Spatially decaying array of vortices

An analysis of two-dimensional vorticity disturbances introduced at a grid and propagating downstream reveals that viscosity causes the x wavenumber to diminish and the phase speed to increase from their inviscid values, while also causing the amplitude to decay exponentially downstream. This decaying disturbance field introduces an adverse mean pressure gradient of strength O (1/RΛ), where RΛ is the Reynolds number based on freestream velocity and vortex diameter. Viscous effects introduce a discrepancy between the two-point and two-time velocity correlations when Taylor’s hypothesis r=U∞t is used to relate the space and time separations. This discrepancy arises because the vortices propagate at a phase speed c greater than the freestream. As RΛ→∞, c→U∞. If Taylor’s hypothesis is modified to r=ct, then the two-point and two-time correlations agree.