Turbulent length‐scales in the marine atmospheric mixed layer

Abstract

AbstractThe spectra of turbulence signals can be characterized by several independent scales. To provide a parametrization of these spectra requires knowledge of the relationships between these scales. This paper focuses on three independent scales: the integral scale (which is influenced by the low‐frequency behaviour of the spectra); the wavelength of the spectrum peak (which characterizes the energy‐containing domain); and the dissipation scale (which is relevant for the inertial subrange). First, we present definitions of these various scales, and the possible relationships between them. The profiles of the scales were computed from airborne measurements made in the atmospheric mixed layer over the open ocean, in a region where horizontal homogeneity can be assumed, at least for several tens of km. Furthermore, the diurnal cycle being very weak in this oceanic area, and aircraft moving at high speed through the air mass, stationarity is well verified on the runs, and Taylor's hypothesis may be used. The meteorological conditions correspond to a slightly unstable mixed layer, with weak to moderate winds. In a first part, we analyse the integral scales of various parameters on a 180‐km run and demonstrate that these parameters cannot be computed with any soundness from horizontal‐wind, temperature and moisture signals, because of the continuous increase in the spectral energy when moving towards lower frequencies. For the same reasons, the spectrum peak and the corresponding wavelength cannot be determined for these parameters. The computation of the integral and energy‐containing scale is therefore restricted to the vertical velocity, and to the various covariances. The turbulence field is characterized by a stretching of the eddies along the mean wind direction which results in greater integral and energy‐containing scales (but not in greater dissipation scales) when computed for along‐wind runs than for the cross‐wind runs. 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, which 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 scales have values comparable with those found in previous work, except for parameters related to temperature fluctuations, which have lower values. The ratio of the energy‐containing scale to the integral scale, which determines the sharpness of the ‘spectral knee’, varies considerably from one parameter to another, and sometimes with altitude. This demonstrates that a single unique parametrization cannot be defined for turbulence spectra. As a consequence, the eddy‐exchange coefficients, which depend on a characteristic length‐scale, should vary from one parameter to another. This would then have to be taken into account in model parametrization based on mixing length‐scales.