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The vigorous turbulence that results from convective instability within rotating stars serves to not only transport heat but also redistribute angular momentum and chemical species, and can yield magnetic dynamo action. A hallmark of such turbulence constrained by rotation and stratification is that large-scale coherent structures and strong mean flows can coexist with the intense smaller-scale turbulence. Helioseismology is suggesting that the resulting differential rotation within the convection zone of a star like the sun yields serious puzzles about the interaction of convection and rotation. Understanding such nonlinear dynamics at a fundamental level raises formidable challenges because of the broad range of scales of motion that must be resolved. High-performance computing offers the opportunity to make substantial inroads in studying the properties of such astrophysical turbulence. An interdisciplinary team of researchers at several institutions is working jointly on problems in geophysical and astrophysical fluid dynamics (GAFD) turbulence to utilize massively parallel architectures to increase the spatial resolution in three-dimensional simulations employing variously pseudo-spectral, finite-difference, multi-grid and PPM approaches in studying the intense turbulence encountered in both planetary and stellar settings. The scale of these simulations requires corresponding progress in the computational sciences, both in order to develop and optimize software for massively-parallel computers and to capture and visualize the resulting massive data sets. A selection of highlights from our turbulence research will be presented, turning for instance to local-area models of turbulent compressible convection within stellar envelopes. The turbulence possesses both intense vortex filaments with intricate interactions and instabilities, and more persistent and spatially-coherent downflow networks, along with strong mean flows when the rotational constraint is prominent. We also consider the convective turbulence and mixing achieved within the full nuclear burning cores of rotating A-type stars, finding that such penetrative convection drives substantial differential rotation.
