ENERGY,ENERGY FLUX AND LAGRANGIAN OF ROSSBY WAVE

The energy flux derived from the barotropic vorticity equation differs from that obtained directly from the momentum equation.We re-study this problem raised in the early 1960s.The results show that if the momentum equation is rewritten in such a way that it contains the same conditions as that for the baro- tropic vorticity equation,then the same form of average energy flux can be obtained for the waves with constant amplitudes.With this new momentum equation,the potential energy of Rossby wave is derived and Lagrangian of nonlinear barotropic vorticity equation can be approximately found with this potential energy.This provides a physical basis for studying the dynamics of nonlinear Rossby wave with the approach of calculus of variation.

Typical Circulation Patterns and Associated Mechanisms for Persistent Heavy Rainfall Events over Yangtze–Huaihe River Valley during 1981–2020

Persistent heavy rainfall events(PHREs)over the Yangtze–Huaihe River Valley(YHRV)during 1981–2020 are classified into three types(type-A,type-B and type-C)according to pattern correlation.The characteristics of the synoptic systems for the PHREs and their possible development mechanisms are investigated.The anomalous cyclonic disturbance over the southern part of the YHRV during type-A events is primarily maintained and intensified by the propagation of Rossby wave energy originating from the northeast Atlantic in the mid–upper troposphere and the northward propagation of Rossby wave packets from the western Pacific in the mid–lower troposphere.The zonal propagation of Rossby wave packets and the northward propagation of Rossby wave packets during type-B events are more coherent than those for type-A events,which induces eastward propagation of stronger anomaly centers of geopotential height from the northeast Atlantic Ocean to the YHRV and a meridional anomaly in geopotential height over the Asian continent.Type-C events have“two ridges and one trough”in the high latitudes of the Eurasian continent,but the anomalous intensity of the western Pacific subtropical high(WPSH)and the trough of the YHRV region are weaker than those for type-A and type-B events.The composite synoptic circulation of four PHREs in 2020 is basically consistent with that of the corresponding PHRE type.The location of the South Asian high(SAH)in three of the PHREs in 2020 moves eastward as in the composite of the three types,but the position of the WPSH of the four PHREs is clearly westward and northward.Two water vapor conveyor belts and two cold air conveyor belts are tracked during the four PHREs in 2020,but the water vapor path from the western Pacific is not seen,which may be caused by the westward extension of the WPSH.