Intermittency in nonlinear dynamics and singularities at complex times

Details Intermittency in nonlinear dynamics and singularities at complex times Intermittency in nonlinear dynamics and singularities at complex times

May 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981phrva..23.2673f&link_type=abstract

Physical Review A - General Physics, 3rd Series, vol. 23, May 1981, p. 2673-2705. Research supported by the Kyburger Oepfelwaeh

Mathematics

Complex Variables

130

Fluctuation Theory, Fluid Dynamics, High Pass Filters, Intermittency, Nonlinear Equations, Signal Processing, Turbulent Flow, Complex Variables, Flow Velocity, Fluid Filters, Singularity (Mathematics), Spectrum Analysis, Statistical Analysis, Stochastic Processes, Time Dependence

Scientific paper

High-pass filtering of turbulent velocity signals is known to produce intermittent bursts. This is, as shown, a general property of dynamical systems governed by nonlinear equations with band-limited random forces or intrinsic stochasticity. It is shown that singularities for complex times determine the very-high-frequency behavior of the solution and show up in the high-pass filtered signal as bursts centered at the real part of the singularity and with overall amplitude decreasing exponentially with the imaginary part. Near a singularity, nonlinear interactions, however weak they may be on the real axis, acquire unbounded strength. Investigations of singularities by nonperturbative methods is thus essential for quantitative analysis of high-frequency or high-wave-number properties. In contrast to results based on two-point closures, the high-frequency dissipation-range spectrum is actually not universal with respect to the low-frequency forcing

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