On the annual variation and spectral distribution of atmospheric energy

Abstract

A study is made of the annual variation of the six components, A,, A,, K,, K,, K,, and K,, of the energy in the atmosphere based on data from a complete year, February 1963-January 1964, and on eight vertical levels. The distribution of the energy with respect to pressure and time of the year is investigated with the result that all forms of energy have a maximum in the beginning of the year and a minimum during the month of July.The energy conversions C ( A , , A , ) , C ( K , , K,) and C(K,, K,) are also investigated during the period. The most remarkable result is the annual variation of C(K,, K,) showing a maximum during the fall, a phenomenon also observed during the previous year.Fourier analysis of the data in time is employed to determine the amplitude and phase of the first few components. The first component contains a considerable fraction of the annual variations, but the second component in in certain cases, as for example C (K,, K,), very important in describing the annual behavior. A similar analysis is niitde of three years of data with essentially the same results. The latter set of energy data is used to determine the annual variation of the generation of available potential energy and the frictional dissipation using the energy equations, while the data for 1!)63 are used to calculate the energy conversion C ( A , K ) and the generation C ( A ) based on the energy equations and an assumption concerning the frictional dissipation.The last section of the paper contains a desrription of the results of an investigation of the energy spectra showing that in the range of wave nuinhers 8 < n . .1R we ran tipproximate the form of the spectra by a power law: E ~~ m'n-'. n and b are determined by regression analysis.W e shall also investigate some propertirs of the spectra, in particular t h e functional relationship between the amorint of energy and t h e wave number.

Progress in research on atmospheric turbulence

“…:/en turbulence hypothesis for the larger scales, . 'nc-dimensional spatial spectra computed from synoptic ^teorological data [Julian et al, 1970;Kao, 1968;,M\ 1969;Winn-Nielsen, 1967] agree in confirming r.e tvistence of a large-scale k~3 range, as predicted '"eoretieally for two-dimensional turbulence by Batche- Kraichnan [1967], and Lcith [1967] and ^daeed in numerical simulation experiments by Lilly ,g t>9, 19716]. Mesoscale spatial spectra are rare, but 11968] shows that they may be obtainable from .^craft-measured Doppler winds.…”

Analysis of the “Spinup” of a general circulation model

“…The KE is actually larger than KZ for the first 26 days but reaches a plateau after about day 60. The total kinetic energy appears to be within 10% of its final value and the KZ appears to be destined for a value very close to the 1365 kJ m -2 of Wiin- Nielsen [1967].…”

A Generalization of Lorenz’s Model for the Predictability of Flows with Many Scales of Motion

“…At the time of the L69 writing, it was just becoming apparent that the observed energy spectrum of the large-scale (presumably two dimensional) flow has a power-law behavior most consistent with p ϭ 3 (Wiin-Nielsen 1967). Moreover it had only recently been discovered that the energy spectra downscale of a largescale forcing is, according to the 2DV, also one with p ϭ 3 (Kraichnan 1967).…”