Representation of eddies in climate models by a potential vorticity flux
Citable URI
http://hdl.handle.net/1912/4721DOI
10.1575/1912/4721Keyword
Eddies; VortexmotionAbstract
This thesis addresses the parameterization of the heat and momentum transporting
properties of eddy motions for use in threedimensional, primitive equation, zcoordinate
atmosphere and ocean models. Determining the transport characteristics of these eddies
is fundamental to understanding their effect on the largescale ocean circulation and
global climate.
The approach is to transform the primitive equations to yield the altered 'transformed
Eulerian mean' (TEM) equations. The assumption is made that the eddy motions obey
quasigeostrophic dynamics while the mean flow obeys the primitive equations. With this
assumption, the TEM framework leads to the eddies appearing as one term, which acts
as a body force in the momentum equations. This force manifests itself as a flux of
potential vorticity (PV)  a quantity that incorporates both eddy momentum and heat
transporting properties. Moreover, the dynamic velocities are those of the residual mean
circulation, a much more relevant velocity for understanding heat and tracer transport.
Closure for the eddy PV flux is achieved through a fluxgradient relationship, which
directs the flux down the large scale PV gradient. For zonal flows, care is taken to ensure
that the resulting force does not generate any net momentum, acting only to redistribute
it. Neglect of relative vorticity fluxes in the PV flux yields the parameterization scheme
of Gent and McWilliams.
The approach is investigated by comparing a zonallyaveraged parameterized model
with a three dimensional eddyresolving calculation of flow in a stressdriven channel. The
stress at the upper surface is communicated down the water column to the bottom by
eddy form drag. Moreover, lateral eddy momentum fluxes act to strengthen and sharpen
the mean flow, transporting eastward momentum up its large scale gradient. Both the
vertical momentum transfer and lateral, upgradient momentum transfer by eddies, are
captured in the parameterized model.
The advantages of this approach are demonstrated in two further zonal cases: 1) the
spindown of a baroclinic zone, and 2) the atmospheric jet stream.
The time mean TEM approach and the eddy PV flux closure are explored in the
context of an eddyresolving closed basin flow which breaks the zonal symmetry. Decomposition of eddy PV fluxes into components associated with advective and
dissipative effects suggest that the component associated with eddy flux divergence, and
therefore forcing of the mean flow, is mainly directed down the large scale gradient
and can be parameterized as before. Thus, the approach can be used to capture eddy
transport properties for both zonal mean and time mean flows.
The PV flux embodies both the eddy heat and momentum fluxes and so presents
a more unified picture of their transferring properties. It therefore provides a powerful
conceptual and practical framework for representing eddies in numerical models of the
atmsophere and ocean.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 1999
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