Piecewise Potential Vorticity Inversion without Far-Field Response?

Abstract

Given a flow domain D with subdomains D1 and D2, piecewise potential vorticity inversion (PPVI) inverts a potential vorticity (PV) anomaly in D2 and assumes vanishing PV in D1 where boundary conditions must be taken into account. It is a widely held view that the PV anomaly exerts a far-field influence on D1, which is revealed by PPVI. Tests of this assertion are conducted using a simple quasi geostrophic model where an upper layer D2 contains a PV anomaly and D1 is the layer underneath. This anomaly is inverted. Any downward physical impact of PV in D2 must also be represented in the results of a downward piecewise density inversion (PDI) based on the hydrostatic relation and the density in D2 as following from PPVI. There is no doubt about the impact of the mass in D2 on the flow in the lower layer D1. Thus results of PPVI and PDI have to agree closely.