  While heat transport by baroclinic turbulence in oceans and planetary
atmospheres is well described by a two-layer model, the relative depth of the
two layers varies greatly depending on the situation of interest, making it an
important parameter governing the transport properties of the system. Focusing
on the low-drag turbulent regime, we extend the vortex-gas scaling theory to
address the case of arbitrary layer depths. To wit, we map the
arbitrary-layer-depth system onto an equivalent equal-depth system with
rescaled parameters, establishing the asymptotic validity of the mapping for
weak bottom drag. This approach leads to quantitative predictions for the
turbulent transport by two-layer baroclinic turbulence with arbitrary layer
depths, without additional free parameters. We validate these predictions using
an extended suite of numerical simulations with either linear or quadratic
bottom drag.
