Coastal vorticity tendency from variable surface drag ($[\nabla \times (-r\mathbf{u}){]}_z=-r\zeta -(\nabla r\times \mathbf{u}{)}_z$)

Spatially varying drag has a vorticity tendency beyond simple damping of existing relative vorticity. The cross-gradient term depends on wind direction and the gradient of surface resistance. Increasing roughness on moving from ocean to land does not alone specify a universal cyclonic or anticyclonic sign. Seasonal heating also changes stratification and isentropic mass thickness, so it cannot generally be replaced by adiabatic PV conservation.