# Simple Analytical Solutions For Potential Vorticity Intrusions

May 9, 2012

Matt Masarik

*Hosted by* Wayne Schubert (Advisor), Dave Randall, Eric Maloney, Richard Eykholt (Physics)

## Abstract

Using potential temperature (theta) as the vertical coordinate, we derive analytical solutions of the potential vorticity (PV) invertibility principle for the case in which the flow is y-independent and an isolated PV anomaly is confined within an ellipse in the (x,theta)-plane. The solutions aid in understanding the dynamics of low latitude PV intrusions whose associated cloud patterns are often referred to as tropical plumes, or atmospheric rivers and whose flow patterns are often referred to as tropical upper tropospheric troughs (TUTTs). The solutions illustrate the phenomenon of isentropic upglide below an upper tropospheric positive anomaly in PV. They also quantify how the partition of PV between vorticity and static stability depends on the shape and strength of the PV anomaly. Reanalysis data is consulted as a check on the solutions. Finally, a numerical model is constructed where approximations made in the analytical theory can be examined.