Ocean Turbulence: Mesoscale Modeling in Isopycnal Coordinates the role of the Spectrum of Vertical Shear - Part 4
We study the tracer subgrid term in isopycnal coordinates, S(sub I). We employ two ingredients: the experimental data on vertical spectra of ocean turbulence measured by Gargett et al.(1981) and the stochastic approach recently developed by Dukowicz and Smith (1997). Our result confirms that S(sub I) is made of two parts: an advection and a diffusion term. However, the tracer bolus velocity u** consists of two terms u** = u(sub 1) + u(sub 2) while in the GM model there is only a term related to u(sub 1) which is shown to be: u(sub 1) = k(bar-q)(sup -1)(delta)(sub rho) where bar-q is the thickness weighted average potential vorticity, a result in agreement with the recent suggestions by Treguier et al. (1997), Lee et al. (1997) and Greatbatch (1998). The second component u(sub 2) IS new. We compute it in the geostrophic approximation using the Gargett et al. data (1981) on ocean vertical turbulence. We find that u(sub 2) much greater than u(sub 1) and that u(sub 2) is orthogonal to u(sub 1).