Abstract:Secondary circulation plays an important role in the intensifying and maintenance of typhoon. The Sawyer Eliassen (SE) equation derived based on gradient wind balance is usually used to diagnose the secondary circulation of typhoon. However, the gradient wind balance has large errors within and near the boundary layer, which leads to large errors of the secondary circulation solved by SE equation within the boundary layer. Based on the full formation of the radial momentum equation, a novel SE equation is derived in this paper. The supergradient force including the radial friction of boundary layer is therefore considered in the novel SE equation. And it turns out that the supergradient force can modulate the secondary circulation by affecting the coefficients related to baroclinicity in SE equation. The diagnostic analysis of the typhoon Sinlaku (2008) shows the novel SE equation can improve the solved secondary circulation remarkably without subjective modifying the flow structure near boundary layer. The novel SE equation can avoid the false convection at the out flank of the eyewall in and near the boundary layer, and can reduce the false strong boundary layer inflow.