3 results
Vortex intensification and collapse of the Lissajous-elliptic ring: single- and multi-filament Biot-Savart simulations and visiometrics
- Victor M. Fernandez, Norman J. Zabusky, Vladimir M. Gryanik
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- Journal:
- Journal of Fluid Mechanics / Volume 299 / 25 September 1995
- Published online by Cambridge University Press:
- 26 April 2006, pp. 289-331
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The collapsing ‘Lissajous-elliptic’ (LE) vortex ring is examined via quantifications of Single- and multi-filament Biot-Savart numerical simulations. In the single-filament simulations, parametric studies show simple relationships between the collapse boundary and the impulse and energy invariants. Collapse becomes non-monotonic in time, for a sufficiently small initial core ‘radius’. Self-similar, singular-like behaviour of the off-filament strain-rate growth has been observed in a small interval, just prior to core overlapping. The computation of the strain-rate eigenvalues and vortex stretching in a diagnostics box surrounding the collapse region yields patterns observed previously in continuum simulations. New diagnostics are presented, including line densities of the energy and the linear and angular momentum, all of which approach zero in the collapse region of the ring. These diagnostics may provide critical parameters for initiating surgery in a topology-changing algorithm. Our multi-filament simulations exhibit layer-like vortex regions and a ‘torus’-shaped vortex stretching pattern observed previously in continuum periodic-domain simulations of vortex reconnection. Quantifications in a cross-section of the collapse region indicate that the circulation tends to concentrate in the head or frontside of the convecting dipolar structure. This is also the location of the incipient ‘bridge’ which is evolving from the weak filaments that have been convected from the initially outer-vortex regions. The formation of this smaller scale vortex structure exhibits the largest vorticity amplification in the variable-core model simulations.
The theory of quasi-geostrophic von Kármán vortex streets in two-layer fluids on a beta-plane
- VLADIMIR M. GRYANIK, HARTMUT BORTH, DIRK OLBERS
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- Journal:
- Journal of Fluid Mechanics / Volume 505 / 25 April 2004
- Published online by Cambridge University Press:
- 21 April 2004, pp. 23-57
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In this study self-organized periodic coherent vortex structures arising in geophysical turbulent flows at low Rossby number are investigated by developing a conceptual model based on an analytical theory of von Kármán vortex streets affected by stratification and differential rotation. In the framework of a quasi-geostrophic (QG) two-layer beta-plane model vortex streets with three different types of vertical structures (barotropic, upper layer and hetonic) are analysed using the point vortex approximation. The streets are found to be exact solutions of the potential vorticity equation and to be characterized by four non-dimensional parameters. Von Kármán streets are semi-localized solutions which form a bridge between vortex pairs (limit of symmetric dilute streets) and two parallel vortex sheets (limit of dense streets). On the beta-plane QG von Kármán streets can only move to the east, i.e. with a speed outside the range of speeds of Rossby waves, so that a dynamical asymmetry in the zonal direction is introduced. A complete classification on a diagram of states shows that critical bounds exist in the parameter space, prescribing for example a maximum distance between vortex rows beyond which no QG vortex streets can be found. Typically a fast and a slow vortex street with different flow structures are found in the region of existence. As a function of distance between vortex rows baroclinic QG vortex streets show a characteristic non-monotonic speed behaviour at scales of the order of the baroclinic Rossby radius. A wide region of possible existence of QG von Kármán streets is found in atmospheric, oceanic and planetary conditions as well as in rotating tank experiments. The theory can be applied to describe the coherent part of turbulent baroclinic intermittent zonal jet-like and frontal flows and provides a scaling for such flows.
The theory of three-dimensional hetons and vortex-dominated spreading in localized turbulent convection in a fast rotating stratified fluid
- VLADIMIR M. GRYANIK, TATIANA N. DORONINA, DIRK J. OLBERS, TORSTEN H. WARNCKE
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- Journal:
- Journal of Fluid Mechanics / Volume 423 / 25 November 2000
- Published online by Cambridge University Press:
- 03 November 2000, pp. 71-125
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The problem of lateral heat/buoyancy transport in localized turbulent convection dominated by rotation in continuously stratified fluids of finite depth is considered. We investigate the specific mechanism of the vortex-dominated lateral spreading of anomalous buoyancy created in localized convective regions owing to outward propagation of intense heton-like vortices (pairs of vortices of equal potential vorticity (PV) strength with opposite signs located at different depths), each carrying a portion of buoyancy anomaly. Assuming that the quasi-geostrophic form of the PV evolution equation can be used to analyse the spreading phenomenon at fast rotation, we develop an analytical theory for the dynamics of a population of three-dimensional hetons. We analyse in detail the structure and dynamics of a single three-dimensional heton, and the mutual interaction between two hetons and show that the vortices can be in confinement, splitting or reconnection regimes of motion depending on the initial distance between them and the ratio of the mixing-layer depth to the depth of fluid (local to bulk Rossby radii). Numerical experiments are made for ring-like populations of randomly distributed three-dimensional hetons. We found two basic types of evolution of the populations which are homogenizing confinement (all vortices are predominantly inside the localized region having highly correlated wavelike dynamics) and vortex-dominated spreading (vortices propagate out of the region of generation as individual hetons or heton clusters). For the vortex-dominated spreading, the mean radius of heton populations and its variance grow linearly with time. The law of spreading is quantified in terms of both internal (specific for vortex dynamics) and external (specific for convection) parameters. The spreading rate is proportional to the mean speed of propagation of individual hetons or heton clusters and therefore depends essentially on the strength of hetons and the ratio of local to bulk Rossby radii. A theoretical explanation for the spreading law is given in terms of the asymptotic dynamics of a single heton and within the frames of the kinetic equation derived for the distribution function of hetons in collisionless approximation. This spreading law gives an upper ‘advective’ bound for the superdiffusion of heat/buoyancy. A linear law of spreading implies that diffusion parameterizations of lateral buoyancy flux in non-eddy-resolving models are questionable, at least when the spreading is dominated by heton dynamics. We suggest a scaling for the ‘advective’ parameterization of the buoyancy flux, and quantify the exchange coefficient in terms of the mean propagation speed of hetons. Finally, we discuss the perspectives of the heton theories in other problems of geophysical fluid dynamics.