As the final Compass Seminar Series lecturer of the academic year, IDSC Core Faculty Member and Assistant Professor of Ocean Sciences, Dr. Milan Curcic spoke at the Rosenstiel School’s series on April 22, 2026. In case you missed it, catch the replay on YouTube.
This “Wave Action Balance in Strongly Varying Currents” lecture took place at the Rosenstiel School of Marine, Atmospheric, and Earth Science in the Seminar Room (SLAB) 103 at 3:00 p.m. Attendees gathered early for cookies and coffee and the lecture was also available via Zoom.
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Read More: The ‘Fluid Dynamics’ That Charted Milan Curcic’s Career | IDSC Magazine Spring 2024
Abstract
Wave action balance is the fundamental equation behind spectral wave models that are used for global wave forecasting. Originated in Whitham’s [1965] variational method and generalized by Bretherton & Garrett [1968] to propagation over slowly-varying currents, wave action conservation has since been taken as accurate within the first order of the relative variation in the current field. Slow variation of currents has been assumed by most wave models to date.
In this work, we analyze an expanded form of the wave action balance that includes 1st-order effects of current gradients within the wavetrain (this term was presented by Bretherton & Garrett but neglected as small).
First, based on a month-long submesoscale (150-m resolution) simulation of ocean circulation, we demonstrate that the contribution of unresolved current gradients to the wave action tendency, at the 1st order, is ~6 times larger than the wave strain / convergence by wave grid-resolved currents, and ~1.2 times larger than the propagation term itself.
Second, we perform numerical simulations of wave propagation over the 150-m resolution surface currents and quantify the adjustment of the wave field to the circulation.
Not suprisingly, strong current gradients act to boost wave action gradients such that the propagation term becomes as dominant as the current strain terms. Although there has been increasing evidence in the past decade of strong impacts of the resolved currents on the wave fields, we believe that this is the first quantitative assessment of subgrid-scale current gradients on the wave field. We expect this effect to be important for the accuracy of swell propagation over large basins, as well as for wave amplification when crossing strong boundary currents.
