  We develop an approach for calculating stationary states of rotating
Bose-Einstein condensates in harmonic traps which is applicable for arbitrary
ratios of the rotation frequency to the transverse frequency of the trap
$\omega_{\perp}$. Assuming the number of vortices to be large, we write the
condensate wave function as the product of a function that describes the
structure of individual vortices times an envelope function, varying slowly on
the scale of the vortex spacing. By minimizing the energy, we derive
Gross-Pitaevskii equations that determine the properties of individual vortices
and the global structure of the cloud. For low rotation rates, the structure of
a vortex is that of an isolated vortex in a uniform medium, while for rotation
rates approaching the frequency of the trap (the mean field quantum Hall
regime), the structure is that of the lowest p-wave state of a particle in a
harmonic trap with frequency $\omega_{\perp}$. The global structure of the
cloud is determined by minimizing the energy with respect to variations of the
envelope function; for conditions appropriate to most experimental
investigations to date, we predict that the transverse density profile of the
cloud will be of the Thomas-Fermi form, rather than the Gaussian structure
predicted on the assumption that the wave function consists only of components
in the lowest Landau level.
