Two-dimensional turbulence properties of the ECMWF reanalyses

Abstract

A spherical harmonic analysis is made of the stationary and transient rotational motions during14 winter and 15 summer seasons from the reanalyses of the European Centre for Medium-Range Weather Forecasts (ECMWF) for the northern hemisphere. Vertically-integrated kineticenergy, enstrophy, rotational non-linear interactions and the baroclinic source term are diagnosedas a function of total wavenumber n. The contributions to the non-linear transfers fromtriads involving wavenumber and frequency bands of meterological relevance are mapped. Theinter-seasonal and intra-seasonal variability are computed. The non-linear energy and enstrophytendencies and fluxes are examined and compared to existing geophysical turbulence theories.The transient divergent kinetic energy is less than the rotational energy. The spectral energyslope seen in the range n ˜ 10—40 is roughly - 2.5 ˜ - 2.6. Based on the variability of the slopeon seasonal and 10-day time scales, this slope is significantly different than - 3. There is noindication of the – 5/3 mesoscale energy regime seen in observations. A broad enstrophy dissipationregimes is seen for n > 40. Non-linear terms transfer transient energy from a band centeredat n ˜ 15 to one at n ˜ 7, with the latter predominantly associated with non-zonal (zonal wavenumberm0) flow. Non-linear terms transfer mean energy from n=7 to the mean zonal flowm=0, n=3 and n=5. The non-linear transfer of transient energy is quite variable, with about 16% of 10-day periods yielding a tendency twice the mean, and 16% showing no upscaletendency whatever. This variability is greatly reduced when interactions involving only synopticscales (n ˜ 10—40) are retained. The latter set of interactions are associated mostly with triadsinvolving both high and low frequencies, with associated periods in the 1–9 day and 11—90range, respectively. Non-local planetary wave advective interactions play an important rôle inthe downscale transfer of enstrophy. More local interactions involving synoptic scales dominatethe non-linear energy transfers. The main seasonal effects are a weakening in summer of thetotal energy and shifting to higher wave number of the peak, and a distinct shift to smallerscales in the transition between the large-scale and synoptic-scale regimes in the energy budget.The predominant time scale for non-linear maintenance of the planetary waves (about 9 days)is roughly the same as that of the baroclinic support of larger synoptic scale waves. The timescale of baroclinic conversion which maintains the smaller synoptic waves (n ˜ 20—40) is shorter(about 4 days).