It can be assumed that the Doppler spectrum is dominated by one single particle population that leads to a strong and narrow peak, which in some (but not all) cases is indicated by high kurtosis. If the spectrum has kurtosis <3 then it is called platykurtic, or platykurtotic. The shape of such a spectrum (in some cases) may have a lower, wider peak around the mean and thinner tails, but it can also be infinitely peaked, so kurtosis is not a good measure of "peakedness." Examples of such shapes can be found in the kurtosis wiki entry.