Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics

Darryl D. Holm*, Erwin Luesink

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
8 Downloads (Pure)


Holm (Proc R Soc A Math Phys Eng Sci 471(2176):20140963, 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin’s circulation theorem, while also allowing for dispersive nonlinear wave propagation, both within a stratified fluid and at its free surface. The present paper combines asymptotic expansions and vertical averaging with the stochastic variational framework to formulate a new approach for developing stochastic parametrisation schemes for nonlinear waves in fluid dynamics. The approach is applied to two sequences of shallow water models which descend from Euler’s three-dimensional fluid equations with rotation and stratification under approximation by asymptotic expansions and vertical averaging. In the entire family of nonlinear stochastic wave–current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.

Original languageEnglish
Article number29
JournalJournal of nonlinear science
Issue number2
Publication statusPublished - Apr 2021
Externally publishedYes


Dive into the research topics of 'Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics'. Together they form a unique fingerprint.

Cite this