  Ertel's potential vorticity theorem is essentially a clever combination of
two conservation principles. The result is a conserved scalar $q$ that
accurately reflects possible vorticity values that fluid parcels can possess
and acts as a tracer for fluid flow. While true at large scales in the ocean
and atmosphere, at increasingly smaller scales and in sharply curved fronts,
its accuracy breaks down. This is because Earth's rotation imparts angular
momentum to fluid parcels and the conservation of absolute angular momentum $L$
restricts the range of centripetal accelerations possible in balanced flow;
this correspondingly restricts vorticity. To address this discrepancy, we
revisit Ertel's derivation and obtain a new conserved scalar $Lq$ that more
properly reflects the behavior of fluid parcels at these small horizontal
scales. Application of the theorem is briefly discussed, with an emphasis on
better understanding oceanic submesoscale and polar mesoscale flows.
