  Discussions on a form of a frequency spectrum of wind-driven sea waves just
above the spectral maximum have continued for the last three decades. In 1958
Phillips made a conjecture that wave breaking is the main mechanism responsible
for the spectrum formation (Phillips, 1958). That leads to the spectrum decay
$\sim \omega^{-5}$, where $\omega$ is the frequency of waves. There is a
contradiction between the numerous experimental data and this spectrum.
Experiments frequently show decay $\sim\omega^{-4}$ (Toba, 1973),(Donelan et
al, 1985), and (Hwang et al, 1999). There are several ways of the explanation
of this phenomenon. One of them (proposed by Banner (Banner, 1990)) takes into
account the Doppler effect due to surface circular currents generated by
underlying waves in the Phillips model.
  In this article the influence of the Doppler effect on an arbitrary averaged
spectrum is considered using both analytic and numerical approaches. Although
we mostly concentrated on the very important case of Phillips model the
developed technique and general formula can be used for the analysis of other
spectra.
  For the particular case of Phillips spectra we got analytic asymptotics in
the vicinity of spectral maximum and for high frequencies. Results were
obtained for two most important angular dependences of the spectra: isotropic
and strongly anisotropic. Together with the analytic investigation we performed
numerical calculations in a wide range of frequencies. Both high and low
frequency asymptotics are in very good agreement with the numerical results.
  It was shown that at least at low frequencies correction to the spectrum due
to the Doppler shift is negligible. At high frequencies there is an asymptotic
with tail $\sim \omega^{-3}$.
