Parameterization of Mixed Layer Eddies. I: Theory and Diagnosis

Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finiteamplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. In particular it is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

[1]  A. Mahadevan Modeling vertical motion at ocean fronts: Are nonhydrostatic effects relevant at submesoscales? , 2006 .

[2]  M. McIntyre,et al.  Generalized Eliassen-Palm and Charney-Drazin Theorems for Waves on Axismmetric Mean Flows in Compressible Atmospheres , 1978 .

[3]  Amit Tandon,et al.  An analysis of mechanisms for submesoscale vertical motion at ocean fronts , 2006 .

[4]  Patrice Klein,et al.  Oceanic Restratification Forced by Surface Frontogenesis , 2006 .

[5]  Peter H. Stone,et al.  On Non-Geostrophic Baroclinic Stability , 1966 .

[6]  N. Nakamura Scale Selection of Baroclinic Instability--Effects of Stratification and Nongeostrophy. , 1988 .

[7]  J. Price,et al.  Upper Ocean Response to a Hurricane , 1981 .

[8]  Libe Washburn,et al.  The evolving structure of an upwelling filament , 1985 .

[9]  B. Fox‐Kemper,et al.  Parameterization of Mixed Layer Eddies. II: Prognosis and Impact , 2007 .

[10]  T. Schneider,et al.  Self-Organization of Atmospheric Macroturbulence into Critical States of Weak Nonlinear Eddy-Eddy Interactions , 2006 .

[11]  Lee E. Branscome,et al.  The Charney Baroclinic Stability Problem: Approximate Solutions and Modal Structures , 1983 .

[12]  J. W. Zhang,et al.  Eddy-induced mixed layer shallowing and mixed layer/thermocline exchange , 2000 .

[13]  R. Weller Overview of the Frontal Air‐Sea Interaction Experiment (FASINEX): A study of air‐sea interaction in a region of strong oceanic gradients , 1991 .

[14]  M. Alford,et al.  Sub‐mesoscale lateral density structure in the oceanic surface mixed layer , 2006 .

[15]  Robert Pinkel,et al.  Diurnal cycling: observations and models of the upper-ocean response to diurnal heating, cooling, and wind mixing. Technical report , 1986 .

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

[17]  Rudnick,et al.  Compensation of horizontal temperature and salinity gradients in the ocean mixed layer , 1999, Science.

[18]  Thierry Penduff,et al.  Mesoscale Eddies in the Labrador Sea and Their Contribution to Convection and Restratification , 2008 .

[19]  M. Spall Baroclinic Jets in Confluent Flow , 1997 .

[20]  Hsien-Wang Ou Geostrophic Adjustment: A Mechanism for Frontogenesis , 1984 .

[21]  I. Howells An approximate equation for the spectrum of a conserved scalar quantity in a turbulent fluid , 1960, Journal of Fluid Mechanics.

[22]  I. Held,et al.  Eddy Amplitudes and Fluxes in a Homogeneous Model of Fully Developed Baroclinic Instability , 1995 .

[23]  R. Ferrari,et al.  Compensation and Alignment of Thermohaline Gradients in the Ocean Mixed Layer , 2003 .

[24]  Andreas Oschlies,et al.  Improved Representation of Upper-Ocean Dynamics and Mixed Layer Depths in a Model of the North Atlantic on Switching from Eddy-Permitting to Eddy-Resolving Grid Resolution , 2002 .

[25]  V. Canuto,et al.  Modeling mesoscale eddies , 2005 .

[26]  Thomas W. N. Haine,et al.  Gravitational, Symmetric, and Baroclinic Instability of the Ocean Mixed Layer , 1998 .

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

[28]  R. Hallberg The Ability of Large-Scale Ocean Models to Accept Parameterizations of Boundary Mixing , and a Description of a Refined Bulk Mixed-Layer Model , 2003 .

[29]  R. Ferrari,et al.  Frontogenesis, and the Stratification of the Surface Mixed Layer, , 2008 .

[30]  John Marshall,et al.  Convection with Rotation in a Neutral Ocean: A Study of Open-Ocean Deep Convection , 1993 .

[31]  C. Rossby,et al.  On the Mutual Adjustment of Pressure and Velocity Distributions in Certain Simple Current Systems, II , 1938 .

[32]  L. Thomas,et al.  Destruction of Potential Vorticity by Winds , 2005 .

[33]  W. Young The Subinertial Mixed Layer Approximation , 1994 .

[34]  C. Garrett,et al.  Mixed Layer Restratification Due to a Horizontal Density Gradient , 1994 .

[35]  John Marshall,et al.  Open‐ocean convection: Observations, theory, and models , 1999 .

[36]  I. Yavneh,et al.  Baroclinic Instability and Loss of Balance , 2005 .

[37]  R. Ferrari,et al.  On the development of thermohaline correlations as a result of nonlinear diffusive parameterizations , 1997 .

[38]  P. Gent,et al.  Parameterizing eddy-induced tracer transports in ocean circulation models , 1995 .

[39]  L. Perelman,et al.  A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers , 1997 .

[40]  William J. Emery,et al.  Data Analysis Methods in Physical Oceanography , 1998 .

[41]  B. Hoskins Baroclinic waves and frontogenesis Part I: Introduction and Eady waves , 1976 .

[42]  M. Prater,et al.  Circulation and mixing at the New England shelfbreak front: Results of purposeful tracer experiments , 2006 .

[43]  R. Ferrari,et al.  Transformed Eulerian-Mean Theory. Part I: Nonquasigeostrophic Theory for Eddies on a Zonal-Mean Flow , 2005 .

[44]  Noboru Nakamura,et al.  Nonlinear Equilibration of Two-Dimensional Eady Waves , 1989 .

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

[46]  D. Rudnick,et al.  On the horizontal density ratio in the upper ocean , 2002 .

[47]  K. Tung,et al.  Nonlinear baroclinic adjustment , 1991 .

[48]  T. Schneider,et al.  The Surface Branch of the Zonally Averaged Mass Transport Circulation in the Troposphere , 1999 .

[49]  R. Samelson,et al.  Evolution of the instability of a mixed-layer front , 1995 .

[50]  P. Killworth Parameterization of Eddy Effects on Mixed Layers and Tracer Transport: A Linearized Eddy Perspective , 2005 .

[51]  G. Holloway,et al.  Stirring and transport of tracer fields by geostrophic turbulence , 1984, Journal of Fluid Mechanics.

[52]  W. Blumen On Short-Wave Baroclinic Instability , 1979 .

[53]  R. Salmon,et al.  Geophysical Fluid Dynamics , 2019, Classical Mechanics in Geophysical Fluid Dynamics.