The increased drift of steep focusing surface gravity waves

Area of Science:

• Fluid dynamics
• Oceanography
• Wave physics

Background:

• Surface gravity waves generate a mean Lagrangian drift, crucial for mass transport and mixing in the ocean.
• Current models often assume additive drift from individual wave components, potentially oversimplifying complex wave interactions.

Purpose of the Study:

• To investigate the accuracy of summing individual wave drifts for total transport in multi-component wave fields.
• To develop and validate a new theoretical framework for calculating local mean Lagrangian drift in focusing wave packets.
• To understand the role of local wave steepness in Eulerian transport enhancement.

Main Methods:

• Laboratory experiments with controlled surface gravity waves.
• Fully nonlinear numerical simulations of two-dimensional steep focusing wave packets.
• Derivation of an exact method for constraining local mean Lagrangian drift in the Lagrangian reference frame.
• Application of the nonlinear Schrödinger equation (NLSE) for narrow-banded wave fields.

Main Results:

• The assumption of additive drift significantly underpredicts average transport in wave-focusing regions by up to 30%.
• A new theoretical expression for local mean Lagrangian drift predicts near-surface enhancements in focusing and steepening wave fields.
• Theoretical predictions align well with laboratory measurements, particularly for narrower bandwidth wave packets.

Conclusions:

• Local wave field steepness, rather than the sum of linear component steepnesses, dictates the magnitude of Lagrangian drift enhancements.
• The findings necessitate a revision of how wave-induced transport and mixing are modeled in the ocean.
• Accurate prediction of ocean mixing requires considering nonlinear interactions and local wave focusing effects.