Despite moderate wind shear, convection soon wrapped around the southeastern side of the low-level circulation. By 21:00 UTC on August 5, the CPHC upgraded the system to a tropical storm, despite continued wind shear. Wind shear quickly decreased, triggering a period of rapid intensification. By the afternoon of August 6, Genevieve intensified to a low-end Category 1 hurricane; the system also developed a central dense overcast and well-organized banding around the newly-developed eye. Passing over very warm ocean temperatures, Genevieve rapidly intensified accelerated that evening. Based on advanced Dvorak technique estimates of as well as the presence of a very well-defined eye surrounded by very cold cloud tops, the CPHC upgraded the hurricane into Category 4 intensity on the Saffir-Simpson Hurricane Wind Scale early on the next day.