A new form of the of the omega equation was produced in the appendix of Hoskins, Mcintyre and Robertson HMR(1986). This new form links together three theories of mid-latitude cyclones, the PV approach, the omega equation approach and the parcel theory approach. The new form splits the vertical motion into three parts which are the isentropic vertical velocity, the boundary temperature advection vertical velocity and the PV advection vertical velocity. The isentropic vertical velocity is the vertical velcity which is required so that air ascends along isentropes. If all the vertical velocity is provided by the isentropic upglide alone when viewing the system- being defined as the major PV or boundary temperature anomaly- at its system speed then the system is said to be steady. The boundary temperature advection vertical velocity is the vertical velocity required to satisfy the boundary conditions. The PV advection vertical velocity is the vertical velocity which advects the isentropes in the vertical associated with the advection of PV. It is the sum of the boundary temperature and PV advection vertical velocity in a system relative framework which tells you about development. The boundary temperature advection vertical velocity giving growth/decay without a change in the structure of the system and the PV advection vertical velocity giving growth/decay with a change in the structure of the system.
The new form has been applied to various idealised states such as the Eady model, the Venetian blind IPV anomaly a delta function in PV and a ball of uniform PV. Where the roles played by the vertical motions in given growth/decay are epmphasised.
The LC1 baroclinic life cycle was also examined in the light of the new form at the inital and later satges. In the initial stages the boundary temperature advection vertical velocity was found to dominate and is responsible for the growth of the mode. During the later stages the boudanry temperature advection vertical velocity becomes less as low-level temperature gradients are wiped out and the PV advection vertical velocity is found to become significant.
Real cases will also be looked at seeing the roles the various terms of the new form give in determining growth and decay of the system.
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