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The devastating power of hurricanes was evident during the 2005 hurricane season, the most active season on record. This has prompted increased efforts by researchers to understand the physical processes that underlie the genesis, intensification, and tracks of hurricanes. This research aims at facilitating an improved understanding into the structure of hurricanes with the aid of visualization techniques. Our approach was developed by a mixed team of visualization and domain experts. To better understand these systems, and to explore their representation in NWP models, we use a variety of illustration-inspired techniques to visualize their structure and time evolution. Illustration-inspired techniques aid in the identification of the amount of vertical wind shear in a hurricane, which can help meteorologists predict dissipation. Illustration-style visualization, in combination with standard visualization techniques, helped explore the vortex rollup phenomena and the mesovortices contained within. We evaluated the effectiveness of our visualization with the help of six hurricane experts. The expert evaluation showed that the illustration-inspired techniques were preferred over existing tools. Visualization of the evolution of structural features is a prelude to a deeper visual analysis of the underlying dynamics.