Lateral coherence in isotropic turbulence and in the natural wind

A short review of experimental findings is given, followed by a theoretical derivation, based on Taylor's hypothesis, of formulas for lateral coherences. It is assumed that the flow is stationary and homogeneous. Explicit formulas are derived assuming an energy spectrum pertaining to the inertial subrange. Even when the last assumption is not fulfilled, there are only four different types of non-zero velocity coherences. These four coherences correspond to the combinations uu, vv, ww, and uv, where u, v, and w are the longitudinal, the transversal, and the vertical component of the turbulent velocity with respect to the direction of the horizontal mean wind velocity U. In the case of small displacements relative to the scale of turbulence, the coherences are shown to be universal functions of the non-dimensional frequency nD/¦U¦, where n is the frequency and D the lateral displacement. It is shown that these theoretical formulas for spectral coherences are in good agreement with atmospheric data. Finally, the role of the scale of the turbulence is discussed.