The field of turbulence theory continues to grapple with profound foundational questions despite extensive progress over recent decades. Central challenges persist around the mechanisms underpinning the onset of turbulence and the closed statistical description of strongly turbulent flows. Intermittency—sudden and irregular fluctuations in the intensity of turbulence—remains central to these concerns, signifying complex dynamics that defy conventional modeling. The development and application of exact solutions to the hydrodynamic equations, particularly through Hamiltonian systems of point vortices in two dimensions and point vortex dipoles in three dimensions, offer promising insight into these unresolved issues. Notably, outstanding debates persist over the universality of turbulence spectra, the characterization of higher statistical moments, and the validity of current theoretical tools to capture scaling behaviors and dissipation such as those highlighted by Onsager.

Efforts to clarify these issues are examining a range of analytical and numerical approaches, with exact solutions serving as idealized laboratories for testing theoretical hypotheses. Recent studies have illuminated the roles of localized vortical structures in the formation and development of turbulence dynamics, while others are probing statistical scaling and intermittency in both compressible and incompressible media. However, these advances have yet to resolve major gaps: most notably, the absence of a fully closed description for turbulent statistical properties and a comprehensive understanding of how turbulence arises in wall-bounded shear flows. These challenges call for integrative approaches combining mathematical theory, statistical mechanics, and high-resolution computation.

This Research Topic aims to consolidate cutting-edge research toward resolving these outstanding problems. Central objectives include developing and testing frameworks for the closed statistical description of turbulence moments and spectra, unraveling the origins and impact of intermittency in various fluid regimes, and clarifying the nature of dynamical anomalies. Explorations into the dynamics and stochastic behavior of localized vortices, particularly in the context of turbulence arising in wall-bounded flows, are welcomed.

To gather further insights into turbulence theory and the statistical characterization of turbulent phenomena, we invite articles addressing, but not limited to, the following themes:
• Development and application of exact solutions to hydrodynamic equations;
• Statistical closure and theoretical models of turbulence spectra;
• Mechanisms of intermittency in different fluid media;
• Onsager’s dissipative anomaly and anomalous scaling in turbulence;
• The emergence of turbulence in wall-bounded shear flows;
• Dynamics and stochasticization of localized vortical structures;
• Innovative mathematical or computational approaches to strong turbulence analysis.

Are you interested in contributing a manuscript to this Research Topic?

Contemporary Problems in Turbulence Theory