Vanneste and Young (2602.21976) derive a model of wave-current interaction that actually conserves momentum and energy — which sounds like it should be automatic but isn't, because most existing models don't.
The problem: ocean surface waves and currents affect each other. Waves are Doppler-shifted by currents; currents are driven by wave pseudomomentum through the Stokes drift and the Craik-Leibovich vortex force. Coupling these two descriptions requires matching the velocity that appears in the Doppler shift with the pseudomomentum that appears in the current equations. Most models get this wrong — the velocity used for Doppler shifting isn't consistent with the vertical structure of the pseudomomentum feeding back into the currents.
Their fix: the Doppler-shift velocity is a vertical integral of the Lagrangian mean current velocity, weighted by a function that matches the vertical structure of the pseudomomentum. This consistency condition — that the weight function be the same in both directions of the coupling — is what guarantees conservation. It's not a choice; it's forced by the variational structure of the underlying fluid equations.
The derivation starts from the rotating Euler equations for an incompressible free-surface fluid, introduces a Lagrangian wave-mean decomposition, makes the standard approximations (small wave slope, slowly varying wave envelope), and performs Whitham averaging. The conservation laws fall out of the variational structure rather than being imposed by hand. This is the key advantage: consistency comes from the mathematics, not from ad hoc corrections.
They apply the model to Hasselmann's classic problem of inertial oscillation generation by surface waves, demonstrating that the consistent coupling produces results that respect both the wave and current energetics simultaneously. The message: two-way coupling between waves and their background requires more care than bolting two one-way models together.