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Kirk Bryan

Abstract

Solutions are obtained for a time dependent, nonlinear model of a wind-driven ocean by a numerical integration of the corresponding initial value problem. Without time dependence the model and boundary conditions are equivalent to those of Munk, Groves and Carrier (1950). The vorticity equation of the model may be put in nondimensional form so that solutions are governed solely by the pattern of the wind stress, a Rossby number for the interior flow, and an effective Reynolds number for the western boundary current. For a Rossby number in the geophysical range, two regimes are found, depending on the Reynolds number. Below a critical value between 50 and 100 a steady-state solution is approached asymptotically. Above this transition a train of moving disturbances forms in the boundary current due to shear flow instability. There is no tendency for the boundary current to break away from the wall in the region of maximum wind curl for the range of Reynolds numbers (0 through 100) investigated.

In examining other mechanisms which might give rise to separation, it is found that recirculations develop behind barriers placed along the western wall. Recirculation in one case increases the transport of the boundary current by 50 per cent compared to the corresponding linear solution. For wind-stress patterns which include areas of both positive and negative curl of the wind stress, southward moving as well as northward moving currents form along the western boundary. The linear response to this pattern includes a diffuse current moving out from the wall where these two currents collide. In the nonlinear model a tendency to conserve vorticity downstream allows this separation current to be as intense as the boundary currents.

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Kirk Bryan

Abstract

The motion of two homogeneous layers of fluid enclosed between horizontal plates, which rotate coaxially at slightly different angular velocities, has been investigated. The solution for the zonally symmetric forced motion is only a slight modification of a solution of Stewartson's (1953) for a single fluid between rotating disks. Experiments with the two-layer system confirmed the existence of symmetric motion, but for a certain range of parameters it was unstable. A criterion for instability of the symmetric flow was developed from appropriate inviscid, quasi-geostrophic frequency equations, using an approximate variational method. A comparison with experiment indicated stability for somewhat greater shear across the interface of the two layers than predicted.

Exploratory experiments in the unstable range demonstrated that the number of disturbances tended to increase directly as the rotation rate and inversely with the density difference. A steady wave pattern was observed only when the horizontal dimensions of the disturbance were comparable to the diameter of the cylindrical container. The shape of the steady disturbance was such as to give a strong transport of momentum inward.

Certain analogies are drawn between eddy circulation observed in the experiments and low-level cyclones in the atmosphere and meanders of upper-level ocean currents.

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Kirk Bryan

Abstract

Solutions corresponding to climatic equilibrium are usually obtained from atmospheric general circulation models by extended numerical integration with respect to time. Because the ocean contains a much wider range of time scales the same procedure is not practical for ocean general circulation models. The ocean contains the same high frequency waves as the atmosphere and in addition, has ultra low frequencies associated with slow diffusion of water mass properties below the main thermocline. For the parameter range in which equilibrium solutions exist, a method based on distorted physics partially circumvents this difficulty. The distorted physics compresses the frequency band of the ocean model by slowing down gravity waves and speeding up abyssal processes. The acceleration of abyssal processes is accomplished by decreasing the local heat capacity without altering the transport and mixing of heat. Numerical integration of the distorted-physics ocean model then converges to equilibrium nearly as efficiently as a atmospheric model of comparable spatial resolution. Equilibrium solutions of the distorted- and nondistorted-ocean models are equivalent because the distortion only involves local derivatives with respect to time. A joint ocean–atmosphere model study provides a practical demonstration of the method.

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CLIMATE AND THE OCEAN CIRCULATION

III. THE OCEAN MODEL

KIRK BRYAN

Abstract

The ocean model used in a calculation of the earth's climate is described in detail. Compared with earlier numerical models used in ocean circulation studies, the present model includes several new features. Temperature and salinity are treated separately. Density is calculated with an accurate equation of state for sea water. The model also includes a method for calculating the growth and movement of sea ice.

Due to the very slow adjustment of the deep water in the ocean model, a numerical integration extending over the equivalent of a century fails to reach a climatic equilibrium. At the termination of the run, the surface layers of the ocean show little change with respect to time, but the average heating rate for the ocean as a whole is 2° per century. The salinity patterns at the termination of the run are highly realistic compared to observations. A halocline forms in the Arctic Zone and a surface salinity maximum is present in the subtropics. A weak salinity minimum at a depth of 1 km indicates an extensive water mass very similar to the Antarctic intermediate water of the Southern Hemisphere. Poleward heat transport is found to be closely related to the intensity of the thermohaline circulation. A vertical mixing coefficient, κ, of 1.5 cm2 sec−1 leads to very reasonable heat exchange with the atmosphere based on estimates of the heat balance of the North Atlantic.

The calculation indicates that the thermal “relaxation” time of the ocean is too long for a numerical integration of the time-dependent equations to be a practical method of finding an equilibrium solution, and new methods should be sought for future calculations of this type.

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Kirk Bryan

Abstract

There are many dynamic similarities between mesoscale eddies in the ocean, and cyclones and anticyclones in the earth's atmosphere. Observational data, however, are still not adequate to explore this analogy in detail. In the present study a new eddy-resolving ocean circulation model, which includes both wind-driving and buoyancy-driving, is used to determine whether mesoscale eddies play a role in poleward buoyancy transport in any way comparable to the role of synoptic scale motions in transporting heat in the atmosphere. Within an Eulerian reference frame, mesoscale eddies transport buoyancy poleward through two mechanisms. One involves the correlation of time-dependent fluctuations of horizontal velocity and buoyancy. The other transport mechanism involves wave-driven cells in the meridional plane. These cells are analogous to the Ferrel cell in the atmosphere, except that the geometry of the ocean basin allows them to be geostrophically balanced. In an eddy-resolving model of ocean circulation, the two mechanisms for buoyancy transport are almost perfectly compensating. Within a Lagrangian framewark, the trajectories of the eddies are largely excursions on isapycnal surfaces. Heat transport may take place by eddies in the renal ocean without eddy buoyancy transport, since temperature gradients always exist on isopycnal surfaces and may be quite strong in polar regions. Mesoscale eddies and the thermohaline circulation in the model can be weakly coupled, because available potential energy created by the large-scale wind stirring provides a primary energy source for baroclinic instability. The model results indicate that the actual measurement of mesoscale eddy transports is extremely difficult, since it involves an accurate determination of the difference between transport by wave-driven, mean flows and by the correlation of the time-dependent fields.

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KIRK BRYAN

Abstract

No Abstract Available.

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Kirk Bryan

Abstract

Michael Cox was a pioneer in the development and application of numerical models to the study of the ocean circulation. His simulation of the response of the Indian Ocean to the monsoons was one of the first applications of a numerical model to seasonal changes in circulation near the equator. Cox's finding that the seasonal reversal of the Somali Current was primarily due to local monsoon-driven coastal upwelling challenged a popular theory that the effects of remote forcing, propagating westward along the equatorial waveguide, were the most important mechanism. In a detailed follow-up study, he was able to demonstrate that remote forcing could only be important near the equator along the Somali Coast and that local driving was the only viable mechanism to explain the amplitude and phase of the main features of the seasonal reversal of the Somali Current.

In another pioneering calculation, Cox was the first to simulate the seasonal changes of the eastern equatorial Pacific, including the Legeckis waves between the South Equatorial Current and the Equatorial Counter Current. From his analysis, he concluded that the Legeckis waves were due to both baroclinic and barotropic instability.

Using observed temperature and salinity data, Cox carried out a new type of diagnostic study of the circulation of the World Ocean. His calculations demonstrated the great importance of adjusting the observed density field in a manner compatible with the constraints imposed by the conservation of mass, temperature, and salinity.

In a detailed comparison of simulations of ocean circulation in eddy- and noneddy-resolving models of simplified geometry, Cox was able to demonstrate that mesoscale eddies could have some very important effects on midlatitude thermocline ventilation by wind-driven downwelling. In particular, the mixing by mesoscale eddies along isopycnal surfaces could be strong enough to erase tracer and potential vorticity gradients over trajectories of less than 2000 km. On the other hand, Cox found that poleward transport of buoyancy was approximately the same in similar runs, which did, or did not, include mesoscale eddies. He concluded that this was due to eddy-time mean flow compensation. A similar phenomenon exists in the weakly driven flows of the earth's stratosphere.

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Kirk Bryan
and
Solomon Hellerman

Abstract

No abstract available.

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Kirk Bryan
and
Elizabeth Schroeder

Abstract

The seasonal range in heat content of the upper two hundred meters of the water column has been calculated for latitude zones between 20N and 65N in the North Atlantic. The calculation was based on 20,000 bathythermograph observations. The average range in heat content from the end of January to the end of August for the entire area is 36 kg-cal per cm2. A maximum heat storage occurs in mid-latitude in an area just north of the mean position of the Gulf Stream.

For comparison, the heat storage due to local heating was computed for the same area. Estimates of net radiation, evaporation and turbulent heat flux by Budyko (1955) were used for this purpose. The average change in heat content over the same period according to this calculation is 31 kg-cal per cm2. The results indicate that, for the Atlantic as a whole, seasonal changes in the transport of heat by ocean currents and/or seasonal changes in the exchange with deeper layers amplify heat storage near the surface at mid-latitudes but reduce it above 50N.

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Syukuro Manabe
and
Kirk Bryan

Abstract

No abstract available.

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