Horizontal cascade structure of atmospheric fields determined from aircraft data
Résumé
Aircraft measurements of the power spectra of the horizontal wind field typically find a transition from approximate to k(-5/3) to approximate to k(-2.4) at scales somewhere around 40 km (k is a wave number). In the usual interpretation this represents a transition between an isotropic three-dimensional (3-D) (k(-5/3)) and an isotropic 2-D(k(-3)) turbulence; we have recently argued that the turbulence is so highly anisotropic that it has different exponents in the horizontal and vertical. When coupled with gently sloping isobaric aircraft trajectories this predicts the break as a transition from a roughly horizontal spectrum at small scales to the spurious appearance of the vertical spectrum at large scales. If the atmosphere indeed has wide-range horizontal scaling, then it is important to test out the multiplicative cascade models that predict its statistical behavior. In this paper, we do this by analyzing wind, temperature, pressure, and humidity data from the Winter Storm 2004 experiment using 24 aircraft legs, each 1120 km long and at 280 m resolution. We analyze both the turbulent fluxes and the fluctuations showing that in spite of the nonflat trajectories, there is good evidence of roughly planetary-scale multiplicative cascades. By carefully determining the scale-by-scale effects of intermittency on the aircraft altitude and measurements, we estimate the corresponding scaling exponents. We argue that our results should finally permit the emergence of a long-needed consensus about the basic scale-by-scale statistical properties of the atmosphere.