Summary: When hurricanes become strong, they sometimes form a second eyewall around the main eyewall. This second ring of strong winds and heavy rain means that strong, damaging winds could cover a larger area than before. However, it also means that the storm might temporarily weaken. Understanding and predicting this process is therefore very important. Data from National Oceanic and Atmospheric Administration hurricane-hunter aircraft and other sources are used to explain how these secondary eyewalls may form when the winds surrounding the storm vary in speed and direction with height (what we call vertical wind shear; see Figure).
(left) Wind speed and direction at different altitudes; (right) wind speed and direction at 5000 ft and 38,000 ft (solid arrows), and vertical wind shear speed and direction between 5000 ft and 38,000 ft altitude (dashed arrow). Left and right of shear marked.
A second hurricane eyewall can start to form when inward-flowing jets of air in the lowest 10,000 feet of the atmosphere reach the outer portion of the hurricane where lines of thunderstorms (called rainbands) occur.
The second eyewall and its strong winds develops first in the area to the left of the direction of the vertical wind shear.
You can read the study at https://journals.ametsoc.org/doi/full/10.1175/JAS-D-17-0348.1