure tensor of macromolecular liquids. A non-newtonian viscosity is obtained which decreases with increasing magnitude of the velocity gradient. For rigid molecules it reaches a finite asymptotic value, viz. the second newtonian viscosity. The friction pressure tensor contains normal components. The magnitude of this normal pressure is closely related to the change of the viscosity caused by the velocity gradient. Flow alignment and the pressure tensor are also studied for time-dependent (alternating) velocity gradients.

Memory Effect in a Turbulent Boundary-Layer Flow Due to a Relatively Strong Axial Variation of the Mean-Velocity Gradient

Abstract: Measurements have been made of the distributions of mean velocity, turbulence intensities and turbulence shear-stress in a turbulent boundary-layer downstream of a hemi-spherical cap attached onto the plane rigid wall. The eddy-viscosity, when computed in the classical way according to Boussinesq's concept from the lateral gradient of the mean velocity and the turbulence shear-stress, showed a very strong non-uniform lateral distribution, also across the outer region of the boundary-layer. More over , the non-dimensional values of the eddy viscosity, using the wall-friction velocity and the boundary-layer thickness as the velocity scale and length scale respectively, were higher than those for the boundary-layer when not disturbed by the wake of the spherical cap. However, when account is taken of an axial memory effect of the streamwise variation of the lateral gradient of the mean-velocity, the values of the non-dimensional eddy viscosity are close to those for the undisturbed boundary-layer.