On the phenomenology underlying Taylor's hypothesis in atmospheric turbulence

Abstract

G.I. Taylor's hypothesis of transposition of turbulent statistics from the spatial to the temporal domain (and vice-versa) is usually explained in terms of smaller features being advected by a large-scale transport velocity, while intrinsic temporal velocity fluctuations are slower than the corresponding inertial terms, and turbulent velocity fluctuations remain small in comparison with the transport velocity. This formulation, widely known as ``frozen turbulence'', is undoubtedly correct in laboratory experiments where the stated conditions are being fulfilled, and perhaps in many natural settings. However, temporal structure functions of measured velocities in the atmospheric boundary layer during periods of higher transport velocities (tropical day time), when compared with periods of low activity (night time), show a very similar behavior, hereby raising the question whether the space--time similarity of turbulent fluctuations in terms of statistical moments is really due only to transport-like advection, or there might exist a different underlying phenomenology leading to the same result, and accounting for the behavior during low-advection periods. Based on the multifractality observed in the structure functions, the alternative explanation of a 4-D space-time multifractal field is suggested.