Ocean climate models are unlikely routinely to have sufficient
resolution to resolve the turbulent ocean eddy field. The need for the
development of improved mesoscale eddy parameterisation schemes
therefore remains an important task. The current dominant mesoscale eddy
closure is the Gent and McWilliams scheme, which enforces the
down-gradient mixing of buoyancy. While motivated by the action of
baroclinic instability on the mean flow, this closure neglects the
horizontal fluxes of horizontal momentum. The down-gradient mixing of
potential vorticity is frequently discussed as an alternative
parameterisation paradigm. However, such a scheme, without careful
treatment, violates fundamental conservation principles, and in
particular violates conservation of momentum.
A new parameterisation framework is presented which preserves
conservation of momentum by construction, and further allows for
conservation of energy. The framework has one dimensional parameter, the
total eddy energy, and five dimensionless and bounded geometric
parameters. The popular Gent and McWilliams scheme exists as a limiting
case of this framework. Hence the new framework enables for the
extension of the Gent and McWilliams scheme, in a manner consistent with
key physical conservations.