Foreign Travel Trip Report John A Krommes February I attended

							                  Foreign Travel Trip Report
                             John A. Krommes
                              February 8, 2006


    I attended the CSIRO/COSNet Workshop (January 10–13) and Summer
School (January 16–20) on “Turbulence and Coherent Structures in Fluids, Plas-
mas, and Granular Flows” at the Australian National University, Canberra. I
was an invited speaker at the Workshop, during which I presented a talk enti-
tled “Transition to Collisionless ITG Plasma Turbulence.” I was also an invited
speaker at the Summer School, during which I presented four lectures on Plasma
Turbulence:
  1. Introduction to Plasma Turbulence
  2. Statistical Closure Theory and Plasma Turbulence
  3. Zonal Flows in Plasmas
  4. Intermittency and Coherent Structures in Plasma Turbulence
These lectures and the others presented at the Summer School will be written
up for publication and collected in a book and should provide an important
resource.
    The quality of the talks and breadth of expertise were very high. Fields
represented included statistical turbulence theory, dynamical systems theory,
pattern formation, atmospheric flows, oceanic circulation, direct numerical sim-
ulation of fluids, plasma turbulence theory and simulation, and others.
    An overall impression was that plasma physicists still have much to learn
from our colleagues in geophysics. It has been understood for some time that the
quasi-geostrophic approximation employed in geophysics is almost identical to
the Hasegawa–Mima paradigm that follows from cold-ion gyrokinetics. However,
plasma physicists have paid inadequate attention to recent developments in
these other fields. For example, simulations of zonal flows are done routinely
in atmospheric studies of weather prediction. The development of what fusion
researchers would call “streamers” is easily seen in atmospheric simulations by
J. Frederiksen directed at the prediction of storm tracks. The related analytical
analyses of linear and nonlinear instabilities of the jet stream are presumably
quite relevant to theories of zonal flows and drift-wave transport regulation in
tokamaks, although detailed connections have not yet been drawn.
    Some nonlinear-dynamics analyses of low-degree-of-freedom models relevant
to the L-H transition were presented by R. Ball. The point was made that

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elementary models (e.g., by Diamond) that have appeared in the plasma lit-
erature are seriously naive and possibly misleading. This is an area in which
serious mathematical expertise is probably essential; most plasma physicists are
inadequately trained in dynamical systems analysis. P. Holmes reviewed some
techniques and results from that discipline.
    Presentations by Krommes and Dewar on the physics of zonal flows high-
lighted a minor controversy over the appropriate way of treating the problem of
zonal-flow generation. Dewar favors an approach based on modulational insta-
bility. Krommes notes that modulational instability merely describes an initial-
value calculation, and argues instead for a self-consistent statistical approach
based on steady-state turbulence.
    The most significant advance in basic turbulence theory that was reviewed
(it is now some years old) was the solution by G. Falkovich and others of the
“Kraichnan model” of passive advection by the methodology of statistical geom-
etry. This problem exhibits anomalous scaling for the exponents of high-order
structure functions. Although initially it was believed that those exponents
depended on the flux of passive scalar through the inertial range, it is now
understood in quantitative detail that they depend instead on various random
geometric properties. Some of these results would in principal be applicable to
plasma fluctuations in the tokamak edge, although at present the difficulty of
accurately measuring high-order structure functions in plasmas is severe.
    Significant advances were also reported in the numerical solution of statis-
tical closures. In plasma physics, the most recent and successful work on that
problem was reported in the 1990’s by Krommes and his colleagues Bowman
and Hu, who numerically integrated Markovian statistical closures. Frederik-
sen’s group (working in the context of atmospheric flows) takes the alternate
approach of integrating DIA-like non-Markovian closures, using non-Gaussian
restarts to significantly reduce the processing of the time-history integrations.
Modifications to ensure random Galilean invariance are also implemented; those
amount to a form of vertex renormalization. Although these integrations are ex-
pensive, they are apparently tractable and quite successful. Any further closure
work in plasmas should seriously consider this method.
    These remarks do not fully capture all topics discussed during the two weeks,
but they are representative of the breadth and quality of the research that was
reported. Plasma theorists would be well advised to pay close attention to these
other well-developed fields of research on turbulence and coherent structures.




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