A solar cycle clock for extreme space weather.

The variable solar cycle of activity is a long-standing problem in physics. It modulates the overall level of space weather activity at earth, which in turn can have significant societal impact. The Hilbert transform of the sunspot number is used to map the variable length, approximately 11 year Schwabe cycle onto a uniform clock. The clock is used to correlate extreme space weather seen in the aa index, the longest continuous geomagnetic record at earth, with the record of solar active region areas and latitudes since 1874. This shows that a clear switch-off of the most extreme space weather events occurs when > 90 % of solar active region areas have moved to within about 15° of the solar equator, from regions of high gradient in solar differential rotation which can power coronal mass ejections, to a region where solar differential rotation is almost constant with latitude. More moderate space weather events which coincide with 27 day solar rotation recurrences in the aa index, consistent with stable, persistent source regions of high speed streams, commence when the centroid of solar active region areas moves to within 15° of the solar equator. This offers a physical explanation for the longstanding identification of a two component cycle of activity in the aa index.

Can high-order moments be meaningfully estimated from experimental turbulence measurements?

Although high-order moments are widely used in the study of fully developed turbulence, their statistical properties remain poorly known. It is well known that beyond a given order, moment estimates based on finite samples cannot be trusted. We provide an empirical criterion for determining that order and illustrate it using a long record of boundary layer turbulence. The results show that even with modest levels of intermittency, structure functions in the inertial range of turbulence cannot be meaningfully assessed for orders as low as 5 or 6.

Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg-Landau equation.

The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensional boundary layers. Our aim is to study the nonlinear properties of the wavefield through a Volterra series equation. The kernels of the Volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then consider describing the wavefield with the complex Ginzburg-Landau equation, and derive analytical relations which express the coefficients of the Ginzburg-Landau equation in terms of the kernels of the Volterra expansion. These relations must hold for a large class of weakly nonlinear systems, in fluid as well as in plasma physics. (c) 2000 American Institute of Physics.