Woods Hole Coastal and Marine Science Center

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Horizontal Mixing

  The horizontal mixing parameterization used the Smagorinsky (1963) formulation in which the magnitude of the horizontal mixing is proportional to horizontal current shear. For the water quality runs, the Smagorinsky coefficient was set to 0.1, which results in typical horizontal eddy viscosities and diffusivities between 5 -- 20 m s over much of Massachusetts Bay. Ideally, the magnitude of this mixing would represent processes occurring at scales smaller than the mesh can resolve. In western Massachusetts Bay the grid cell spacing is 1--2 km, and using the rule of thumb that 6--8 grid cells motions are the minimum length that are realistically represented, the model should well resolve mixing processes occurring at scales of 10 km or so. From Okubo (1971), we expect that observed horizontal mixing at a scale of 10 km should be about 10 m s , and at a scale of 1 km should be about 1 m s . Since the model partially resolves shear (and thus produces mixing) at scales between 1 and 10 km, the ideal mixing level should probably be somewhere between 1 and 10 m s . To test the sensitivity to the mixing level in this range, the model was subsequently rerun for a 3 month period using a Smagorinsky coefficient of 0.02 (five times smaller than the water quality run), and only small quantitative differences were observed in the resulting velocity, temperature, salinity and effluent concentration fields. This indicates that the modeled fields are dominated by resolved mixing and transport processes rather than the parameterized mixing of the Smagorinsky formulation. This is consistent with observations made during the outfall siting process, where it was concluded that a value of 45 m s best represented the dispersion of material over the 20 km scale of western Massachusetts Bay (Adams et al, 1990), suggesting that the effective mixing in this region may be a bit higher than Okubo's empirical curve. This would not be surprising considering the strong current shears in this region. The level of 45 m s was also used in the outfall siting model studies described by Walton et al (1990).

In addition to the specified horizontal viscosity, the velocity field was Shapiro filtered every 2 hours to remove 2 grid length energy. This was necessary to prevent 2 grid length energy along the open boundary from growing large enough to violate the advective CFL condition. By applying a 4th order Shapiro filter at 2 hour intervals, the longer wavelength energy is largely unaffected. For example, it can be shown over 20 filter applications (two days of simulation), the amplitude of 6 grid length structure is reduced less than 5% (see appendix of Signell, 1989).

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Next: Surface and Bottom Up: Model Implementation Previous: Vertical Mixing

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