Eddy advection model

Equation (12), when used in large-scale coarse resolution (non-eddy resolving) models, is incomplete in one other respect. The effect of mesoscale eddies on tracer transport includes an additional, advective-like mechanism sometimes referred to as bolus transport (see Gent and McWilliams, 1990 Gent et al., 1995). This can be included in Equation (12) as... 

A good fit of the measured oxygen concentrations by a curve calculated from the eddy diffusion-advection model has been obtained by... 

The quantity k is related to the intensity of the turbulent fluctuations in the three directions, k = 0.5 u u. Equation 41 is derived from the Navier-Stokes equations and relates the rate of change of k to the advective transport by the mean motion, turbulent transport by diffusion, generation by interaction of turbulent stresses and mean velocity gradients, and destmction by the dissipation S. One-equation models retain an algebraic length scale, which is dependent only on local parameters. The Kohnogorov-Prandtl model (21) is a one-dimensional model in which the eddy viscosity is given by... 

The same physical principles are utilized to develop isotopic models which better account for the transport of air masses at a regional scale, such as done by Fisher (1992) using a regional stable isotope model coupled to a zonally averaged global model. Other authors such as Eriksson (1965) and more recently Hendricks et al. (2000) considered the transport of water both by advective and eddy diffusive processes, the latter inducing less fractionation. 

The first attempts to model flow and transport in plant canopies that accommodated (i) the distinct microclimates of different stands of vegetation (ii) the separation of soil surface and layers of canopy as distinct sources and sinks of heat and mass and (iii) the influence of atmospheric stability or advection effects, applied gradient transfer to diffusion within the canopy space ([493]). In this procedure, a flux density is expressed as the product of a diffusion coefficient (turbuient or eddy diffusivity) and the gradient of the time average of the quantity of interest, as in the following examples ... 

It is illuminating to study the time evolution of a river plume as an initial value problem. It can be shown that the current pattern is governed by a geostrophically adjusted eddy confined to the buoyancy patch (near field) and a coastally trapped flow that develops in the wake of a Kelvin wave (far field). Behind the front of the first Kelvin wave mode, undercurrents are set up. Although the velocities of the flow forced by the momenrnm of the river mnoff are small enough to justify a linear treatment, there are important nonlinear effects owing to the advection of density, which limits the validity of the linear analytical models. In particular, the structure of the near field in front of the river mouth is dominated by the response to the buoyancy flux associated with the river discharge. 

The distribution of a number of dissolved species (02, C-14, Ra-226, salinity) in the Central Pacific water column, at depths between 1 and 4 km, has been shown (11) to be consistent with a steady-state model of the water column in which the concentration-depth profiles are stationary and the concentrations at the boundaries 1 and 4 km are stipulated at their present values. The physical model of the water column is based on two transport mechanisms vertical eddy diffusion (eddy diffusion coefficient K — 1.3 cm2 sec"1) and upwelling of deep water (advection velocity U = 1.4 X 10 5 cm sec"1, or approximately 1 cm per day) (11). 

In the context of plankton dynamics an interesting development that has some common ideas with the KiSS approach but introduces a new and important element is described in Martin (2000). The idea is that dispersion of a patch is not only controlled by eddy diffusivity, but also by the geometric characteristics of the mean flow. It turns out that if an incompressible fluid flow induces dispersion in one direction it necessarily produces convergence in another, to conserve the fluid volume. This was already exploited in Sect. 2.7.1, and includes the ingredient of advection, in addition to the reaction-diffusion processes which are the subject of this Chapter. Nevertheless, since this case can be analyzed easily and extends the KiSS model, we consider it here. 

Ra distribution in the ocean has been modeled to derive eddy diffusivities and advection rates taking into consideration its input by diffusion from sediments, loss by radioactive decay, and dispersion... 

These stresses are similar to the classical Reynolds stresses that result Irom time or ensemble averaging of the advection fluxes, but differ in that they are consequences of a spatial averaging and go to zero if the filter width A goes to zero. For LES performed in physical space, the basic sub-grid stress model is the eddy-viscosity... 

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