Bibliography - M D Cox

1. Cox, M D., 1989: An idealized model of the world ocean. Part I: The global-scale water masses. Journal of Physical Oceanography, 19(11), 1730-1752.
   Abstract PDF

   A primitive equation, three-dimensional numerical model of the ocean, employing idealized versions of the real topography and surface boundary conditions, is used to study the water mass structure of the World Ocean. In particular, the response of the model to three fundamental changes in boundary conditions is investigated in an attempt to identify the mechanisms in the model which are responsible for the establishment of the largest scale features of the global water-mass structure. With the Drake Passage closed, thermohaline driving alone, and a fresh North Atlantic surface salinity specified, only the coarsest aspects of the observed T and S structure are reproduced and the entire World Ocean below the thermocline is dominated by water formed at the southern boundary. The salinity configuration, in particular, lacks much of its observed structure in this case. When the Drake Passage is opened, the resulting circumpolar flow serves to isolate the extreme southern ocean. This allows waters of northern and midlatitude origin to invade the subthermocline zones, producing the familiar tongues of fresh water at intermediate depths. Wind driving further isolates the extreme Southern Ocean and improves the shape and positioning of the fresh water lenses, particularly in the Southern Ocean. Finally, increasing the salinity of water formed at the surface of the northern Atlantic produces distinct salinity maxima in the deep water throughout the World Ocean, bringing the overall salinity structure into broad agreement with observations. Passive tracers are used to establish water mass origins.

2. Böning, C, and M D Cox, 1988: Particle dispersion and mixing of conservative properties in an eddy-resolving model. Journal of Physical Oceanography, 18(2), 320-338.
   Abstract PDF

   We examine the diffusive behavior of the flow field in an eddy-resolving, primitive equation circulation model. Analysis of fluid particle trajectories illustrates the transport mechanisms, which are leading to uniform tracer and potential vorticity distributions in the interior of the subtropical thermocline. In contrast to the assumption of weak mixing in recent analytical theories, the numerical model indicates the alternative of tracer and potential vorticity homogenization on isopycnal surfaces taking place in a nonideal fluid with strong, along-isopycnal eddy mixing. The eastern, ventilated portion of the gyre appears to be sufficiently homogeneous to allow the concept of an eddy diffusivity to apply. A break in a random walk behavior of particle statistics occurs after about 100 days when along-flow dispersion sharply increases, indicative of mean shear effects. During the first months of particle spreading, eddy dispersal and mean advection are of similar magnitude. Eddy kinetic energy is if O(60-80 cm² s^-2) in the model thermocline, comparable to the pool of weak eddy intensity found in the eastern parts of the subtropical oceans. Eddy diffusivity in the model thermocline (K_xx = 8 x 10⁷, K_yy = 3 x 10⁷ cm² s^-1) seems to be higher by a factor of about 3 than oceanic values estimated for these areas. Below the thermocline, model diffusivity decreases substantially and becomes much more anisotropic, with particle dispersal preferentially in the zonal direction. The strong nonisotropic behavior, prominent also in all other areas of weaker eddy intensity, appears as the major discrepancy when compared with the observed behavior of SOFAR floats and surface drifters in the ocean.

3. Cox, M D., 1987: An eddy-resolving numerical model of the ventilated thermocline: Time dependence. Journal of Physical Oceanography, 17(7), 1044-1056.
   Abstract PDF

   A primitive equation, eddy-resolving numerical model is used to study the inherent time scales of variability in the subtropical ocean, assuming temporally constant surface forcing. Three primary scales arise: mesoscale variability of roughly 50-day period, zonally elongated barotropic bands of a 1.1-year period, and basin-scale undulations of approximately 4-year period. The latter are identified as first baroclinic mode Rossby waves, associated with bursts of ventilation at isopycnal outcrops. As a result, the equatorward transport required by the Sverdrup theory in the subtropics occurs not as a broad, sluggish drift throughout the interior, but as a succession of more intense flows that slowly propagate westward. The zonally elongated bands agree in characteristics to those predicted from the theory of homogeneous turbulence. Eddy energy that is generated by baroclinic instability leaks from baroclinic to barotropic mode and thereafter, due to rotational constraints, seeks low zonal wavenumbers. The group velocity of the zonal bands is such that they tend to concentrate in the western interior of the subtropical gyre. The resulting anisotropy in eddy energy produces stronger zonal than meridional mixing by eddy processes in the model.

4. Cox, M D., 1985: An eddy resolving numerical model of the ventilated thermocline. Journal of Physical Oceanography, 15(10), 1312-1324.
   Abstract

   A three-dimensional, primitive equation numerical model is used to study the effects of mesoscale eddies within the subtropical thermocline. Solutions are obtained for an ocean bounded by idealized topography and driven by simple wind and buoyancy forcing at the surface. Results using an eddy-resolving, fine grid are compared to those using a noneddy-resolving, coarser grid. Relatively little difference is realized in the basic, mean flow patterns of the two solutions. However, more significant differences are seen in the distributions of a passive tracer and the potential vorticity. Mixing by eddies in the westward flowing sector of the subtropical gyre is quite effective in homogenizing these quantities on isopycnals. Whereas previous theory has predicted homogenization of potential vorticity on long time scales within recirculating gyres, the present model demonstrates homogenization on a much shorter time scale, across recirculationg/ventilating flow boundaries. Anomalous potential vorticity that is advected into the thermocline from isopycnal outcrops by ventilated flow causes changes in sign of the meridional gradient of local potential vorticity, which in turn gives rise to baroclinic instability. The resulting eddies serve to homogenize the anomalous potential vorticity with its environment. Net poleward heat transport is quite similar in the two solutions. Equatorward heat transport by time variant flow due to eddies is compensated by an additional contribution of the eddies to the mean meridional circulation, producing a net heat transport nearly the same as that of the noneddy-resolving solution.

5. Cox, M D., and Kirk Bryan, 1984: A numerical model of the ventilated thermocline. Journal of Physical Oceanography, 14(4), 674-687.
   Abstract PDF

   A steady state numerical solution is found for an idealized, rectangular ocean basin driven by wind and surface buoyancy flux. A three-dimensional primitive equation model is used. In agreement with recent analytical modeling, the thermocline in the numerical solution consists of three regions, quite distinct in their ventilation characteristics. Forming the greater part of the subtropical thermocline is an unventilated "pool" zone located in the core of the subtropical gyre, and a "ventilated" zone to the east. The unventilated "shadow" zone lies farther east and toward the equator. Analysis of potential vorticity on constant density surfaces is used to study the structure of the thermocline. A small but intense zone of convection located in the western boundary outflow, caused by rapid heat loss to the atmosphere, produces source water for the ventilated zone. This water of extremely low potential vorticity (mode water), is distributed widely into the subtropical thermocline. The pool zone forms equatorward of the convective influence, although lateral mixing in the western boundary current provides indirect ventilation within this region. Trajectory analysis is used to illustrate the effects of the individual terms in the density equation on potential vorticity.

6. Cox, M D., August 1984: A Primitive Equation, 3-Dimensional Model of the Ocean: GFDL Ocean Group Technical Report No. 1, Princeton, NJ: Geophysical Fluid Dynamics Laboratory / NOAA, 163pp.
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7. Cox, M D., 1983: A numerical model of the ventilated thermocline. Ocean Modelling, 49, 5-7.
8. Cox, M D., 1981: A numerical study of surface cooling processes during summer in the Arabian Sea In Monsoon Dynamics, Cambridge, UK, Cambridge University Press, 529-540.
   Abstract

   One of the primary causes of surface cooling in the Arabian Sea during late spring and early summer is upwelling along the Somali and Arabian coasts. Along the Somali coast, upwelling apparently occurs as rather intense mesoscale phenomena associated with variations in the Somali Current. A three-dimensional numerical model of an equatorial ocean indicates that the formation and behaviour of these upwelling areas is sensitive to the orientation of the western boundary. Analysis of the local vorticity sources and sinks in the model solution indicates that the movement of the systems along the coast is caused by an imbalance between advective effects, producing northeastward motion, vortex stretching and the beta-effect producing southwestward motion, and the curl of the wind stress which is capable of producing either. These results suggest that surface cooling may be very sensitive to wind scales of the order of the baroclinic radius of deformation of the ocean near the coast.

9. Cox, M D., 1980: Generation and propagation of 30-day waves in a numerical model of the Pacific. Journal of Physical Oceanography, 10(8), 1168-1186.
   Abstract

   A multilevel numerical model is applied to the equatorial Pacific Ocean, driven by long-term averaged, monthly varying winds. In agreement with satellite-observed sea surface temperatures, the solution is unstable at certain times of year and gives rise to waves of 1.1 month period and 1000 km wavelength just north of the equator in the central and eastern longitudes. A stability analysis of the flow indicates that the initial eddy energy is drawn from the mean flow via horizontal shearing instability between the South Equatorial Current and the North Equatorial Countercurrent. However, as the waves reach larger amplitude, significant conversion from potential to eddy kinetic energy takes place as well. The growth rate is found to increase strongly as vertical stratification is decreased. There are various planetary waves which are available to carry the wave energy away from the generation area. Internal Rossby-gravity and Rossby waves can carry energy downward and eastward, while external Rossby waves can carry energy poleward and eastward. Evidence for these mechanisms is investigated in the model solution. Vertical radiation by the internal waves is found to provide a significant sink of energy from the surface layers. The existence of wave energy of approximately a 1 month period in the real ocean at locations remote from the generation area may be explained by one or more of these propagating modes.

10. Cox, M D., 1979: A numerical study of Somali Current eddies. Journal of Physical Oceanography, 9(2), 311-326.
    Abstract

    A three-dimensional numerical ocean model is used to study the transient response of the western boundary region of a tropical ocean to the sudden onset of winds parallel to the boundary. In particular, the behavior of resulting western boundary current eddies is studied as a function of various parameters of the model. Alongshore eddy movement is found to decrease and vanish as the horizontal orientation of the western boundary is changed from northward to northeastward. A similar retarding effect is produced upon increasing the nonlinearity of the flow by using weaker vertical turbulent friction or stronger wind stress. Little sensitivity is found to the magnitude of the horizontal turbulent friction coefficient. A term-by-term evaluation of the vorticity balance in the region of the eddies is used to analyze their behavior. A case is run in which the western boundary configuration and applied wind stress approximate that of the northwestern Indian Ocean. An eddy structure evolves which is similar to that observed, indicating that the vorticity balances found in the model may be similar to those determining eddy behavior in the real ocean.

11. Cox, M D., 1979: 30-day waves in a numerical model of the equatorial Pacific. Ocean Modelling, 28, 1-4.
12. Cox, M D., 1976: Equatorially trapped waves and the generation of the Somali Current. Deep-Sea Research, Part I, 23, 1139-1152.
    Abstract

    A three-dimensional numerical model is used to study and compare two previously proposed theories for the development of the Somali Current. The rapid propagation of internal planetary waves at the equator provides a means whereby a baroclinic western boundary current can be established quickly, even by remote winds. This theory, first developed for the linear case by Lighthill, is studied numerically and extended to the nonlinear case. Local winds, parallel to the western boundary, and the accompanying Ekman suction, also produce a western boundary current, although different in spatial and temporal characteristics from the above. Comparison with observations indicates that local driving is dominant during the establishment of the current. Remote forcing may produce significant alterations in the flow later. In the nonlinear cases, horizontal shearing instability produces eddy-like features in the western boundary current similar to those observed.

13. Cox, M D., 1975: A baroclinic numerical model of the world ocean: Preliminary results In Numerical Models of Ocean Circulation, Washington, DC, National Academy of Sciences, 107-120.
14. Orlanski, Isidoro, and M D Cox, 1973: Baroclinic instability in ocean currents. Geophysical Fluid Dynamics, 4, 297-332.
    Abstract PDF

    Unstable waves in a western boundary current are investigated in a full three-dimensional, numerical model. A numerical integration is carried out which traces the evolution of a growing wave on an initially uniform current with vertical shear. As indicated in earlier analytic studies based on simpler 2-layer models (Orlanski, 1969) the current is baroclinically unstable for the observed parameter range of the Gulf Stream. Large meanders of the jet in the western boundary current are noticeable within 10 days. Finite amplitude effects, which can be investigated by the numerical model, reduce the growth rate of the disturbance by nearly an order of magnitude compared to linear theory. Comparison with observations indicate that the meanders of the Florida Current between Miami and Hatteras are probably baroclinically unstable waves.

15. Bryan, Kirk, and M D Cox, 1972: The circulation of the world ocean: A numerical study. Part I, An homogenous model. Journal of Physical Oceanography, 2(4), 319-335.
    Abstract PDF

    Calculations are carried out for an homogenous model of the World Ocean. Solutions for the large-scale, wind-driven circulation are obtained by numerical integration with respect to time of a numerical model. The model includes 9 levels in the vertical and has an horizontal resolution of 2 degrees x 2 degrees in latitude and longitude. Subgrid-scale motions are included implicitly through the eddy viscosity hypothesis. The level of viscosity is adjusted so that only scales of motion large enough to be resolved by the numerical model will have appreciable amplitude. Compared with available observations, the model with uniform depth tends to underpredict the strength of the transport in the Northern Hemisphere boundary currents, but overpredict the strength of the Antarctic Circumpolar Current and the East Australian Current. When bottom topography is taken into account, the Northern Hemisphere transport patterns are not greatly altered, but transport of the Antarctic Circumpolar Current and the East Australian Current are drastically reduced.

16. Cox, M D., 1970: A mathematical model of the Indian Ocean. Deep-Sea Research, Part I, 17(1), 47-75.
    Abstract

    A numerical model is formulated to study the current and water mass properties of the Indian Ocean. Particular emphasis is placed on the investigation of the Somali Current and its seasonal response to the monsoonal wind field. The model is three dimensional and, within the limits of the resolution of the numerical network used, has the observed shape of the Indian Ocean with respect to both lateral and bottom boundaries. Observed, seasonally varying data are used for boundary conditions. With these features, the ocean circulation calculations of this study are probably the most detailed that have ever been carried out. The problem is solved by an extended numerical integration of the time-dependent equations. A coarse net is used at the beginning, and is replaced by successively finer nets as equilibrium is approached. The total period of integration is two centuries. The final solution compares favorably with observed current and water mass data. The seasonal behavior of the Somali Current in the model is in particularly good agreement with that observed. Its phase relationship to the driving monsoons is studied and an analogy is drawn with a simple externally driven oscillating system with damping.

17. Bryan, Kirk, and M D Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating: Part I. Description of the three-dimensional velocity and density fields. Journal of the Atmospheric Sciences, 25(6), 945-967.
    Abstract PDF

    A numerical experiment is carried out to investigate the circulation of an ocean, driven by a prescribed density gradient and wind stress at the surface. The mathematical formulation includes in one model most of the physical effects that have been considered in previous theoretical studies. Starting out from conditions of uniform stratification and complete rest, an extensive numerical integration is carried out with respect to time. Care is taken in the final stages of the calculation to use a finite difference net which resolves the very narrow boundary layers which form along the side walls of the basin. A detailed description is made of the three-dimensional velocity and temperature patterns obtained from the final stage of the run. Since inertial effects play an important role in the western boundary current, it is possible to verify with a baroclinic model two results obtained previously with barotropic ocean models: 1) a concentrated outflow from the western boundary takes place along the upper boundary of the subtropic wind gyre; and 2) inertial recirculation may increase the total transport of the boundary current to a value well above that given by linear theory. In addition to the western boundary current, a strong eastward flowing current is found along the equator. Taking into account a difference in Rossby number between model and prototype, the intensity of the computed currents agrees very closely to observations in the Gulf Stream and the Equatorial Current.

18. Bryan, Kirk, and M D Cox, 1968: A nonlinear model of an ocean driven by wind and differential heating: Part II. An analysis of the hear, vorticity and energy balance. Journal of the Atmospheric Sciences, 25(6), 968-978.
    Abstract PDF

    An analysis is made of the heat and vorticity balance of a numerical model of a baroclinic ocean. The computation is carried out on a three-dimensional grid designed to resolve the thermocline, and the narrow sidewall boundary layers at the coasts. A vorticity analysis indicates almost perfect geostrophic balance in the interior. In the immediate vicinity of the western wall the vorticity balance at a given level is dominated by lateral friction and vortex stretching associated with upwelling. The "beta" effect plays an important, but somewhat lesser role. A study of the heat balance in the interior shows that lateral advection is of primary importance in the upper part of the model ocean as it removes heat received at the surface in areas of wind-induced downwelling. Some of this heat is carried to the western boundary where is compensates the cooling due to upwelling and convective transfer through the surface. An examination of the time-dependent motion indicates a regular downstream movement of eddies in the western boundary current. These eddies extend throughout the water column and give rise to a Reynolds stress which acts to retard the time-averaged flow. In a test run with bottom friction included, these eddies are slowly damped.

19. Bryan, Kirk, and M D Cox, 1967: A numerical investigation of the oceanic general circulation. Tellus, 19(1), 54-80.
    Abstract

    An oceanic basin of uniform depth is considered. It is bounded laterally by two meridians. Temperature and wind stress are specified as functions of latitude at the upper surface. The physical model is similar to that used in previous models of the oceanic thermocline, except that the momentum equations of the horizontal velocity components are retained in nearly complete form. Solutions are obtained by the direct numerical integration of a corresponding initial value problem using an electronic computer. Dimensional analysis indicates that the system depends on 5 basic parameters. The geophysically significant range of these parameters is investigated in 8 numerical experiments. Computations with and without wind stress show the interaction of the thermohaline and the wind-driven components of the large scale circulation. Without wind a single large anticyclonic gyre extends over the entire surface of the basin. There is a shallow western boundary current, extending to high latitudes, and a vertically uniform southward drift in the interior from the surface down to the base of the thermocline. A sluggish cyclonic gyre exists below the thermocline. The addition of a wind stress pattern corresponding to a maximum in the westerlies at 45 degrees N leads to the formation of an additional cyclonic gyre in subarctic latitudes. In spite of the simplified boundary conditions the solutions with wind stress reproduce many details of the observed density structure in the North Atlantic, particularly in the subtropical gyre. A more quantitative comparison with North Atlantic data indicates that choice of the vertical diffusion coefficient to be 1 cm²/s gives an approximate fit to the thermocline depth and estimates of the total poleward transport of heat. The corresponding renewal time for deep water, however, is considerably less than that indicated by C¹⁴ data.

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