M. Núñez, J. Álvarez and J.
A direct method to calculate the
energy evolution of a turbulent flow, Appl.
Math. Modelling, 31 (2007), pp. 1067-1078.
The classical configuration
of the power spectrum of a homogeneous turbulent flow provides a
functional relation between energy and enstrophy which may be used to
find the evolution of energy in the intermediate stages of finite time
and viscosity to which the usual asymptotic arguments do not apply. The
method has a minimal computational cost compared with the direct
numerical integration of the whole Navier-Stokes system. It is applied
here to study the energy evolution both theoretically and numerically,
obtaining the minima of energy compatible with the power spectra as
well as the rate of decay of the energy towards them. The results may
be useful to study the compatibility of the Kolmogorov and Kraichnan
spectra with the observed energy evolution of a turbulent flow.
PACS classification codes: 47.27.Gs; 47.27.Cn; 02.60.Lj; 02.30.Nw
Preprint file as PDF energy.pdf