Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change

Abstract

Understanding and predicting extreme events and their anomalous statistics in complex nonlinear systems are a grand challenge in applied sciences as well as for engineering design. Recent controlled laboratory experiments in weakly turbulent shallow water with abrupt depth change exhibit a remarkable transition from nearly Gaussian statistics to extreme anomalous statistics with large positive skewness of the surface height. We develop a statistical dynamical model to explain and quantitatively predict the anomalous statistical behavior. Incoming and outgoing waves are modeled by the truncated Korteweg–de Vries equations statistically matched at the depth change. The statistical matching of the known nearly Gaussian incoming Gibbs state completely determines the predicted anomalous outgoing Gibbs state and successfully captures key features of the experiment.

Document Details

Document Type
Pub Defense Publication
Publication Date
Feb 13, 2019
Source ID
10.1073/pnas.1820467116

Entities

People

  • Andrew J. Majda
  • Di Qi
  • M. N. J. Moore

Organizations

  • Florida State University
  • New York University
  • Office of Naval Research
  • Simons Foundation

Tags

Fields of Study

  • Physics

Readers

  • Oceanography.
  • Regression Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.