English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The particle trajectories in irrotational, incompressible and invisciddeep-water surface gravity waves are open, leading to a net drift in thedirection of wave propagation commonly referred to as the Stokes Drift, whichis responsible for catalysing surface wave-induced mixing in the ocean andtransporting marine debris. A balance between phase-averaged momentum density,kinetic energy density and vorticity for irrotational, monochromatic andperiodic two-dimensional water waves is derived by working directly within theLagrangian reference frame, which tracks particle trajectories as a function oftheir labels and time. This balance should be expected as all three of thesequantities are conserved following particles in this system. Vorticity inparticular is always conserved along particles in two-dimensional inviscidflow, and as such even in its absence it is the value of the vorticity whichfundamentally sets the drift, which in the Lagrangian frame is identified asthe phase-averaged momentum density of the system. A relationship between thedrift and the geometric mean water level of particles is found at the surfaceand applications for potential new ways of inferring drift are discussed.Finally, an example of an initially quiescent fluid driven by a wavelikepressure disturbance is considered, showing how the net momentum and energyfrom the surface disturbance transfer to the wave field, recognizing the sourceof the mean Lagrangian drift as the net momentum required to generate anirrotational surface wave by any conservative force.

Momentum, energy and vorticity balances in deep-water surface gravity waves