Von Kármán originally deduced his spectrum of
wind speed fluctuation based on the Stockes-Navier equation.
That derivation, however, is insufficient to exhibit
the fractal information of time series, such as wind velocity
fluctuation. This paper gives a novel derivation of
the von Kármán spectrum based on fractional Langevin
equation, aiming at establishing the relationship between
the conventional von Kármán spectrum and fractal dimension.
Thus, the present results imply that a time series
that follows the von Kármán spectrum can be taken as
a specifically fractional Ornstein-Uhlenbeck process with
the fractal dimension 5/3, providing a new view of the famous
spectrum of von Kármán’s from the point of view
of fractals. More importantly, that also implies a novel relationship
between two famous spectra in fluid mechanics,
namely, the Kolmogorov’s spectrum and the von Kármán’s.
Consequently, the paper may yet be useful in practice,
such as ocean engineering and shipbuilding.