On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex

Rypina, Irina I.; Brown, Michael G.; Beron-Vera, F. J.; Koçak, Hüseyin; Olascoaga, M. J.; Udovydchenkov, Ilya A.

doi:10.1175/jas4036.1

Cited by 106 publications

(153 citation statements)

References 67 publications

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“…Notably, the encounter volume is also large along the northern and southern flanks of the Gulf Stream jet, with two separate yellow curves running parallel to each other and a valley in between (although the curves could not be traced continuously throughout the entire region). This enhanced mixing on both flanks of the Gulf Stream extension current is reminiscent of chaotic advection driven by the tangled stable and unstable manifolds at the sides of the jet (del-Castillo-Negrete and Morrison, 1993;Rogerson et al, 1999;Rypina et al, 2007;Rypina and Pratt, 2017), and is also consistent with the existence of critical layers (Kuo, 1949;Ngan and Sheppard, 1997).…”

Section: Application To the Altimetric Velocities In The Gulfsupporting

confidence: 54%

Connection between encounter volume and diffusivity in geophysical flows

Rypina

Smith

Pratt

2018

Nonlin. Processes Geophys.

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Abstract. Trajectory encounter volume -the volume of fluid that passes close to a reference fluid parcel over some time interval -has been recently introduced as a measure of mixing potential of a flow. Diffusivity is the most commonly used characteristic of turbulent diffusion. We derive the analytical relationship between the encounter volume and diffusivity under the assumption of an isotropic random walk, i.e., diffusive motion, in one and two dimensions. We apply the derived formulas to produce maps of encounter volume and the corresponding diffusivity in the Gulf Stream region of the North Atlantic based on satellite altimetry, and discuss the mixing properties of Gulf Stream rings. Advantages offered by the derived formula for estimating diffusivity from oceanographic data are discussed, as well as applications to other disciplines.

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Section: Application To the Altimetric Velocities In The Gulfsupporting

confidence: 54%

Connection between encounter volume and diffusivity in geophysical flows

Rypina

Smith

Pratt

2018

Nonlin. Processes Geophys.

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“…As with FTLEs, complexity measures (Rypina et al, 2011), Lagrangian descriptors (Mendoza et al, 2014) and other techniques from the dynamical systems theory (BeronVera et al, 2013;Budisic and Mezic, 2012;Froyland et al, 2007;Haller et al, 2016), V can be computed for forwardand backward-time trajectories, with the backward computation revealing the unstable manifolds. Our encounter number could plausibly be related, in a limiting case, to the mixing geometry of Karrash and Keller (2017).…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The meandering Bickley jet flow is an idealized, but linearly dynamically consistent, model for the eastward zonal jet in the Earth's stratosphere (del-Castillo-Negrete and Morrison, 1993;Rypina et al, 2007Rypina et al, , 2011. This flow consists of a steady eastward zonal jet on which two eastward propagating Rossby-like waves are superimposed.…”

Section: Bickley Jetmentioning

confidence: 99%

Trajectory encounter volume as a diagnostic of mixing potential in fluid flows

Rypina

Pratt

2017

Nonlin. Processes Geophys.

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Abstract. Fluid parcels can exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter mass and a related simplified quantity, the encounter volume, are introduced as a measure of the mixing potential of a flow. The encounter volume quantifies the volume of fluid that passes close to a reference trajectory over a finite time interval. Regions characterized by a low encounter volume, such as the cores of coherent eddies, have a low mixing potential, whereas turbulent or chaotic regions characterized by a large encounter volume have a high mixing potential. The encounter volume diagnostic is used to characterize the mixing potential in three flows of increasing complexity: the Duffing oscillator, the Bickley jet and the altimetry-based velocity in the Gulf Stream extension region. An additional example is presented in which the encounter volume is combined with the u * approach of Pratt et al. (2016) to characterize the mixing potential for a specific tracer distribution in the Bickley jet flow. Analytical relationships are derived that connect the encounter volume to the shear and strain rates for linear shear and linear strain flows, respectively. It is shown that in both flows the encounter volume is proportional to time.

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“…The Bickley jet, another analytical example, is frequently used as a model of zonal jets in the Earth's atmosphere 16 . It is a quasi-periodic flow comprising a spatially undulatory jet with counter-rotating vortices above and below.…”

Section: B Bickley Jetmentioning

confidence: 99%

Identification of individual coherent sets associated with flow trajectories using coherent structure coloring

Schlueter-Kuck

Dabiri

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks. Keywords: fluid mechanics, clustering, graph theoryIn recent years, there has been a proliferation of techniques that aim to characterize fluid flow kinematics on the basis of Lagrangian trajectories of collections of tracer particles. Most of these techniques depend on presence of tracer particles that are initially closely-spaced, in order to compute local gradients of their trajectories. In many applications, the requirement of close tracer spacing cannot be satisfied, especially when the tracers are naturally occurring and their distribution is dictated by the underlying flow. Moreover, current methods often focus on determination of the boundaries of coherent sets, whereas in practice it is often valuable to identify the complete set of trajectories that are coherent with an individual trajectory of interest. We extend the concept of Coherent Structure Coloring, an approach based on spectral graph theory, to achieve identification of the coherent set associated with individual Lagrangian trajectories. The method does not require a priori determination of the number of coherent structures in the flow, nor does it require heuristics regarding the eigenvalue spectrum corresponding to the generalized eigenvalue problem. Importantly, although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.

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On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex

Cited by 106 publications

References 67 publications

Connection between encounter volume and diffusivity in geophysical flows

Connection between encounter volume and diffusivity in geophysical flows

Trajectory encounter volume as a diagnostic of mixing potential in fluid flows

Identification of individual coherent sets associated with flow trajectories using coherent structure coloring

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