Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation
TL;DR: In this article, the authors consider the evolution of an isolated elliptical vortex in a weakly dissipative fluid and derive a simple geometrical formula relating the rate of change of the aspect ratio of a particular vorticity contour to its orientation relative to the streamlines.
Abstract: We consider the evolution of an isolated elliptical vortex in a weakly dissipative fluid. It is shown computationally that a spatially smooth vortex relaxes inviscidly towards axisymmetry on a circulation timescale as the result of filament generation. Heuristically, we derive a simple geometrical formula relating the rate of change of the aspect ratio of a particular vorticity contour to its orientation relative to the streamlines (where the orientation is defined through second-order moments). Computational evidence obtained with diagnostic algorithms validates the formula. By considering streamlines in a corotating frame and applying the new formula, we obtain a detailed kinematic understanding of the vortex's decay to its final state through a primary and a secondary breaking. The circulation transported into the filaments although a small fraction of the total, breaks the symmetry and is the chief cause of axisymmetrization.
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TL;DR: A perspective on the recently discovered realm of submesoscale currents in the ocean, where intermediate-scale flow structures in the form of density fronts and filaments, topographic wakes and persistent coherent vortices are created from mesoscale eddies and strong currents.
Abstract: This article is a perspective on the recently discovered realm of submesoscale currents in the ocean. They are intermediate-scale flow structures in the form of density fronts and filaments, topographic wakes and persistent coherent vortices at the surface and throughout the interior. They are created from mesoscale eddies and strong currents, and they provide a dynamical conduit for energy transfer towards microscale dissipation and diapycnal mixing. Consideration is given to their generation mechanisms, instabilities, life cycles, disruption of approximately diagnostic force balance (e.g. geostrophy), turbulent cascades, internal-wave interactions, and transport and dispersion of materials. At a fundamental level, more questions remain than answers, implicating a programme for further research.
611 citations
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...More importantly, they are advective attractor states in the sense that asymmetric perturbations tend to be stretched out in the symmetry direction and transfer their energy into the symmetric current [29,30], as long as the latter has a stable shear profile....
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TL;DR: In this article, the physics of vortex axisymmetrization was examined further, with the goal of elucidating the dynamics of outward-propagating spiral bands in hurricanes.
Abstract: In this paper we examine further the physics of vortex axisymmetrization, with the goal of elucidating the dynamics of outward-propagating spiral bands in hurricanes. the basic shysics is illustrated most simply for stable vorticity monopoles on an f-plane. Unlike the dynamics of sheared disturbances in rectilinear shear flow, axisymmetrizing disturbances on a vortex are accompanied by outward-propagating vortex Rossby-waves whose restoring mechanism is associated with the radial gradient of storm vorticity. Expressions for both phase and group velocities are derived and verified; they confirm earlier speculations on the existence of vortex Rossbywaves in hurricanes. Effects of radially propagating vortex Rossby-waves on the mean vortex are also analysed. In conjunction with sustained injection of vorticity near the radius of maximum winds, these results reveal a new mechanism of vortex intensification. the basic theory is then applied to a hurricane-like vortex in a shallow-water asymmetric-balance model. the wave mechanics developed here shows promise in elucidating basic mechanisms of hurricane evolution and structure changes, such as the formation of secondary eye-walls. Radar observations possessing adequate temporal resolution are consistent with the predictions of this work, though more refined observations are needed to quantify further the impact of mesoscale banded disturbances on the evolution of the hurricane vortex.
569 citations
TL;DR: In this paper, the authors reviewed the current understanding of tropical cyclone structure and intensity changes and found that the maximum intensities reached by real TCs in all ocean basins are generally lower than those inferred from the theoretical MPI, indicating that internal dynamics and external forcing from environmental flow prohibit the TC intensification most and limit the TC intensity.
Abstract: Current understanding of tropical cyclone (TC) structure and intensity changes has been reviewed in this article. Recent studies in this area tend to focus on two issues: (1) what factors determine the maximum potential intensity (MPI) that a TC can achieve given the thermodynamic state of the atmosphere and the ocean? and (2) what factors prevent the TCs from reaching their MPIs? Although the MPI theories appear mature, recent studies of the so-called superintensity pose a potential challenge. It is notable that the maximum intensities reached by real TCs in all ocean basins are generally lower than those inferred from the theoretical MPI, indicating that internal dynamics and external forcing from environmental flow prohibit the TC intensification most and limit the TC intensity. It remains to be seen whether such factors can be included in improved MPI approaches.
350 citations
Cites background from "Axisymmetrization and vorticity-gra..."
...Building on earlier work, which has identified vortex axisymmetrization as a universal process of smoothly distributed perturbed vortices ( Melander et al, 1987; Guinn and Schubert, 1993; Smith and Montgomery, 1995), Montgomery and Kallenbach (1997) developed a theoretical framework on the VRW-guide model of vortex axisymmetrization (see also a later refinement by Brunet and Montgomery, 2002; Montgomery and Brunet, 2002)....
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...Building on earlier work, which has identified vortex axisymmetrization as a universal process of smoothly distributed perturbed vortices (Melander et al, 1987; Guinn and Schubert, 1993; Smith and Montgomery, 1995), Montgomery and Kallenbach (1997) developed a theoretical framework on the VRW-guide…...
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TL;DR: In this paper, the authors propose contour surgery, an extension of contour dynamics, which enables the modelling of complex inviscid flows in wholly Lagrangian terms, overcomes the buildup of small-scale structure by truncating, in physical space, the modelled range of scales.
327 citations
TL;DR: In this article, the authors present a quantitative description of the cause and mechanism behind the restricted process of symmetric vortex merger, which occurs if the original two vortices are sufficiently close together and if the distance between the vorticity centroids is smaller than a certain critical merger distance.
Abstract: Two like-signed vorticity regions can pair or merge into one vortex. This phenomenon occurs if the original two vortices are sufficiently close together, that is, if the distance between the vorticity centroids is smaller than a certain critical merger distance, which depends on the initial shape of the vortex distributions. Our conclusions are based on an analytical/numerical study, which presents the first quantitative description of the cause and mechanism behind the restricted process of symmetric vortex merger. We use two complementary models to investigate the merger of identical vorticity regions. The first, based on a recently introduced low-order physical-space moment model of the two-dimensional Euler equations, is a Hamiltonian system of ordinary differential equations for the evolution of the centroid position, aspect ratio and orientation of each region. By imposing symmetry this system is made integrable and we obtain a necessary and sufficient condition for merger. This condition involves only the initial conditions and the conserved quantities. The second model is a high-resolution pseudospectral algorithm governing weakly dissipative flow in a box with periodic boundary conditions. When the results obtained by both methods are juxtaposed, we obtain a detailed kinematic insight into the merger process. When the moment model is generalized to include a weak Newtonian viscosity, we find a ‘metastable’ state with a lifetime depending on the dissipation timescale. This state attracts all initial configurations that do not merge on a convective timescale. Eventually, convective merger occurs and the state disappears. Furthermore, spectral simulations show that initial conditions with a centroid separation slightly larger than the critical merger distance initially cause a rapid approach towards this metastable state.
325 citations
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TL;DR: In this article, a study of two-dimensional and geostrophic turbulent flows is presented, showing that the flow structure has vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time).
Abstract: A study is made of some numerical calculations of two-dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time). When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large-scale flow, except for relatively rare encounters with other centres of concentration. These structures can arise from random initial conditions without vorticity concentration, evolving in the midst of what has been traditionally characterized as the ‘cascade’ of isotropic, homogeneous, large-Reynolds-number turbulence: the systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. When the vorticity concentrations are a sufficiently dominant component of the total vorticity field, the cascade processes are suppressed. The demonstration of persistent vorticity concentrations on intermediate scales - smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales - does not invalidate many of the traditional characterizations of two-dimensional and geostrophic turbulence, but I believe it shows them to be substantially incomplete with respect to a fundamental phenomenon in such flows.
1,091 citations
TL;DR: In this paper, the motion of an elliptic vortex in a uniform straining and vorticity flow is solved exactly, and the elliptic shape is preserved and the area of the vortex is conserved but the axis ratio of the ellipse changes in general.
Abstract: Motion of an elliptic vortex of uniform vorticity in a uniform straining and vorticity flow is solved exactly. The elliptic shape is preserved and the area of the vortex is conserved but the axis ratio of the ellipse changes in general. Depending on the magnitudes of the vorticity in the vortex and the strain and the vorticity of the shear flow, this vortex exhibits various types of motion such as rotation and nutation around its centre. When the strain is very strong, the vortex is always elongated infinitely in the direction of the strain. A stationary elliptic vortex can exist in a weaker straining flow.
373 citations
TL;DR: In this article, a contour dynamics algorithm for the Euler equations of fluid dynamics in two dimensions is presented, which is applied to regions of piecewise-constant vorticity within finite-area-vortex regions (FAVRs).
348 citations
TL;DR: Using a variety of flow-visualization techniques, the flow behind a circular cylinder has been studied in this article, and the results obtained have provided a new insight into the vortex-shedding process.
Abstract: Using a variety of flow-visualization techniques, the flow behind a circular cylinder has been studied. The results obtained have provided a new insight into the vortex-shedding process. Using time-exposure photography of the motion of aluminium particles, a sequence of instantaneous streamline patterns of the flow behind a cylinder has been obtained. These streamline patterns show that during the starting flow the cavity behind the cylinder is closed. However, once the vortex-shedding process begins, this so-called ‘closed’ cavity becomes open, and instantaneous ‘alleyways’ of fluid are formed which penetrate the cavity. In addition, dye experiments also show how layers of dye and hence vorticity are convected into the cavity behind the cylinder, and how they are eventually squeezed out.
279 citations
TL;DR: In this paper, an improved contour dynamical algorithm with node insertion and removal to maintain the a p r i o r i i accuracy is used. But the algorithm is not suitable for the case of finite-area vortex regions (FAVRs).
Abstract: Numerical simulations of the instability, merger, and breaking of two piecewise‐constant finite‐area vortex regions (FAVR’s) are presented. An improved contour dynamical algorithm with node insertion‐and‐removal to maintain the a p r i o r i accuracy is used. Corotating ’’V states’’ (symmetric steady‐state FAVR’s) were found to be unstable when properly perturbed if their centroid‐effective radius ratio, x/R, is <1.6, thereby verifying an estimate of Saffman and Szeto. This causes the FAVR’s to approach at an exponential rate, merge, and reform into a stable perturbed elliptical structure with filamentary arms (to conserve angular momentum). For larger x/R ratios, regular perimeter oscillations were observed and estimates of an eigenfrequency of the perturbed stable V states were obtained. When regions of different vorticity density merge, the larger‐density region is eventually entrained within the smaller‐density region. These simulations elucidate the self‐consistent close interactions of isolated vortex regions in two‐dimensional high Reynolds number flows.
178 citations