Fluid Dynamics in Earth and Planetary Sciences (FDEPS)
24th FDEPS workshop, Nov. 26 - Nov. 29, 2024 at Kansai Seminar House

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Twenty-fourth Workshop "Fluid Dynamics in Earth and Planetary Sciences"

Date:
Nov. 26 - Nov. 29, 2024

Co-organizer:
  • Research Institute for Mathematical Sciences (RIMS), Kyoto University
  • Center for Planetary Science (CPS), Kobe University
Place:
Kansai Seminar House
23 Takenouchi-cho, Ichijojii, Sakyo-ku, Kyoto 606-8134 JAPAN
Phone:+81-75-711-2115 FAX:+81-75-701-5256

Program

Lecturer: David G. Dritschel (Professor of Applied Mathematics, Mathematical Institute, University of St Andrews)

  • Intensive Lecture Series and Free Discussion
    Vortex dynamics in rotating systems

    • Nov. 26 (Tue)
      • 9:00 - 12:00
        Lecture 1. Fluid dynamics, vortex dynamics, and model building
        • The basics, with a twist or two
          • What is a fluid?
          • A brief history
          • Vorticity
          • Circulation and Potential Vorticity
          • Balance and PV inversion
        • Geophysical fluids
        • Modelling
          • How do we do it?
          • Modelling geophysical fluid dynamics
          • From shallow water to quasi-geostrophy
          • From 3D to shallow water
        • Summary
        • Movies [Lecture 1-a] [Lecture 1-b] [Lecture 1-c] [Lecture 1-d]
        • [Slide PDF1]
      • 14:00 - 17:00
        Lecture 2. Vortex patch dynamics
        • V-states for the Euler equations
          • Origins
          • Contour Dynamics
          • A brief history
        • V-states for the quasi-geostrophic shallow-water equations
          • Two-fold symmetric V-states
          • Three-fold symmetric V-states
          • Nonlinear evolution
            • Animations (Vortex patches and stabilties, cases with gamma=0, see P.34) [m=1] [m=3] [m=4]
            • Animations (Vortex patches and stabilties, cases with gamma=3.6, see P.35) [m=1] [m=3] [m=4]
        • V-states of opposite-signed (potential) vorticity
        • V-states in 3D quasi-geostrophic flows
          • Equilibria and linear stability
          • Nonlinear evolution
        • Conclusions
        • Movies [Lecture 2-a] [Lecture 2-b] [Lecture 2-c] [Lecture 2-d]
        • [Slide PDF2]
      • Evening : Free discussion
    • Nov. 27 (Wed)
    • Nov. 28 (Thr)
      • 9:00 - 12:00
        Lecture 4. Lagrangian-based approaches in GFD, and associated advanced numerical methodsGeophysical turbulence
      • 14:00 - 17:00
        Lecture 5. Fronts, jets and PV staircases in geophysical flows
        • Potential vorticity as a material tracer
        • Linear and nonlinear stability of monotonic PV
        • The Rhines scale
        • Inhomogeneous mixing
        • Jet spacing and PV staircases
        • Small Rossby deformation length
        • The ubiquity of PV staircases
        • Recipe for jet formation in atmospheres and oceans
        • Conclusions
        • Movies [Lecture 5-a] [Lecture 5-b] [Lecture 5-c] [Lecture 5-d]
        • [Slide PDF5]
    • 11/29 (Fri.) Seminar
      • 09:30 - 11:30
        Research Seminar : Jet formation in topographically-forced spherical shallow water flows
        Banded, quasi-zonal jets are a conspicuous feature of planetary atmospheres in the solar system, and likely common to planetary atmospheres beyond. The most dramatic examples occur in Jupiter's atmosphere, which exhibits a large number of alternating high-speed flows (jets), punctuated by intense vortices, the most famous and long-lived being the Great Red Spot. Research for decades has tried to unravel the fundamental mechanisms underpinning observed jet patterns in planetary atmospheres. We know that the planetary rotation plays a primary role, since idealised `barotropic' models which include only a thin fluid layer of constant depth can produce jet patterns. Such patterns arise both in freely-decaying turbulence and in forced turbulence. The fundamental mechanism at play is `inhomogeneous potential vorticity (PV) mixing'. The background rotating state has variable PV (`planetary vorticity') which supports Rossby waves. These waves only persist in linear theory; in the nonlinear dynamics, these waves tend to steepen and break, leading to mixing. This mixing locally reduces mean PV gradients. As Rossby waves depend on PV gradients for their restoring mechanism, weakening PV gradients means that Rossby waves in these regions have a greater tendency to steepen, break and mix. Hence, there is a positive feedback mechanism: mixing reduces PV gradients, which encourages further mixing and further reduction of PV gradients. This process is only limited by the available energy in the initial perturbations, or the amount of forcing and damping present. In the limit of weak forcing and damping, this process leads to `PV staircase' formation, a situation in which the planetary vorticity is re-arranged approximately into steps of uniform PV separated by near discontinuities. In this talk, new results are presented for specifically topographic-like forcing, thought to be most relevant to outer planetary atmospheres driven by convective storms from below. This type of forcing has long been advocated but rarely implemented. Instead, researchers have almost unanimously considered vorticity forcing, which however has weaker justification. Topographic-like forcing on the other hand generates imbalanced motions (inertia-gravity waves), and such waves have long been considered a highly-undesirable feature of numerical models of planetary atmospheres. To overcome these difficulties, we employ a state-of-the-art Lagrangian-based model based on `contour advection'. This model enables a comprehensive exploration of parameter space at ultra-high resolution. We thereby uncover the conditions which favour the formation of jets.

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