Investigation of the frozen-turbulence hypothesis for temperature spectra in a convectively mixed layer

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Abstract
Taylor’s frozen turbulence hypothesis is investigated in a laboratory free‐convection mixed layer which can simulate buoyancy‐driven turbulence in an atmospheric mixed layer (of height h) for mean wind speeds of up to several meters per second. For large turbulence intensities the temperature spectra at the height 0.1h are found to be spuriously enhanced at higher wavenumbers based on the frozen turbulence hypothesis, as deduced theoretically by previous investigators. The excess is borrowed from spectral intensities within the energy‐containing range. A theory based on the concept of longitudinal‐temporal isotropy, after proper scaling of the coordinates, is shown to predict a simple shift of the entire spectrum toward higher wavenumbers with increasing turbulence intensity. The failure of the observed spectra to behave this simply is associated with a complicated structure of the correlation coefficient as a function of longitudinal‐temporal lag coordinates when the former is measured relative to a frame moving with the mean flow speed. The temperature spectrum based on the frozen‐turbulence hypothesis appears to be a satisfactory representation of the true spectrum in wavenumber space, in tubulence dominated by thermal convection, if the mean wind speed exceeds 2.7–3.6 times the root‐mean‐square horizontal velocity fluctuation.