Effects of Isopycnal and Diapycnal Mixing on the Stability of Oceanic Currents

Abstract This paper considers several influences of mixing on the stability of oceanic boundary currents, analyzed primarily in terms of the effects of mixing on the distribution of potential vorticity. This perspective relates both to the Charney–Stern criterion for the stability of currents and the Haynes–McIntyre constraints on the evolution of potential vorticity when mixing occurs. It is shown that diapycnal mixing can alter the structure of a stable current so that it becomes potentially unstable according to the Charney–Stern criterion. The effects of isopycnal diffusion and a viscous lateral boundary layer are also considered. Occurrences of instability are then illustrated with both computational solutions and experiments in a rotating tank. Finally, subsurface float trajectories are shown near the coast of Portugal that are suggestive of the instability of the boundary current downstream from the Mediterranean outflow, known to be subject to strong mixing.

[1]  C. Mauritzen,et al.  On the influence of Mediterranean Water on the Central Waters of the North Atlantic Ocean , 2001 .

[2]  Laurent M. Chérubin,et al.  Instability of the Mediterranean Water undercurrents southwest of Portugal : effects of baroclinicity and of topography , 2000 .

[3]  Robert Hallberg,et al.  Time Integration of Diapycnal Diffusion and Richardson Number–Dependent Mixing in Isopycnal Coordinate Ocean Models , 2000 .

[4]  Maria Valdivieso Da Costa.  Numerical Simulations of Boundary Currents of Intermediate Density in Comparaison with Laboratory Experiments : Eddy Formation and Transport. , 1999 .

[5]  B. Le Cann,et al.  Real‐time tracking of a Galician Meddy , 1999 .

[6]  K. Speer,et al.  Mixing in the Romanche Fracture Zone , 1998 .

[7]  M. Spall,et al.  Mesoscale Variability in Denmark Strait: The PV Outflow Hypothesis* , 1998 .

[8]  J. McWilliams,et al.  Localization of Deep Ocean Convection by a Mesoscale Eddy , 1998 .

[9]  M. Baringer,et al.  Mixing and Spreading of the Mediterranean Outflow , 1997 .

[10]  M. Baringer,et al.  Momentum and Energy Balance of the Mediterranean Outflow , 1997 .

[11]  P. Klein,et al.  Effects of an Asymmetric Friction on the Nonlinear Equilibration of a Baroclinic System , 1997 .

[12]  D. Nof,et al.  The eddy cannon , 1996 .

[13]  D. Hu.  The Computation of Diapycnal Diffusive and Advective Scalar Fluxes in Multilayer Isopycnic-Coordinate Ocean Models , 1996 .

[14]  P. Kushner.  A generalized Charney–Stern theorem for semi-geostrophic dynamics , 1995 .

[15]  T. Evans,et al.  On vorticity shedding by unstable jets , 1994 .

[16]  W. Large,et al.  Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization , 1994 .

[17]  G. Johnson,et al.  Stress on the Mediterranean Outflow Plume: Part I. Velocity and Water Property Measurements , 1994 .

[18]  J. Lamarque,et al.  Cross-Tropopause Mass Exchange and Potential Vorticity Budget in a Simulated Tropopause Folding , 1994 .

[19]  B. Cushman-Roisin.  Introduction to Geophysical Fluid Dynamics , 1994 .

[20]  R. Pingree.  Winter warming in the southern Bay of Biscay and Lagrangian eddy kinematics from a deep-drogued Argos buoy , 1994, Journal of the Marine Biological Association of the United Kingdom.

[21]  R. Pingree,et al.  A shallow meddy (a smeddy) from the secondary Mediterranean salinity maximum , 1993 .

[22]  Barry A. Klinger.  Gyre formation at a corner by rotating barotropic coastal flows along a slope , 1993 .

[23]  M. Baringer.  Mixing and dynamics of the Mediterranean outflow , 1993 .

[24]  Bruno Blanke,et al.  Variability of the Tropical Atlantic Ocean Simulated by a General Circulation Model with Two Different Mixed-Layer Physics , 1993 .

[25]  S. Legg,et al.  A heton model of the spreading phase of open-ocean deep convection , 1993 .

[26]  M. Rhein,et al.  Modification of Mediterranean Water in the Gulf of Cadiz, studied with hydrographic, nutrient and chlorofluoromethane data , 1993 .

[27]  Rainer Bleck,et al.  Salinity-driven Thermocline Transients in a Wind- and Thermohaline-forced Isopycnic Coordinate Model of the North Atlantic , 1992 .

[28]  R. Pingree,et al.  Anticyclonic eddy X91 in the southern Bay of Biscay, May 1991 to February 1992 , 1992 .

[29]  R. Pingree,et al.  Three anticyclonic slope water oceanic eDDIES (SWODDIES) in the Southern Bay of Biscay in 1990 , 1992 .

[30]  M. Prater.  Observations and Hypothesized Generation of a Meddy in the Gulf of Cadiz , 1992 .

[31]  J. McWilliams,et al.  The Generation and Evolution of Mushroom-like Vortices , 1991 .

[32]  D. Nof.  Lenses generated by intermittent currents , 1991 .

[33]  P. Ripa.  General stability conditions for a multi-layer model , 1991, Journal of Fluid Mechanics.

[34]  R. Rotunno,et al.  On the formation of potential-vorticity anomalies in upper-level jet-front systems , 1990 .

[35]  M. McIntyre,et al.  On the Conservation and Impermeability Theorems for Potential Vorticity , 1990 .

[36]  J. Whitehead,et al.  Separation of a boundary jet in a rotating fluid , 1990, Journal of Fluid Mechanics.

[37]  Rainer Bleck,et al.  A Wind-Driven Isopycnic Coordinate Model of the North and Equatorial Atlantic Ocean 1 , 1990 .

[38]  M. McIntyre,et al.  Dissipative wave-mean interactions and the transport of vorticity or potential vorticity , 1990, Journal of Fluid Mechanics.

[39]  J. Marshall.  Submarine salt lenses , 1988, Nature.

[40]  Eric A. D'Asaro,et al.  Generation of submesoscale vortices: A new mechanism , 1988 .

[41]  J. Toole,et al.  On the parameterization of equatorial turbulence , 1988 .

[42]  Peter H. Haynes,et al.  On the Evolution of Vorticity and Potential Vorticity in the Presence of Diabatic Heating and Frictional or Other Forces , 1987 .

[43]  Rainer Bleck,et al.  Wind‐driven spin‐up in eddy‐resolving ocean models formulated in isopycnic and isobaric coordinates , 1986 .

[44]  Nelson G. Hogg,et al.  The heton, an elementary interaction between discrete baroclinic geostrophic vortices, and its implications concerning eddy heat-flow , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[45]  R. Pacanowski,et al.  Parameterization of Vertical Mixing in Numerical Models of Tropical Oceans , 1981 .

[46]  P. Gent,et al.  Intermediate Models of Planetary Circulations in the Atmosphere and Ocean , 1980 .

[47]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[48]  J. Charney,et al.  On the Stability of Internal Baroclinic Jets in a Rotating Atmosphere. , 1962 .

[49]  E. O. Holipainen.  On the Effect of Friction in Baroclinic Waves , 1961 .

[50]  John W. Miles,et al.  On the stability of heterogeneous shear flows , 1961, Journal of Fluid Mechanics.

[51]  Louis N. Howard,et al.  Note on a paper of John W. Miles , 1961, Journal of Fluid Mechanics.

[52]  J. Fortuin.  Theory and application of two supplementary methods of constructing density gradient columns , 1960 .

[53]  C. Rossby.  Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action , 1939 .

[54]  T. Labasque,et al.  Descriptive analysis of the hydrology and currents on the Iberian shelf from Gibraltar to Cape Finisterre : preliminary results from the Semane and Interafos experiments , 1997 .

[55]  Jean-Michel Baey.  Instabilites d'un courant d'eau intermediaire , 1997 .

[56]  Molly O. Baringer,et al.  Outflows and deep water production by marginal seas , 1994 .

[57]  J. Lamarque.  Analysis of mass transport and potential vorticity budget in a simulated tropopause folding , 1993 .

[58]  J. Pedlosky.  Geophysical Fluid Dynamics , 1979 .

[59]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .