Publication Date:
1994-12-10
Description:
The equilibrium dynamics in a homogeneous forced-dissipative f-plane shallow-water system is investigated through numerical simulations. In addition to classical two-dimensional turbulence, inertio-gravity waves also exist in this system. The dynamics is examined by decomposing the full flow field into a dynamically balanced potential-vortical component and a residual ‘free’ component. Here the potential-vortical component is defined as part of the flow that satisfies the gradient-wind balance equation and that contains all the linear potential vorticity of the system. The residual component is found to behave very nearly as linear inertio-gravity waves. The forcing employed is a mass and momentum source balanced so that only the large-scale potential-vortical component modes are directly excited. The dissipation is provided by a linear relaxation applied to the large scales and by an eighth-order linear hyperdiffusion. The statistical properties of the potential-vortical component in the fully developed flow were found to be very similar to those of classical two-dimensional turbulence. In particular, the energy spectrum of the potential-vortical component at scales smaller than the forcing is close to the ~ k~3 expected for a purely two-dimensional system. Detailed analysis shows that the downscale enstrophy cascade into any wavenumber is dominated by very elongated triads involving interactions with large scales. Although not directly forced, a substantial amount of energy is found in the inertio-gravity modes and interactions among inertio-gravity modes are principally responsible for transferring energy to the small scales. The contribution of the inertio-gravity modes to the flow leads to a shallow tail at the high-wavenumber end of the total energy spectrum. For parameters roughly appropriate for the midlatitude atmosphere (notably Rossby number ~ 0.5), the break between the roughly — k~3 regime and this shallower regime occurs at scales of a few hundred km. This is similar to the observed mesoscale regime in the atmosphere. The nonlinear interactions among the inertio-gravity modes are extremely broadband in spectral space. The implications of this result for the subgrid-scale closure in the shallow-water model are discussed. © 1994, Cambridge University Press. All rights reserved.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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