Abstract
Making use of a Lagrangian description, we interpret the kinematics and analyze the mean transport due to numerically generated transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced, air–water, two-phase Navier–Stokes solver. These transient waves produce transient transport, which can sometimes be larger than what would be estimated using estimates developed for translationally invariant progressive waves. We identify the critical assumption that makes our standard notion of the steady Stokes drift inapplicable to the data and explain how and in what sense the transport due to transient waves can be larger than the steady counterpart. A comprehensive analysis of the data in the Lagrangian framework leads us to conclude that much of the transport can be understood using an irrotational approximation of the velocity, even though the simulations use Navier–Stokes fluid simulations with moderately high Reynolds numbers. Armed with this understanding, it is possible to formulate a simple Lagrangian model that captures the mean transport and variance of transport for a large range of wave amplitudes. For large-amplitude waves, the parcel paths in the neighborhood of the free surface exhibit increased dispersion and lingering transport due to the generation of vorticity. We examined the wave-breaking case. For this case, it is possible to characterize the transport very well, away from the wave boundary layer, and approximately using a simple model that captures the unresolved breaking dynamics via a stochastic parameterization.
| Original language | English |
|---|---|
| Pages (from-to) | 2323-2336 |
| Number of pages | 14 |
| Journal | Journal of Physical Oceanography |
| Volume | 49 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2019 |
Funding
We thank L. Deike and K. Melville for sharing their data and for helpful discussions. We also thank James C. McWilliams for stimulating discussions and for suggesting improvements to the manuscript. An anonymous reviewer made many and significant comments and suggested changes that when addressed, improved the presentation as well as the breadth of its intended audience. This work was supported through a grant by the National Science Foundation, NSF OCE1434198. JMR wishes to thank the Kavli Institute of Theoretical Physics at the University of California, Santa Barbara. The KITP is supported in part by the National Science Foundation under Grant NSF PHY-1748958. Acknowledgments. We thank L. Deike and K. Melville for sharing their data and for helpful discussions. We also thank James C. McWilliams for stimulating discussions and for suggesting improvements to the manuscript. An anonymous reviewer made many and significant comments and suggested changes that when addressed, improved the presentation as well as the breadth of its intended audience. This work was supported through a grant by the National Science Foundation, NSF OCE1434198. JMR wishes to thank the Kavli Institute of Theoretical Physics at the University of California, Santa Barbara. The KITP is supported in part by the National Science Foundation under Grant NSF PHY-1748958.