The role of bottom friction in determining plume entrainment and mixing in a quasi-isopycnal model is examined. The model configuration is similar to the DOME working notes' proposal, with a modification for explicit mass inflow at the northern end of a narrow embayment. Experiments for the Gibraltar outflow are also presented.

An entrainment parameterization for deep overflows was introduced in MICOM, based on Hallberg's scheme (2000), including a Richardson number parameterization of turbulent mixing. Experiments to test the sensitivity to the parameters were performed with a regional model for the Gulf of Cadiz. The parameterization was also introduced in a very high resolution simulation of the North Atlantic ocean and Mediterranean. Meddies are obtained both in the regional and North Atlantic model. The results of the regional model experiments and the North Atlantic simulation will be discussed for the Mediterranean outflow. The characteristics of the Denmark Straits overflow as obtained in the North Atlantic simulation will also be presented.

In circulation models of the North Atlantic, overflows across the Greenland-Iceland-Scotland Ridge have long been a component that was not adequately represented. Using the new parameterizations and numerics under investigation in DOME, the modelling community is now beginning to remedy this deficit. As a consequence, the question arises in what respects an improved representation of dense overflow waters actually changes large-scale circulation features. Here, a series of numerical experiments is presented that examines the response of key properties (meridional overturning, heat transport, strength of the Subpolar Gyre, etc.) to prescribed changes in the density and transport of Denmark Straits Overflow Water and to different mixing parameterizations. The ocean model is part of FLAME (Family of Linked Atlantic Model Experiments), a PE-model based on the GFDL-MOM code. Horizontal resolution in the standard experiments is 1/3 degree * cos(latitude), and 45 z-levels are used in the vertical. The bottom boundary layer parameterization is that proposed by Beckmann and Doescher (1997).

A generalization of the vertical coordinate system in the Princeton Ocean Model allows a direct comparison of the behavior of bottom boundary layers in a sigma and in a z-level models, using different vertical grids but identical numerics. Preliminary experiments involve deep water formation in coarse resolution ocean models and overflow processes in high resolution models. One interesting result is that the good representation of bottom boundary layers and overflow processes in terrain-following ocean models may relate to the way horizontal diffusion is treated and the fact that sigma-coordinate models can handle smaller horizontal diffusion than z-level models do. Large horizontal diffusion in z-level models may interfere with the structure of the bottom boundary layer along sloping bottoms and dilute dense water masses. Experiments also show the sensitivity of simulated overflows to advection schemes.

In a rapid high-resolution survey with expendable (XCP/XCTD) profilers in 1998, we collected velocity, temperature and salinity data from the region of the Denmark Strait sill and initial overflow descent. It is in this first descent that most entrainment occurs and the properties of the subsequent deep boundary current are effectively determined. In the same region a train of cyclonic surface eddies appear to be generated by the deep flow through either an instability during the transition of the broad sill or vortex stretching of the overlying water during the initial descent. Despite large spatial and temporal variability in velocity, thickness and transport from our profiles, we have observed a remarkable consistency in both the overflow's pathway and its dilution with distance from the sill. Measurements of near-bottom shear stress (from logarithmic velocity fits) confirm the importance of bottom friction in the momentum balance and descent of the overflow. In addition, the shape of the background density profile into which the plume descends appears to be an important factor in setting the rate of entrainment as well as determining the type of water entrained.

The draft plan for the idealized DOME test cases will be presented. Examples of the 7 suggested test cases will be shown at several different resolutions. The reasoning behind this particular set of cases will be described, as will the key nondimensional parameters which are being altered.

The known intrinsic behavior of the various types of ocean models (sigma-, geopotential-, and isopycnal-coordinate models) will be briefly summarized. The range of published approaches to representing bottom boundary layers in primitive equation ocean models will be briefly described. The works of Beckman and Doescher (JPO, 1997), Campin and Goosse (Tellus, 1999), Killworth and Edwards (JPO, 1999), Gnanadesikan (unpublished), and Song and Chao (JAOT, 2000) for use with Z-coordinate models will be described and contrasted. The work of Hallberg (2000) on entrainment in isopycnal- coordinate models will also be described, including some examples from regional Mediterranean overflow simulations from Stephens and Hallberg (in prep.) or Papadakis and Chassignet (in prep.). It is intended that this talk will provide a common background for many subsequent talks.

An evaluation of the Beckmann-Doescher BBL in a global configuration of NCAR's MOM-based ocean model will be discussed. In addition to hydrography, modeled CFC's are also compared with observational sections. Some improvement is found with use of the BBL, while more substantial improvement is found when under-ice fresh-water forcing is adjusted in a physically plausible way. Testing of the diffusive portion of the BD BBL in conjunction with the inclusion of partial bottom cells in the Los Alamos POP model, which will be the ocean component of version 2 of the CCSM, will also be discussed.

An overview of conservation laws for mass, momentum, and energy at a sharp mixing front, such as generated by a strong downslope flow, is presented. One special type of mixing front being considered is that generated by an internal hydraulic jump in a stratified fluid where turbulence processes lead to vertical mixing of waters. We are investigating physical constraints on the amount of mixing produced by such a feature and also speculating on its relevance to real downslope flows, for example along the Antarctic continental slope. Additionally, a brief depiction of angular momentum conservation is given in this context of downslope shallow water flows and is related to the other, more usual, conservation laws.

The path taken by dense turbulent outflows usually requires the numerical solution of along-flow equations for mass, tracers, and momentum and cannot easily be predicted. Instead, we consider the consequences of two simple assumptions. First, there is a quadratic turbulent bottom drag. Second, the outflow is assumed to be approximately in local equilibrium so that a best-fit formula from atmospheric and ocean surface layer observations, plus large-eddy simulations, due to Zilitinkevich and Mironov, can be used to predict the local thickness. (No energy budget for turbulent bottom layers is known, which is a constant difficulty for numerical models of such layers.) The equilibrium solution is approximately equivalent, for most oceanic conditions, to a constant bulk Richardson or Froude number. It is shown that dense turbulent overflows follow a simple trajectory, in which the rate of depth increase is a constant, until the level of turbulence drops sufficiently that the equilibrium solution becomes invalid. This result is independent of the detailed thermodynamics, entrainment or detrainment, and of the quadratic drag coefficient. Trajectories for the major overflow regions give reasonable results when compared with the limited available data. An argument is given as to why entrainment should only occur over limited regions, with detrainment elsewhere.

A brief description of the development of the Killworth, Edwards, Nurser and Alderson momble code (which has a dynamic-thermodynamic layer embedded beneath MOMA) will be given; recent improvements will be discussed in another talk.

The DOME collaboration is concerned with accurate representation of overflow processes in general circulation models. However, it is difficult to assess this accuracy simply by comparison with observations, where there may be many complicating factors. An alternative is to carry out very high resolution calculations of idealized overflow scenarios in which the physics responsible for entrainment and mixing is explicitly represented. Here we use the MIT ocean model to carry out nonhydrostatic simulations of dense flows over sloping topography with and without rotation. Without rotation a gravity plume descends the slope with entrainment of ambient fluid triggered by shear instability. Strong rotation inhibits the initial descent of dense fluid, and instead baroclinic instability is necessary to carry fluid down the slope. Mixing with ambient fluid now occurs more in the horizontal plane than vertical plane, and the net entrainment of ambient fluid is reduced.

A chronic defect of z-level ocean circulation models is their tendency to overestimate the mixing associated with overflows and downslope currents. A promising way to avoid these problems is to introduce a sub-model of the bottom boundary layer (BBL) into such a code. The strength of such an approach is that advection now takes place along the bottom layer. However it is now necessary to calculate the pressure gradient force driving such flow. As is well known in the sigma-coordinate modelling community, this is difficult to do accurately, and spurious pressure gradients are readily generated.

Here we calculate the net pressure gradient force in the BBL as proportional to the difference between the pressures at different points in the BBL (which may lie at different depths) plus the depth difference between the points times the buoyancy at the *upstream* point; that is the buoyancy at the point from which the flow comes. This is energetically consistent with upstream advection of tracers within the BBL. The conventional (centered) method of calculating the net pressure force has been to use the BBL pressure difference plus the depth difference times the average of the buoyancies upstream and downstream.

This upstream bottom pressure gradient, together with a novel evaluation of pressure consistent with the conservation of the sum of potential, internal, and kinetic energy, has been inserted into a global implementation of the Killworth and Edwards model of the BBL in the z-coordinate MOMA model. With the previous centered pressure gradient, strong spurious flow and eventually violent instability developed over the equatorial BBL. The new upstream pressure gradient formulation gives plausible, much weaker, flows within the BBL. These remain stable.

Observations of the flow into the Indian Ocean sub-basins through Makassar Strait, Bab el Mandeb, and the Straits of Hormuz are reviewed. The nature of the flow through the straits varies with both the Red Sea and Throughflow involving a three layer flow throughout at least a portion of the year. The resulting counterflow in the straits leads to a different type of mixing product than that from a two layer outflow. The Arabian or Persian Gulf also differs from the classical two layer outfall in that at least in the summer condition there is top to bottom outflow. The Gulf outflow is unique in the sense that there is not actually a sill in the Straits of Hormuz. The Gulf outflow instead moves along a paleo-river valley to the continental shelf edge in the Gulf of Oman. Here a portion pours into the Gulf of Oman while another portion appears to continue on along the edge of the shelf. The properties of the different outfall layers in each of these systems is contrasted based on hydrographic stations downstream from the straits.

Numerical simulations of two-dimensional gravity currents on a sloping bottom are conducted as a step toward developing a better understanding of the details of entrainment processes in oceanic overflows. These simulations do not include rotation or ambient stratification, and the model is quite simple, however the main mechanism of entrainment, the Kelvin-Helmholtz instability, is captured. The results are analyzed in detail, in comparison to laboratory experiments of bottom gravity currents and by defining various metrics of entrainment. In general, the simulations indicate that laboratory results remain valid despite the geophysical scales and parameters of the numerical experiments.

The problem of how entraining overflow dynamics can control the stratification evolution in a finite basin is reconsidered, allowing for finite separation of centers of ventilation action. The mean field interaction approximation in earlier studies must then be tempered by consideration of how regional circulation effects induced by the localized ventilation can modify the interaction of multiple ventilation sites.

In the Arctic shelf region, dense water is formed by surface cooling. Then, the dense water is carried to the continental slope and the Arctic basin. It is suggested that the high density water is one of the sources of the mid and deep layer water in the Arctic Ocean. The transportation mechanism is thought to be important as maintenance of the halocline. Several mechanisms (baroclinic instability, bottom Ekman layer etc.) have been investigated as transportation mechanisms of the dense water. In this study, we shed light on eddy-induced transportation effects and topographic effects on transportation mechanisms of the dense water. A reduced-gravity model is used for a homogeneous bottom layer beneath an infinitely thick upper layer. Only the bottom layer has motion, while the upper layer does not. A Gaussian type eddy is put as an initial condition. The layer depth is 50 meters and a thickness of the initial eddy is 200 meters. A flat bottom case and several sloped bottom cases are tested for the purpose of comparison. In the case of flat bottom, the eddy moves westward, and hardly moves meridionary. On the other hand, the eddy moves northeastward in the case of bottom slope, which has an inclination, dz/dy, of 0.0001. The northward transportation is interpret as the topographic beta effect. The result implies the effect of topography on dense water transportation.

A theoretical, two-layer, reduced-gravity model for descending dense water flow on continental shelves/slopes has been developed to investigate the dynamics of bottom dense water plumes. The model is non-steady state and includes vertical viscosity, the Coriolis force, and bottom friction. An integral solution rather than a perfect analytical expression is derived and, thus, the Simpson's 1/3 rule to approximate the integral is applied. At the very bottom, the dense water plume moves about 45^o to the right (left) in the northern (southern) hemisphere, looking downslope. From the bottom, the velocity vector rotates anticyclonically upward, indicating a bottom Ekman spiral that mimics the atmospheric Ekman boundary layer. The dense water within the bottom Ekman layer obeys a three-force balance, while the dense water above the bottom Ekman layer is governed by a two-force balance, which is a geostrophic flow with superimposed cycloidal inertial oscillations oriented from about 25^o to 140^o to the right (left) of the downslope direction in the northern (southern) hemisphere. The transport within the bottom Ekman layer is directed about 60-70^o to the right (left) of the downslope direction in the northern (southern) hemisphere, forming an offshore (cross-isobath) transport in the absence of eddy flux and wind forcing. The ratio of offshore transport to alongshore transport within the bottom Ekman layer is about 0.19 (19%), while the ratio above the bottom Ekman layer (i.e., geostrophic layer of the dense water) is only 3% (negligible compared to its alongshore transport), which, however, is equivalent in magnitude to its counterpart in the bottom Ekman layer if O(DE/H)þ0.1, (where DE is the bottom Ekman layer thickness and H is the dense water layer thickness) i.e., each contributes 50% offshore transport of dense water. The magnitude of the descending dense water velocity depends linearly on reduced gravity and sin(theta) (slope angle).

A new nonlinearly dispersive closure for turbulence modeling in the ocean is presented. This closer is derived as Euler-Poincare systems (the Lagrangian analogue of Lie-Poisson Hamiltonian systems). These equations describe the effect of the fluctuations on the mean flow through the mechanism of nonlinear dispersion (not diffusion) and have important consequences for large-scale, rotating, stratified flows. We will present some theoretical and numerical results. We expect to apply this new closer to overflow problems in a hybrid coordinate model (one that uses isopycnal layers near the ocean's floor and cartesian coordinates near the ocean's surface).