Lateral Mixing in the Eddying Regime and a New Broad‐Ranging Formulation

We survey a number of issues associated with lateral dissipation in eddyresolving ocean models and present two effective techniques. The first is a specification of lateral viscosity that is closely related to that of Chassignet and Garraffo [2001], involving the combined application of biharmonic and Laplacian forms of viscosity. The specification can in principle be applied across a broad range of model resolution, although our testing was performed only at eddy-resolving scale where a relatively simple form suffices. The second is the implementation of the Lagrangian Averaged Navier Stokes (LANSα) alpha subgridscale turbulence scheme in a primitive equation ocean model, with our presentation here being largely a summary of the recent work of Hecht et al. [2008] and Petersen et al. [2008]. As an inherently non-dissipative turbulence parameterization, one can understand the higher levels of eddy variability with LANS-α as coming about through an increase in the effective Rossby radius of deformation.

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

[2]  Eric P. Chassignet,et al.  Impact of wind forcing, bottom topography, and inertia on midlatitude jet separation in a quasigeostrophic model , 1997 .

[3]  M. Maltrud,et al.  Numerical simulation of the North Atlantic Ocean at 1/10 degrees , 2000 .

[4]  Darryl D. Holm,et al.  Implementation of the LANS-α turbulence model in a primitive equation ocean model , 2008, J. Comput. Phys..

[5]  Darryl D. Holm Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics , 2001 .

[6]  M. Maltrud,et al.  An eddy resolving global 1/10° ocean simulation , 2005 .

[7]  Beth A. Wingate,et al.  Efficient form of the LANS-α turbulence model in a primitive-equation ocean model , 2008, J. Comput. Phys..

[8]  É. Deleersnijder,et al.  Overshootings and spurious oscillations caused by biharmonic mixing , 2007 .

[9]  A. Adcroft,et al.  Representation of Topography by Shaved Cells in a Height Coordinate Ocean Model , 1997 .

[10]  A. Nurser,et al.  Spurious diapycnal mixing of the deep waters in an eddy-permitting global ocean model , 2002 .

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

[12]  P. Gent,et al.  Anisotropic GM Parameterization for Ocean Models , 2004 .

[13]  Darryl D. Holm,et al.  Navier-Stokes-alpha model: LES equations with nonlinear dispersion , 2001, nlin/0103036.

[14]  W. R. Holland,et al.  Application of a Third-Order Upwind Scheme in the NCAR Ocean Model* , 1998 .

[15]  T. Rossby The North Atlantic Current and surrounding waters: At the crossroads , 1996 .

[16]  Philip J. Rasch,et al.  Upwind‐weighted advection schemes for ocean tracer transport: An evaluation in a passive tracer context , 1995 .

[17]  Darryl D. Holm,et al.  Baroclinic Instabilities of the Two-Layer Quasigeostrophic Alpha Model , 2005 .

[18]  Darryl D. Holm,et al.  The Navier–Stokes-alpha model of fluid turbulence , 2001, nlin/0103037.

[19]  Y. Mintz,et al.  Numerical simulation of the Gulf Stream and Mid-Ocean eddies , 1977 .

[20]  Stephen M. Griffies,et al.  Fundamentals of Ocean Climate Models , 2004 .

[21]  Patrick J. Hogan,et al.  Impact of 1/8° to 1/64° resolution on Gulf Stream model–data comparisons in basin-scale subtropical Atlantic Ocean models , 2000 .

[22]  Darryl D. Holm,et al.  Implementation of the LANS-alpha turbulence model in a primitive equation ocean model , 2007 .

[23]  Jerrold E. Marsden,et al.  EULER-POINCARE MODELS OF IDEAL FLUIDS WITH NONLINEAR DISPERSION , 1998 .

[24]  Darryl D. Holm Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion , 1999, chao-dyn/9903034.

[25]  Darryl D. Holm,et al.  Modeling Mesoscale Turbulence in the Barotropic Double-Gyre Circulation , 2003 .

[26]  Rainer Bleck,et al.  An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates , 2002 .

[27]  M. Maltrud,et al.  On the grid dependence of lateral mixing parameterizations for global ocean simulations , 2008 .

[28]  Robert Hallberg,et al.  The Role of Eddies in Determining the Structure and Response of the Wind-Driven Southern Hemisphere Overturning: Results from the Modeling Eddies in the Southern Ocean (MESO) Project , 2006 .

[29]  D. G. Andrews,et al.  An exact theory of nonlinear waves on a Lagrangian-mean flow , 1978, Journal of Fluid Mechanics.

[30]  David P. Marshall,et al.  Do We Require Adiabatic Dissipation Schemes in Eddy-Resolving Ocean Models? , 1998 .

[31]  Darryl D. Holm,et al.  Direct numerical simulations of the Navier–Stokes alpha model , 1999, Physica D: Nonlinear Phenomena.

[32]  James C. McWilliams,et al.  Anisotropic horizontal viscosity for ocean models , 2003 .

[33]  Beth A. Wingate The Maximum Allowable Time Step for the Shallow Water α Model and Its Relation to Time-Implicit Differencing , 2004 .

[34]  F. Bryan,et al.  Climate impacts of systematic errors in the simulation of the path of the North Atlantic Current , 2006 .

[35]  Stephen M. Griffies,et al.  Biharmonic Friction with a Smagorinsky-Like Viscosity for Use in Large-Scale Eddy-Permitting Ocean Models , 2000 .

[36]  Walter Munk,et al.  ON THE WIND-DRIVEN OCEAN CIRCULATION , 1950 .

[37]  Stephen M. Griffies,et al.  Spurious Diapycnal Mixing Associated with Advection in a z-Coordinate Ocean Model , 2000 .

[38]  Frank O. Bryan,et al.  Resolution convergence and sensitivity studies with North Atlantic circulation models. Part I: The western boundary current system , 2007 .

[39]  Richard Smith,et al.  Toward a Physical Understanding of the North Atlantic: A Review of Model Studies in an Eddying Regime , 2013 .

[40]  Darryl D. Holm,et al.  Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow , 1998, chao-dyn/9804026.

[41]  Darryl D. Holm,et al.  Regularization modeling for large-eddy simulation , 2002, nlin/0206026.

[42]  Willem Hundsdorfer,et al.  Method of lines and direct discretization: a comparison for linear advection , 1994 .

[43]  Darryl D. Holm,et al.  The Camassa-Holm equations and turbulence , 1999 .