Two-Dimensional Turbulence

Kafiabad, Hossein; Rodda, Costanza

Abstract

This article offers a foundational understanding of the phenomenology of two-dimensional turbulence. We begin by presenting the classical theory, which hinges on the conservation of energy and enstrophy, giving rise to two distinct inertial ranges: the inverse energy cascade and the forward enstrophy cascade. The associated scaling laws for the energy spectra of these ranges are introduced, along with the mathematical reasoning behind them. We then review numerical and experimental studies that investigated this theory, as well as complementary theoretical contributions. Drawing on over five decades of research, we conclude that the theoretical predictions are remarkably accurate in the limit of (asymptotically) large Reynolds numbers, while many intriguing phenomena observed in finite Reynolds regimes hold significant relevance for geophysical flows.

Citation

Kafiabad, H., & Rodda, C. (2025). Two-Dimensional Turbulence. In Reference Module in Earth Systems and Environmental Sciences. Elsevier. https://doi.org/10.1016/b978-0-323-96026-7.00216-2

• Publication Date: 2025
• Deposit Date: Aug 14, 2025
• Peer Reviewed: Peer Reviewed
• Series Title: Reference Module in Earth Systems and Environmental Sciences
• Book Title: Reference Module in Earth Systems and Environmental Sciences
• ISBN: 9780124095489
• DOI: https://doi.org/10.1016/b978-0-323-96026-7.00216-2
• Public URL: https://durham-repository.worktribe.com/output/4426209