The structure and dynamics of buoyant plumes arising from surface-based heat sources in a vertically sheared ambient atmospheric flow are examined via simulations of a three-dimensional, compressible numerical model. Simple circular heat sources and asymmetric elliptical ring heat sources that are representative of wildland fires of moderate intensity are considered. Several different coherent vortical structures that dominate the plume structure and evolution are evident in the simulations, and these structures correspond well with those observed in plumes from wildland fires. For the circular source, these structures include: (i) a counter-rotating vortex pair aligned with the plume trajectory that is associated with a bifurcation of the plume, (ii) transverse shear-layer vortices on the upstream face of the plume, and (iii) vertically oriented wake vortices that form periodically with alternating sign on either side of the downstream edge of the plume base. For the elliptical ring source, a streamwise counter-rotating vortex pair is apparent on each flank, and a transverse horizontal vortex is observed above the head of the source. In all simulations the plume cross section is represented poorly by a self-similar Gaussian distribution.