where f is the wave frequency, V = u + va is the inertial-frame speed (u is the solar wind plasma velocity, and va - the Alfven velocity), r - the heliocentric distance. The given form of the spectral flux function F(f, r) corresponds to the Kolmogorov cascade phenomenology. It is proportional to the cascade constant a = 1.25 and to the square root of the ratio of the inward and outward wave intensity, a1, which is a model parameter taken to depend on r, only. The flux-tube cross-sectional area A is inversely proportional to the magnetic field B, which is taken to point in the radial direction.

According to Vainio et al. (2003a) the Alfven wave power spectrum can be solved in an analytic form if a1 is a given function of position. In this case the spectrum can be given as

Vas f53 Pf0

where the dimensionless function I(x,r) fulfils the equation

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