On Taylor’s hypothesis and the acceleration terms in the Navier-Stokes equation

Abstract

1. Introduction. For turbulence produced behind the grid in a wind tunnel, Taylor1 introduced the assumption that the spatial pattern of turbulent motion is carried past a fixed point by the mean wind speed without any essential change. The assumption has been applied to connect the time spectrum with space correlation, and Taylor found indeed good agreement between theory and experiment. The success of Taylor's hypothesis in the case of wind tunnel turbulence has led people to use it also for shear flow. This is obviously a tentative step until justification can be found. In wind-tunnel turbulence, the justification of this hypothesis is essen-tially based upon the follbwing two conditions: (a) the main flow is uniform, (b) the level of turbulence is low. One purpose of this paper is to demonstrate this justification explicitly as a basis for a similar discussion for shear flow, in which case neither of these conditions are as well satisfied. It seems plausible that an eddy of considerable size would change considerably by the shearing motion while it is carried past a given point by the main flow. In 6, estimates are made for the limitation, due to this cause, of the eddy size in the boundary layer, to which Taylor's hypothesis can be applied; and it appears that the major part of the shear contributing fluctuations are of such low time frequencies that Taylor's hypothesis cannot be immediately justified for its use in the determination of their space