Bryan-Cox Model Research Articles

A numerical study of barotropicly forced intrusion in DeSoto Canyon

The intrusion of open ocean water across the head of DeSoto Canyon offshore of Pensacola, Florida, is investigated using a version of the Bryan‐Cox model of the entire Gulf of Mexico. The Loop Current‐forced model circulation in DeSoto Canyon features an eastward, nearly along‐isobath, current with a weak cross‐isobath velocity component. In contrast, the southward wind‐driven currents over the west Florida shelf in response to northerly winds induce strong cross‐isobath flow at the head of DeSoto Canyon. The flow is diagnosed to be the bottom Ekman flow associated with the strong along‐isobath currents. In addition, transient responses of sea levels to the northerly wind bursts give rise to pressure gradient‐forced currents up the canyon during the collapse phase of the winds. A case study in November 1997 is conducted, and the above arguments are substantiated with the simulated and the observed currents.

A Numerical Model Calculation of the Flow in DeSoto Canyon in Response to Northerly Wind Bursts in Winter

The continental shelf currents observed at the head of DeSoto Canyon offshore of Pensacola, FL, during Nov, 1997-Feb. 1998, are studied with the aid of a Bryan-Cox model of the entire Gulf of Mexico. The basic model circulation with no winds features a Loop Current and a weak flow in DeSoto Canyon. In contrast, the model response to northerly wind bursts produces strong canyon currents. Wind-driven southward currents on the West Florida Shelf (WFS) appear to pull a strong flow around DeSoto Canyon, giving rise to a strong up-canyon flow on the west flank The wind-enhanced flow in DeSoto Canyon is reproduced with a model run that incorporates wind stresses derived from the NCEP-NCAR reanalysis winds for March 1997-April 1998. The model flow for the winter period (Nov. 1997-Feb. 1998) is compared with observed currents at three canyon-head locations in 100 m of water available from a Science Applications International Corporation mooring experiment. Model and observed velocities in the general around-canyon direction track each other reasonably well, with peaks synchronized roughly with but lagging slightly northerly wind bursts. The lag time appears consistent with the generation at Key West of first-mode continental shelf waves responsible for wind-driven alongshore currents on the WFS. Pressure gradient slightly in excess of that necessary for a geostrophic balance with the (eastward) alongshore flow appears to generate onshore flows, giving rise to midshelf upwelling after northerly wind bursts.

A numerical model comparison of baroclinic instability in the presence of topography

The development of meanders along a front and subsequent eddy formation results in the exchangeof water-mass properties across the front. This is an important phenomenon, both for continentalshelf and basin-scale thermodynamics. In this study, we are concerned with the authenticity ofgrowing baroclinic waves over bottom slope topography in commonly-used primitive equationmodels, as they are such a widely used tool for understanding the dynamics of the ocean. Baroclinicinstability is simulated in a cyclic channel, in 2 such models: the Bryan–Cox model (Cox, 1984)and the Bleck–Boudra (1986) isopycnal model. We focus on the linear stage of instability and onthe effects of topography, with isobaths running parallel to the front. Initially, a quasi-geostrophic(QG), subsurface front is used as a basic state for baroclinic instability in the 2 models. A series ofexperiments with topography are performed, introducing successively steeper topography parallelto the front. The results from the 2 models are verified by comparison with QG theory and resultsfrom a QG numerical simulation. Two versions of the isopycnal model, which employ differentnumerical schemes for advection in the thickness equation, are run for the flat-bottomed experiments. We demonstrate how this choice of numerical scheme can affect baroclinic wave activity.Linear growth rate curves are plotted for each model experiment. The fastest-growing baroclinicwave in a flat channel is shorter in the Bryan-Cox model than that predicted by QG theory, QGnumerical model results, and the Bleck–Boudra isopycnal primitive equation model. This featureis a consequence of the vertical discretization used in this model. The magnitude of the lineargrowth rates is significantly smaller in the Bleck–Boudra isopycnal model than in the Bryan–Coxmodel and the QG simulation, because of implicit diffusion inherent in the numerical scheme usedby this model. The experiments with topography show that this implicit diffusion becomes mostactive in more stable environments. The modifying effects of topography expected from QG resultsare found in both primitive equation models: for topography of positive slope (i.e., with the sameinclination as the isopycnals), the fastest-growing wavelength increases and is damped; for topographyof negative slope, the fastest-growing wavelength decreases. The 2 primitive equationmodels are then initialized with an ageostrophic, outcropping front; and their results are comparedin the light of experience gained from the subsurface front simulations. Again, a series of experimentswith topography are performed. The results from these simulations show how ageostrophic effectsact to stabilize baroclinic waves, but do not change the way that topography modifies them. Similar, numerically-induced, features were found in all the experiments with the ageostrophic, outcroppingfront, as was found with the subsurface front. By focusing on the linear growth of baroclinic waves, this investigation has pinpointed some artificial tendencies inherent in the 2 primitive equationmodels, which modellers will find useful when interpreting the results of their simulations. The important lesson for oceanographers is to remember, that although waves in the numerical modelsare physically well-behaved, the wave characteristics may have been modified by numerical errors, and therefore to exercise care in interpretating the results.

Momentum Fluxes in the Bryan–Cox Ocean Circulation Model

Abstract The velocities used by the original, standard version of the Bryan–Cox model to advect momentum are shown to be inconsistent with the main velocities over steps in the bathymetry. In particular, the vertical shears of the two sets of horizontal velocities disagree at the top edges of steps in the bathymetry. This is shown to be related to the way in which the velocities are divided into baroclinic and barotropic parts when the barotropic flow is represented by a streamfunction. A list of desirable properties for the velocities at the faces of the velocity cells is suggested. Five schemes for calculating them, including Webb’s scheme and two new schemes (which are modified versions of the original scheme), are discussed and their properties derived. Simple estimates are also made of the effect of grid-scale noise in the streamfunction and thermal fields on these horizontal and vertical velocities. The velocities from short integrations of a 1° global model using these schemes are compared. The hor...

Eddy Processes in Semienclosed Seas: A Case Study for the Black Sea

Abstract The enclosed boundaries and small scales of some seas lead to the formation of specific physical balances, which motivates the oceanographic interest in studying the dynamics of semienclosed ocean basins. The focus in the paper is on the specific appearances of eddy processes when the basin scales and the ones of the topographic features are comparable with the baroclinic radius of deformation. The Black Sea is used as a test basin. Eddy variability is analyzed using simulation results and compared with existing observations. The Bryan–Cox model with horizontal resolution Δφ = 1/10° and Δλ = 1/6° is forced with annual-mean wind stress data. Buoyancy flux at the sea surface is proportional to the deviation of the model density from the annual-mean climatological data. Sensitivity studies on different forcing and on the topographic control are carried out. Synoptic periods are estimated to be about 0.5 yr. Eddies form in the eastern Black Sea and propagate westward with a speed of about 3 cm s−1. T...

An Intercomparison of a Bryan–Cox-Type Ocean Model and an Isopycnic Ocean Model. Part I: The Subpolar Gyre and High-Latitude Processes

Abstract This paper describes a model intercomparison between a Bryan-Cox-type ocean model and an isopycnic-coordinate ocean model. The two models are integrated for 30 years on a domain of the North Atlantic stretching from 20°S to 82°N. The main purpose of this work is to illuminate aspects of the respective models that give a realistic representation of the North Atlantic circulation and the physical processes that occur therein, and to identify those which need to be improved. To this end, the same forcing fields and as many of the same parameter settings as possible were chosen so that differences between the models would be due to distinct model features rather than choice of parameters. Where we felt that using the same setup between the models was inappropriate or impossible, we examined the possible difference this could make to the simulators. In the isopycnic model, the path of the North Atlantic Current after separation is simulated quite realistically, whereas in the Bryan-Cox model it become...

Parameter sensitivity study of the saline circulation

Saline circulation forced by fresh water alone is studied for a broad region of parameter space by varying the amplitude and profile of evaporation minus precipitation, the vertical and horizontal mixing of salt, vertical and horizontal dissipation of momentum, and the horizontal resolution. The model is a modified Bryan-Cox model with a freshwater flux as the natural boundary condition for the salinity balance. For a model forced by a linear freshwater flux profile, as the amplitude of freshwater flux is increased from 0.01 m year −1 to 1 m year−1 with other parameters fixed, the system evolves from a steady state of no oscillation to a state of periodic oscillation whose frequency increases almost linearly with the amplitude of freshwater flux. When the freshwater flux is fixed and the vertical mixing coefficient is increased from 0.5 to 2.5 cm2s−1, the system evolves from a steady state to a state of single-period oscillation, chaotic, a single period, and finally to a chaotic state when the vertical mixing coefficient is larger than 2 cm2 s−1. One set of numerical experiments forced by a cosine shape of freshwater flux clearly reveals the transition from a state of single period oscillation to period doubling, period quadrupling, and a state of chaotic oscillation. Simple scaling analysis and numerical experiments indicate that the strength of the meridional overturning increases with the square-root of the vertical mixing and the 1/4 power of the freshwater flux. The mean sea surface salinity (deviation from 35 psu) increases with the 3/4 power of the freshwater flux and decreases with the 1/2 power of the vertical salt mixing.

Mesoscale stability of an ocean current over the continental slope in the Bryan-Cox primitive equation model

The Bryan-Cox primitive equation model is examined in terms of stability of a frontal current over a straight continental slope. The current is produced by a positive or a negative buoyancy anomaly initially given in a limited area over the shelf. The slope current is always stable when a positive buoyancy anomaly is given. Stability of the current produced by a negative anomaly is dependent on the background density stratification: it is stable (unstable) if the background state is such that the pycnocline is shallower (deeper) than the shelf bottom. In the unstable case, the instability is stronger with finer alongshore resolution. A sensitivity study of the instability to topography resolution is carried out by resolving the slope with two kinds of steps: deepening by one level at each grid or by two levels at alternatekinds. The instability is stronger with the smaller steps. A linear stability analysis for the quasi-geostrophic version over a flat bottom shows that baroclinic instability is greatly overestimated in the Bryan-Cox model and sensitive to vertical resolution. The sensitivity of the instability to the step size is related to this character of the baroclinic instability. A careful study of the stability character of the Bryan-Cox model is recommended before the eddy-resolving version is used for forecast purposes.