Interface-Inflection Geophysics

This paper that a couple of people alerted me to is likely one of the most radical research findings that has been published in the climate science field for quite a while:

Topological origin of equatorial waves
Delplace, Pierre, J. B. Marston, and Antoine Venaille. Science (2017): eaan8819.

An earlier version on ARXIV was titled Topological Origin of Geophysical Waves, which is less targeted to the equator.

The scientific press releases are all interesting

  1. Science Magazine: Waves that drive global weather patterns finally explained, thanks to inspiration from bagel-shaped quantum matter
  2. Science Daily: What Earth’s climate system and topological insulators have in common
  3. Physics World: Do topological waves occur in the oceans?

What the science writers make of the research is clearly subjective and filtered through what they understand.

To me, it’s clear that the connection is between the anti-vortex interface at the equator and the physics of curl equations in low-dimensional magnetoelectric structures. I said as such in a set of comments at the Azimuth blog describing the recent Nobel prize award in physics:

@whut says: 9 October, 2016 at 8:04 pm

These curl equations are fascinating and are of course endemic in applications from electromagnetics to fluid dynamics. Perhaps there is some overlap with the model of the QBO equatorial winds that we are working on at John’s Azimuth Forum (see sidebar) and at my blog. Have some notes here:

Paul Pukite

  • A closely related topological phase transition is described by the Quantum Hall Effect and Fractional Quantum Hall Effect. That was a hot topic when I was in grad school growing GaAs quantum well structures. Stormer and Tsui eventually won a Nobel Prize after they experimentally discovered the fractional effect that Laughlin had predicted.

    I mention this because in last month’s blog post linked in my comment above, I stated that I applied knowledge of the Hall effect in solving the QBO problem. The two phenomenon share similar curl terms. The math is the common tie between these systems.

    from “Modeling water waves beyond perturbations”

    “– The perturbation theory is useful when there is a small dimensionless parameter in the problem, and the system is exactly solvable when the small parameter is sent to zero.
    – … it is not required that the system has a small parameter, nor that the system is exactly solvable in a certain limit. Therefore it has been useful in studying strongly correlated systems, such as the fractional Quantum Hall effect.”

    Making progress in one area certainly has application in other disciplines.

I actually gave a graduate solid-state physics research presentation on this topic years ago, so the mathematical analogy was drawn from my early exposure to the concept. On the blog comment, I added this

… the equivalent of the equator runs along the diagonal in this case. Notice that right along the diagonal, the arrows point only in one of two directions — the equivalent of east and west.

The problem is that the math gets complicated quickly as so much remains underdetermined. It seems that the equator is at a perfect position for a metastable vortex/antivortex pair, in that the Coriolis forces exactly cancel and which direction the winds blow right along the equator is very sensitive to forcing.

What I used in my derivation of the QBO (and later ENSO) model was that change of sign in the Coriolis force ( f ) at the equatorial interface. The figure below from Delplace et al shows the inflection point at the equator:

The blog paper has a recently added parenthetical comment to where the Berry curvature may be applicable,

Here are a few MP4s from the Delplace et al paper uploaded to YouTube which show the equatorial simulation:

The change of sign at the equator being sensitive to the forcing leads to the lunisolar forced models of QBO and ENSO.  Recall that both of these are equatorial behaviors. The low dimensionality (turning it into almost a 1D problem) is enforced by the equatorial inflection waveguide in one dimension (North-South) and the stratification of the fluids in the vertical direction.  That’s what causes the QBO to turn into a monopole annular or toroidal structure with the velocity propagating in the only free-direction (East-West) :


I will be presenting the recent research at the AGU in December, and probably make some connection to the Delplace et al work:

GC41B-1022 Biennial-Aligned Lunisolar-Forcing of ENSO: Implications for Simplified Climate Models

Thursday, 14 December 2017

08:00 – 12:20

  • New Orleans Ernest N. Morial Convention Center
  • – Poster Hall D-F

A few years ago, I referenced this paper by Marston, who is a co-author of the above topology paper, which was a call-to-arms to solving climate problems:

Marston is a colleague of Nobel-winner Kosterlitz at Brown University and I am sure some of that research on explaining the magnetic flux interfaces (and Quantum Hall Effect) intrigued him.

And this paper by Vallis is a good inspiration to look at simplifying the physics before doing CFD

This last paper is one the earlier preliminary papers on applying geometric phase spaces to stratified fluid problems in climate from another French researcher:

ELASTIC WAVE EQUATION, Yves Colin de Verdière, Séminaire de théorie spectrale et géométrie, Grenoble Volume25 (2006-2007) 55-69

3 thoughts on “Interface-Inflection Geophysics

  1. I must admit, when I pointed out the Delplace paper to you I vaguely recalled a comment of yours at Azimuth, I didn’t realize your thinking was so closely aligned to the subject matter. If I had, I would have put a ‘Red Alert’ on the tip rather than just ‘you might find this interesting’

    I’ll give you a pat on the back if no one else will 🙂


    • Thanks Kevin, Jan (hypergeometric) at Azimuth also alerted me to the paper.

      I want to drum up lots of interest in the math that they describe in the event that it reveals a simple and elegant formulation. That’s what many of the solid state models turn into, much more elegant than what is seen in climate science.


  2. Another abstract by Marston

    “Atmospheric and oceanic jets can be surprisingly robust to perturbations. Do dynamics alone account for this stability, or are there deeper principles at work? A clue may be provided by classical systems with topologically protected chiral modes. These optical, acoustic, and mechanical systems realize physics that was first discovered in the context of condensed matter such as the quantum Hall effect and topological insulators. They share the common feature that low-energy waves propagate in only one direction with no backscattering. We address the question of whether or not such topological protection of chiral modes can be found at geophysical or even astrophysical scales by studying idealized models of geophysical jets.”


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