On the spectral distribution of kinetic energy in large-scale atmospheric flow

Abstract

Abstract. A one-dimensional form of the equation of motion with forcing and dissipation is formulated in the spectral domain and used to make long term integrations from which the spectral distribution of the kinetic energy is determined The forcing in the wave number domain is determined in advance and kept constant for the duration of the time integrations. The dissipation is proportional to the second derivative of the velocity. The applied equation is made non-dimensional by selecting a length scale from which the time scale and the velocity scale may be determined. The resulting equation contains no parameters apart from the forcing. The integrations use a large number of spectral components and no approximation is made with respect to the non-linear interaction among the spectral components. Starting from an initial state in which all the velocity components are set to zero the equation is integrated for a long time to see if it reaches a steady state. The spectral distribution of the kinetic energy is determined in the steady state, and it is found that the distribution, in agreement with observational studies, may be approximated by a power law of the form n-3 within certain wave number regions. The wave numbers for which the -3 power law applies is found between the region of maximum forcing and the dissipation range. The intensity of the maximum forcing is varied to see how the resulting steady state varies. In addition, the maximum number of spectral components is varied. However, the available computing power sets an upper limit to the number of components.