Thermal Wind Imbalance along the Curved Streamline of the Secondary Circulation in Tropical Cyclones

The thermal wind balance in tropical cyclone (TC) eyewalls has been controversial for decades. This study reveals the relationship between the acceleration and curvature on the TC secondary circulation streamline, providing a way to judge thermal wind balance or imbalance in TCs from a simple but clear perspective. According to the relationship between the curvature and acceleration on the streamline, the vertical and radial components of the acceleration cannot be zero simultaneously on the streamline curve, implying that the thermal wind imbalance corresponds to the curvature of the streamline. On the regular scales of TCs, we discuss the conditions of the thermal wind balance approximation and find that the conditions become more stringent with increasing altitudes. In the TC secondary circulation, as an indication of thermal wind imbalance, gradient wind imbalance can be found in the low-level eyewall since there is usually a large curvature when the inflow in the low-level eyewall turns into updrafts sharply. Additionally, gradient wind imbalance also appears at the top level of TC eyewalls because the stringent conditions are too easily broken there.