# Barriers to the Transport of Diffusive Scalars in Compressible Flows

@article{Haller2020BarriersTT, title={Barriers to the Transport of Diffusive Scalars in Compressible Flows}, author={George Haller and Daniel Karrasch and Florian Kogelbauer}, journal={SIAM J. Appl. Dyn. Syst.}, year={2020}, volume={19}, pages={85-123} }

Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located directly from the deterministic component of the velocity field without diffusive or stochastic simulations. Here we extend these results to compressible flows and to diffusive concentration fields affected by sources or sinks, as well as by spontaneous decay. We…

## Figures from this paper

## 16 Citations

Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows

- PhysicsPhysical Review Fluids
- 2020

We put forward the idea of defining vortex boundaries in planar flows as closed material barriers to the diffusive transport of vorticity. Such diffusive vortex boundaries minimize the leakage of…

Heat-content and diffusive leakage from material sets in the low-diffusivity limit

- MathematicsNonlinearity
- 2021

We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing…

Objective barriers to the transport of dynamically active vector fields

- PhysicsJournal of Fluid Mechanics
- 2020

Abstract We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the…

A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit

- Mathematics
- 2021

We study mass preserving transport of passive tracers in the lowdiffusivity limit using Lagrangian coordinates. Over finite-time intervals, the solution-operator of the nonautonomous diffusion…

Lagrangian Transport and Chaotic Advection in Three-Dimensional Laminar Flows

- PhysicsApplied Mechanics Reviews
- 2019

3D practical flows are categorised into canonical problems to expose the diversity of Lagrangian transport and create awareness of its broad relevance and to reconcile practical flows with fundamentals on Lagrangia transport and chaotic advection.

A Geometric Heat-Flow Theory of Lagrangian Coherent Structures

- MathematicsJ. Nonlinear Sci.
- 2020

This approach facilitates the discovery of connections between some prominent methods for coherent structure detection: the dynamic isoperimetry methodology, the variational geometric approaches to elliptic LCSs, a class of graph Laplacian-based methods and the effective diffusivity framework used in physical oceanography.

Harnessing stratospheric diffusion barriers for enhanced climate geoengineering

- Environmental ScienceAtmospheric Chemistry and Physics
- 2020

Abstract. Stratospheric sulfate aerosol geoengineering is a proposed method
to temporarily intervene in the climate system to increase the reflectance of shortwave radiation and reduce mean global…

Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

- Physics
- 2019

We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective…

Measures of path-based nonlinear expansion rates and Lagrangian uncertainty in stochastic flows

- Computer Science
- 2018

We develop a probabilistic characterisation of trajectorial expansion rates in nonautonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent…

Genesis, evolution, and apocalypse of Loop Current rings

- Physics, Environmental Science
- 2020

We carry out assessments of the life cycle of Loop Current vortices, so-called rings, in the Gulf of Mexico by applying three objective (i.e., observer-independent) coherent Lagrangian vortex…

## References

SHOWING 1-10 OF 45 REFERENCES

Material barriers to diffusive and stochastic transport

- MathematicsProceedings of the National Academy of Sciences
- 2018

This work seeks transport barriers and transport enhancers as material surfaces across which the transport of diffusive tracers is minimal or maximal in a general, unsteady flow and finds that such surfaces are extremizers of a universal, nondimensional transport functional whose leading-order term in the diffusivity can be computed directly from the flow velocity.

A Geometric Heat-Flow Theory of Lagrangian Coherent Structures

- MathematicsJ. Nonlinear Sci.
- 2020

This approach facilitates the discovery of connections between some prominent methods for coherent structure detection: the dynamic isoperimetry methodology, the variational geometric approaches to elliptic LCSs, a class of graph Laplacian-based methods and the effective diffusivity framework used in physical oceanography.

Scalar Flux Kinematics

- Environmental Science
- 2016

The first portion of this paper contains an overview of recent progress in the development of dynamical-systems-based methods for the computation of Lagrangian transport processes in physical…

Transport in 3D volume-preserving flows

- Physics
- 1994

SummaryThe idea of surfaces of locally minimal flux is introduced as a key concept for understanding transport in steady three-dimensional, volume-preserving flows. Particular attention is paid to…

A Dynamic Laplacian for Identifying Lagrangian Coherent Structures on Weighted Riemannian Manifolds

- MathematicsJ. Nonlinear Sci.
- 2020

The main results include generalised versions of the dynamic isoperimetric problem, the dynamic Laplacian, Cheeger’s inequality, and the Federer–Fleming theorem.

Efficient computation of null geodesics with applications to coherent vortex detection

- Physics, MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null geodesics of appropriate Lorentzian metrics defined on the flow…

Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

- Physics
- 2019

We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [Haller & Beron-Vera, 2013], objective…

Plasma Physics: Confinement, Transport and Collective Effects

- Physics
- 2007

The use of computational methods is discussed for plasma edge physics and plasma turbulence studies. The problem of plasma-wall interaction requires multi-scale methods (molecular dynamics, kinetic…

Coherent Lagrangian vortices: the black holes of turbulence

- PhysicsJournal of Fluid Mechanics
- 2013

Abstract We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian…