Comparison of Temporal and Spatial Scales in Atmospheric Flow

Taylor’s frozen turbulence is the central assumption in atmospheric boundary layer turbulence studies, where turbulent fluxes are typically observed by sensors recording wind velocity fluctuations as a function of time. Many studies have investigated the validity of Taylor’s hypothesis, and found it strongly scale dependent. In this presentation, we will present an alternative method to Taylor’s hypothesis. It is based on comparison of peak factors. The peak factor is the difference between the maximum and the mean of the time series normalized by its standard deviation. It can be calculated using various temporal (or spatial) scales. The maximum of the time series depends on the duration of the sample but also on the width of the moving average window. The mean wind speed and the standard deviation depend on the sample duration too, but not on the moving average window, because both of these are calculated from the raw data. When peak factors are calculated with varying time (or length) scales of the moving average window, it is possible to construct a 2-dimensional field of median peak factors as a function of sample duration (or length) and width of the moving average window in terms of time (or distance). When these median peak factors are calculated from turbulence measurements collected at a single point as a function of time or from data measured as a function of distance, such as that from a research aircraft, one can obtain two 2-dimensional peak factor fields, which can be fitted together on the basis of linear least squares. The result provides the length scale counterparts for the time scales. First experimental results have shown firm results that do not satisfy the assumption of Taylor’s hypothesis. Possible reasons for this will be discussed in the presentation.