Turbulent length-scales in the marine atmospheric mixed layer

The spectra of turbulence signals can be characterized by several independe nt scales. To provide a parametrization of these spectra requires knowledge of the relationships between these scales. This paper focuses on three ind ependent scales: the integral scale (which is influenced by the low-frequen cy behaviour of the spectral; the wavelength of the spectrum peak (which ch aracterizes the energy-containing domain); and the dissipation scale (which is relevant for the inertial subrange). First, we present definitions of t hese various scales, and the possible relationships between them. The profi les of the scales were computed from airborne measurements made in the atmo spheric mixed layer over the open ocean, in a region where horizontal homog eneity can be assumed, at least for several tens of km. Furthermore, the di urnal cycle being Very weak in this oceanic area, and aircraft moving at hi gh speed through the air mass, stationarity is well verified on the runs, a nd Taylor's hypothesis may be used. The meteorological conditions correspon d to a slightly unstable mixed layer, with weak to moderate winds. in a fir st part, we analyse the integral scales of various parameters on a 180-km r un and demonstrate that these parameters cannot be computed with any soundn ess from horizontal-wind, temperature and moisture signals, because of the continuous increase in the spectral energy when moving towards lower freque ncies. For the same reasons, the spectrum peak and the corresponding wavele ngth cannot be determined for these parameters. The computation of the inte gral and energy-containing scale is therefore restricted to the vertical ve locity, and to the various covariances. The turbulence field is characteriz ed by a stretching of the eddies along the mean wind direction which result s in greater integral and energy-containing scales (but not in greater diss ipation scales) when computed for along-wind runs than for the cross-wind r uns. The profiles of the various scales increase with altitude and are well defined in the lower half of the mixed layer, but are much more scattered in the upper half. This behaviour is related to the source of turbulence, w hich lies in the surface buoyancy flux in the lower half of the mixed layer and comes from higher altitude sources in the upper half. The integral sca les have values comparable with those found in previous work, except for pa rameters related to temperature fluctuations, which have lower values. The ratio of the energy-containing scale to the integral scale, which determine s the sharpness of the 'spectral knee', varies considerably from one parame ter to another, and sometimes with altitude. This demonstrates that a singl e unique parametrization cannot be defined for turbulence spectra. As a con sequence, the eddy-exchange coefficients, which depend on a characteristic length-scale, should vary from one parameter to another. This would then ha ve to be taken into account in model parametrization based on mixing length -scales.