Interpretation of Clarke's Doppler power spectral density
A simple, "non-technical" way of thinking of it is the fact that the Doppler frequency is proportional to $\cos\theta$. The amplitudes of cosine, however, are not uniformly distributed, but are heavily weighted towards $\pm 1$. 

Example plot to demonstrate, using Python/Pylab code:

theta = linspace(0, 2*pi, 1001)
x = cos(theta)
hist(x)




More rigor can be seen by noting that 
\begin{align}
f &amp;= f_d \cos\theta\\
\theta &amp;= \cos^{-1}\left(\frac{f}{f_d}\right)
\end{align}
and the power received at any angle is proportional to a small angle increment $d\theta$:

$$
P(\theta) \propto d\theta = \frac{-1}{f_d\sqrt{1-\left(\frac{f}{f_d}\right)^2}} df
$$

And the total power can be determined by integrating the above quantity, which is identically what defines a power spectral density.