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Vallis, GK, Carnevale GF, Young WR.  1989.  Extremal energy properties and construction of stable solutions of the Euler equations. Journal of Fluid Mechanics. 207:133-152.   10.1017/s0022112089002533   AbstractWebsite

Certain modifications of the Euler equations of fluid motion lead to systems in which the energy decays or grows monotonically, yet which preserve other dynamically important characteristics of the field. In particular, all topological invariants associated with the vorticity field are preserved. In cases where isolated energy extrema exist, a stable steady flow can be found. In two dimensions, highly constrained by vorticity invariants, it is shown that the modified dynamics will lead to at least one non-trivial stationary, generally stable, solution of the equations of motion from any initial conditions. Numerical implementation of the altered dynamics is straightforward, and thus provides a practical method for finding stable flows. The method is sufficiently general to be of use in other dynamical systems.Insofar as three-dimensional turbulence is characterized by a cascade of energy, but not topological invariants, from large to small scales, the procedure has direct physical significance. It may be useful as a parameterization of the effects of small unresolved scales on those explicitly resolved in a calculation of turbulent flow.

Verzicco, R, Orlandi P, Eisenga AHM, vanHeijst GJF, Carnevale GF.  1996.  Dynamics of a vortex ring in a rotating fluid. Journal of Fluid Mechanics. 317:215-239.   10.1017/s0022112096000730   AbstractWebsite

The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier-Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a 'degree of polarization'. If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown. Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.