Small-Scale Excitations in Large Systems
In the development of instability in extended systems, the prevalence of fluctuations is a disquieting reminder of our failure to understand completely the nonlinear aspects of instability theory. Experimental studies, such as those of Ahlers (1975) in thermal convection, show fluctuations that are plausibly interpreted in terms of the wandering of defects through the underlying patterns engendered by the instability. These defects are small-scale structures not easily accessible to the slowly varying wave theory that has been used in the study of unstable extended systems. However, they are not filtered out by the gauge field approach that Procaccia advocates in these proceedings. Perhaps they may relate to modes already known in the standard theory, as in Pocheau’s (1989) interpretation of the vertical vorticity modes of convection theory as a gauge field.
KeywordsGauge Field Unstable Mode Stable Mode Vlasov Equation Instability Theory
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