Conditions for baroclinically driven inertia to break the Taylor–Proudman constraint at the Tangent Cylinder

Determine the conditions under which inertia driven by baroclinicity near the Tangent Cylinder boundary is sufficient to break the Taylor–Proudman constraint and permit radial flow across the boundary, including identifying the relevant thresholds in thermal forcing and rotational parameters.

Background

Baroclinicity arises from the misalignment of gravity and temperature gradients promoted by rotation, especially near the cold lateral boundary of the vessel, driving thermal winds and potentially significant inertia at the Tangent Cylinder boundary.

The authors emphasize that while such baroclinic inertia could break the Taylor–Proudman constraint, the specific conditions enabling this breakdown are not established a priori and are crucial for understanding mass and heat exchange across the Tangent Cylinder in planetary cores.