Universal fluctuations of the Danube water level: A link with turbulence, criticality and company growth

¹ University College London, Department of Chemistry 20 Gordon Street, London WC1H 0AJ, UK
² The Royal Institution of Great Britain 21 Albemarle Street, London W1X 4BS, UK
³ Laboratoire de Physique, ENS-Lyon and CNRS 46 Allée d'Italie, 69007 Lyon, France

Corresponding authors: s.t.bramwell@ucl.ac.uk peter.holdsworth@ens-lyon.fr

Received: 10 September 2001
Accepted: 13 November 2001

Abstract

A global quantity, regardless of its precise nature, will often fluctuate according to a Gaussian limit distribution. However, in highly correlated systems, other limit distributions are possible. We have previously calculated one such distribution and have argued that this function should apply specifically, and in many instances, to global quantities that define a steady state. Here we demonstrate, for the first time, the relevance of this prediction to natural phenomena. The river level fluctuations of the Danube are observed to obey our prediction, which immediately establishes a generic statistical connection between turbulence, criticality and company growth statistics.