A three‐dimensional Lagrangian hurricane eyewall computation

Rutherford, Blake; Dangelmayr, Gerhard

doi:10.1002/qj.703

Cited by 9 publications

(19 citation statements)

References 23 publications

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“…The method of separating shear in two-dimensional flows was extended to 3-D in Rutherford and Dangelmayr (2010). The method was used to compute the Lagrangian boundary separating the eye and eyewall during a mature TC simulation.…”

Section: Lcs Definitionmentioning

confidence: 99%

“…Additionally, the hyperbolic fields converged faster than FTLE's and the field associated closely with the horizontal plane eliminated the need for rescaling vertical motions due to the small vertical:horizontal aspect ratio that typifies a tropical cyclone vortex. A specific choice of coordinates adapted to the helical trajectory motion rather than general orthogonal coordinates made the approach of Rutherford and Dangelmayr (2010) easier to implement. Whereas the VHT interaction is clearly more complex than the evolution of a single mature hurricane vortex, the coordinate system proposed by Rutherford and Dangelmayr (2010) nonetheless resolves LCSs under shorter timescales.…”

Section: Lcs Definitionmentioning

confidence: 99%

“…A specific choice of coordinates adapted to the helical trajectory motion rather than general orthogonal coordinates made the approach of Rutherford and Dangelmayr (2010) easier to implement. Whereas the VHT interaction is clearly more complex than the evolution of a single mature hurricane vortex, the coordinate system proposed by Rutherford and Dangelmayr (2010) nonetheless resolves LCSs under shorter timescales. We note that other studies (Truesdell, 1954;Saffman, 1981;Provenzale, 1999;Prieto et al, 2003;Shadden et al, 2006) have investigated the interaction between and entrainment of particles by vortices using different methods, while the ridges of FTLE fields in relation to two vortices was studied by Lapeyre (2002).…”

Section: Lcs Definitionmentioning

confidence: 99%

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Lagrangian coherent structures in tropical cyclone intensification

2012

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Abstract. Recent work has suggested that tropical cyclones intensify via a pathway of rotating deep moist convection in the presence of enhanced fluxes of moisture from the ocean. The rotating deep convective structures possessing enhanced cyclonic vorticity within their cores have been dubbed Vortical Hot Towers (VHTs). In general, the interaction between VHTs and the system-scale vortex, as well as the corresponding evolution of equivalent potential temperature (θ e ) that modulates the VHT activity, is a complex problem in moist helical turbulence.To better understand the structural aspects of the threedimensional intensification process, a Lagrangian perspective is explored that focuses on the coherent structures seen in the flow field associated with VHTs and their vortical remnants, as well as the evolution and localized stirring of θ e . Recently developed finite-time Lagrangian methods are limited in the three-dimensional turbulence and shear associated with the VHTs. In this paper, new Lagrangian techniques developed for three-dimensional velocity fields are summarized and we apply these techniques to study VHT and θ e phenomenology in a high-resolution numerical tropical cyclone simulation. The usefulness of these methods is demonstrated by an analysis of particle trajectories.We find that VHTs create a locally turbulent mixing environment. However, associated with the VHTs are hyperbolic structures that span between adjacent VHTs or adjacent vortical remnants and represent coherent finite-time transport barriers in the flow field. Although the azimuthally-averaged inflow is responsible for the inward advection of boundary layer θ e , attracting Lagrangian coherent structures are coincident with pools of high boundary layer θ e . Extensions of boundary layer coherent structures grow above the boundary layer during episodes of convection and remain with the convective vortices. These hyperbolic structures form initially as boundaries between VHTs. As vorticity aggregates into a ring-like eyewall feature, the Lagrangian boundaries merge into a ring outside of the region of maximal vorticity.

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Section: Lcs Definitionmentioning

confidence: 99%

Section: Lcs Definitionmentioning

confidence: 99%

Section: Lcs Definitionmentioning

confidence: 99%

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Lagrangian coherent structures in tropical cyclone intensification

2012

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“…Lagrangian methods have been developed that are suitable for three-dimensional flows, (Haller, 2005(Haller, , 2011Rutherford and Dangelmayr, 2010). However, the interpretation of boundaries is easier also in two dimensions since the manifolds are one-dimensional.…”

Section: Simplifications Used For This Studymentioning

confidence: 99%

A Lagrangian analysis of a developing and non-developing disturbance observed during the PREDICT experiment

Rutherford

Montgomery

2012

Atmos. Chem. Phys.

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Abstract. The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in timedependent flows that relax the steady flow approximation.Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance.The methods are applied to both a developing and nondeveloping disturbance observed during the recent predepression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

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“…In oceanic contexts these surfaces have been identified by stitching together 2-D Lagrangian structures in different layers (Branicki and Kirwan, 2010) or connecting ridges computed from finite-size Lyapunov exponent fields (Bettencourt et al, 2014). In the field of atmospheric sciences, these structures have similarly been obtained by connecting ridges computed from finite-time Lyapunov exponents (FTLE) (Rutherford and Dangelmayr, 2010;du Toit and Marsden, 2010;Lekien and Ross, 2010). More recently, also in atmospheric contexts, 3-D Lagrangian information has been extracted by means of 2-D slices of the full 3-D FTLE field computed from 3-D trajectories (Rutherford et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

Curbelo

García-Garrido²,

Mechoso

et al. 2017

Nonlin. Processes Geophys.

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Abstract. In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.

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A three‐dimensional Lagrangian hurricane eyewall computation

Cited by 9 publications

References 23 publications

Lagrangian coherent structures in tropical cyclone intensification

Lagrangian coherent structures in tropical cyclone intensification

A Lagrangian analysis of a developing and non-developing disturbance observed during the PREDICT experiment

Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

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