A closure for meso-scale eddy fluxes based on linear instability theory

Abstract Linear instability theory is used to predict the lateral diffusivity K for eddy buoyancy fluxes in an idealized channel model, following a suggestion by Killworth (1997) . The vertical structure and magnitude of K agree approximately with the non-linear model results. The lateral structure of K from linear theory lacks minima within eddy-driven zonal jets, pointing towards a non-linear mechanism for mixing barriers in the channel model. This effect can be accounted for by a modification of K from linear theory by the kinematic effect of the background flow following a recent suggestion by Ferrari and Nikurashin (2010) . Implementation of this closure for K in an eddy mixing framework based on potential vorticity mixing in a zonally averaged model version yields approximate agreement with the zonally resolved version over a certain range of external parameters, in particular with respect to the reproduction of eddy-driven zonal jets.

[1]  Raffaele Ferrari,et al.  Suppression of Eddy Diffusivity across Jets in the Southern Ocean , 2010 .

[2]  D. Gurarie,et al.  Rhines scale and spectra of the beta-plane turbulence with bottom drag. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  J. Pedlosky,et al.  A mechanism of formation of multiple zonal jets in the oceans , 2009, Journal of Fluid Mechanics.

[4]  Peter D. Killworth,et al.  On the parameterization of eddy transfer. Part I. Theory , 1997 .

[5]  J. Marshall,et al.  Enhancement of Mesoscale Eddy Stirring at Steering Levels in the Southern Ocean , 2010 .

[6]  Isaac M. Held,et al.  Parameterization of Quasigeostrophic Eddies in Primitive Equation Ocean Models. , 1997 .

[7]  Patrick Heimbach,et al.  Estimating Eddy Stresses by Fitting Dynamics to Observations Using a Residual-Mean Ocean Circulation Model and Its Adjoint , 2005 .

[8]  M. Spall,et al.  Specification of eddy transfer coefficients in coarse resolution ocean circulation models , 1997 .

[9]  Richard J. Greatbatch,et al.  A Diagnosis of Thickness Fluxes in an Eddy-Resolving Model , 2007 .

[10]  Carsten Eden,et al.  Thickness diffusivity in the Southern Ocean , 2006 .

[11]  John Marshall,et al.  On the Parameterization of Geostrophic Eddies in the Ocean , 1981 .

[12]  J. Gregory.  Middle atmosphere dynamics , 1981, Nature.

[13]  D. Olbers,et al.  Interpreting Eddy Fluxes , 2007 .

[14]  F. Bretherton.  Critical layer instability in baroclinic flows , 1966 .

[15]  P. Killworth.  Boundary Conditions on Quasi-Stokes Velocities in Parameterizations , 2001 .

[16]  M. Maltrud,et al.  Assessing Eddy Heat Flux and its Parameterization: A Wavenumber Perspective from a 1/10 ocean simulation , 2009 .

[17]  M. McIntyre,et al.  Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers , 2008 .

[18]  Carsten Eden,et al.  Parameterising meso-scale eddy momentum fluxes based on potential vorticity mixing and a gauge term , 2010 .

[19]  P. Gent,et al.  Isopycnal mixing in ocean circulation models , 1990 .

[20]  J. Green,et al.  Transfer properties of the large‐scale eddies and the general circulation of the atmosphere , 1970 .

[21]  J. Marshall,et al.  Scales, Growth Rates, and Spectral Fluxes of Baroclinic Instability in the Ocean , 2011 .

[22]  John Marshall,et al.  Estimates and Implications of Surface Eddy Diffusivity in the Southern Ocean Derived from Tracer Transport , 2006 .

[23]  P. Welander,et al.  Lateral friction in the oceans as an effect of potential vorticity mixing , 1973 .

[24]  P. Gent,et al.  Eliassen–Palm Fluxes and the Momentum Equation in Non-Eddy-Resolving Ocean Circulation Models , 1996 .

[25]  C. Eden,et al.  Towards a mesoscale eddy closure , 2008 .