An elliptic model for space-time correlations in turbulent shear flows is proposed based on a second order approximation to the iso-correlation contours, while Taylor's hypothesis implies a first-order approximation. It is shown that the space-time correlations are mainly determined by their space correlations and the convection and sweeping velocities. This model accommodates two extreme cases: Taylor's hypothesis at vanishing sweeping velocity and the sweeping hypothesis at vanishing convection velocity. The result is supported by the data from the direct numerical simulation of turbulent channel flows.
Analytical and numerical studies of secondary electro-osmotic flow ͑EOF͒ and its mixing in microchannels with heterogeneous zeta potentials are carried out in the present work. The secondary EOFs are analyzed by solving the Stokes equation with heterogeneous slip velocity boundary conditions. The analytical results obtained are compared with the direct numerical simulation of the Navier-Stokes equations. The secondary EOFs could transport scalar in larger areas and increase the scalar gradients, which significantly improve the mixing rate of scalars. It is shown that the heterogeneous zeta potentials could generate complex flow patterns and be used to enhance scalar mixing.
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