A note on Taylor's hypothesis under large-scale flow variation
- 1Department of Mechanical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
- 2Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Fassberg 17, 37077 Göttingen, Germany
- 3Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria
- 4Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany
Abstract. Experimental investigations of turbulent velocity fields often invoke Taylor's hypothesis (also known as frozen turbulence approximation) to evaluate the spatial structure based on time-resolved single-point measurements. A crucial condition for the validity of this approximation is that the turbulent fluctuations are small compared to the mean velocity, in other words, that the turbulence intensity must be low. While turbulence intensity is a well-controlled parameter in laboratory flows, this is not the case in many geo- and astrophysical settings. Here we explore the validity of Taylor's hypothesis based on a simple model for the wavenumber-frequency spectrum that has recently been introduced as a generalization of Kraichnan's random sweeping hypothesis. In this model, the fluctuating velocity is decomposed into a large-scale random sweeping velocity and small-scale fluctuations, which allows for a precise quantification of the influence of large-scale flow variations. For turbulence with a power-law energy spectrum, we find that the wavenumber spectrum estimated by Taylor's hypothesis exhibits the same power-law as the true spectrum, yet the spectral energy is overestimated due to the large-scale flow variation. The magnitude of this effect, and specifically its impact on the experimental determination of the Kolmogorov constant, are estimated for typical turbulence intensities of laboratory and geophysical flows.