Oblique-wave instabilities affect spilling breaking waves when the local wave steepness exceeds H/λ_o > 0.08, where H is the height and λ_o is the wavelength. Close to the ocean surface, spilling breaking waves resonate with Langmuir circulations in both the atmosphere and ocean. Away from the ocean surface, larger Langmuir circulations form under the action of inverse energy cascades. Surface currents due to Langmuir circulations and surfing effects due to spilling breaking waves affect the formation of windrows. The formation of meandering flows with broad spatial and temporal scales affects mixing in the atmosphere and ocean. Meandering drift currents have spatial and temporal scales conducive to the formation of internal waves in the ocean.
Modeling the Ocean’s Heartbeat
Wave breaking affects turbulent fluctuations close to the free surface in the atmosphere and ocean. Away from the free surface, the large coherent structures that form through an inverse energy cascade in the atmosphere and ocean are not very sensitive to wave breaking. The formation of windrows is affected by the surfing and scrubbing actions of spilling breaking waves (Dommermuth, 2020f,g) and the surface currents that are induced by coherent structures transverse to the wind (Langmuir, 1938). Recent videos of windrows are suggestive of the complex interplay that can occur between wave breaking and surface currents (Tunli, 2021a,b,c,d,e).
An Annotated Bibliography of the Ocean’s Heartbeat
Dommermuth (2020) shows that Langmuir circulations form under the action of an inverse energy cascade. The Ocean’s Heartbeat (OH) is an inverse energy cascade that occurs through interactions between surface gravity waves and organized vortical structures in the atmosphere and the ocean. Windrows are visible manifestations of the inverse energy cascade. The vortical portion of the flow and spilling breaking waves work in combination to generate windrows. Breaking waves generate meandering currents and winds in the oceanic and atmospheric boundary layers. This report provides an annotated bibliography of research on the Ocean’s Heartbeat.
The Ocean’s Heartbeat
The effects of the Ocean’s Heartbeat on the ocean and atmosphere are profound. My ultimate aim is to help establish a research group to study the Ocean’s Heartbeat using petascale supercomputing resources. Data assimilation will be used to nudge iLES of two-phase flows with VOF interface capturing to improve our understanding of the Ocean’s Heartbeat. I also feel that it is important to lay the foundation for graduate studies in this research area. I welcome opportunities to work with research groups from other countries. If you share my vision, contact me at [email protected].
Whitecaps, Inverse Energy Cascades, and Energy Budgets
https://www.researchgate.net/publication/350874498
Ocean waves induce vortical flows in the oceanic and atmospheric boundary through an inverse energy cascade. Depending on the growth rate, the energy density in the vortical portion of the flow is about 6-10% of the wave kinetic energy. I call the mechanics of the energy transfer the Ocean’s Heartbeat (Dommermuth, 2020g). The depths and heights of the computational domain are currently 1/2 a wavelength, but the vortical portion of the flow will diffuse higher into the atmosphere and deeper into the ocean. Over 50-100 wave periods, large-scale coherent structures fill the width of the computational domain, which at present is no greater than one wavelength wide due to the limits of my computational resources. The length of the computational domain should be greater than two wavelengths to permit interactions between successive whitecaps. There are strong interactions between the vortical and wavy portions of the flow that induce whitecaps. The shedding of vorticity out the back of whitecaps feeds the vortical portion of the flow. This study of the energy density of the vortical portion of the flow is driven by atmospheric forcing. Another study of the energy density is underway whereby log profiles of the wind and wind drift are imposed using data assimilation.
Research Papers and Reports
Langmuir Circulations and Meandering Flows
- Dommermuth, D. G., Rhymes, L. E., and Rottman, J. W., “Direct Simulations of Breaking Ocean Waves with Data Assimilation,” OCEANS, 2013, San Diego, California, USA, 2013. https://www.researchgate.net/publication/269573554
- Dommermuth, D. G., Lewis, C. D., Tran, V. H., and Valenciano, M. A., “Direct Simulations of Wind- Driven Breaking Ocean Waves with Data Assimilation,” Proceedings of the 30th Symposium on Naval Hydrodynamics, Hobart, Tasmania, Australia, 2014. https://www.researchgate.net/publication/266396605
- Dommermuth, D. G., “Meandering Flows in the Oceanic and Atmospheric Boundary Layers due to Breaking Ocean Waves,” ResearchGate preprint, Oct 2020. https://www.researchgate.net/publication/344482927
Windrows
- Dommermuth, D. G., “Further Observations on how Wave Breaking Affects the Formation of Windrows,” ResearchGate preprint, Oct 2020. https://www.researchgate.net/publication/344482865
- Dommermuth, D. G., “Windrows,” ResearchGate preprint, Oct 2020. https://www.researchgate.net/publication/344943225
The Ocean’s Heartbeat
- Dommermuth, D.G., “The Ocean’s Heartbeat,” ResearchGate preprint, Dec 2020. https://www.researchgate.net/publication/347514163
- Dommermuth, D.G., “Spilling Breaking Ocean Waves and Inverse Energy Cascades,” ResearchGate preprint, Jan 2021. https://www.researchgate.net/publication/348136300
- Dommermuth, D.G., “Frequency Downshifting and Inverse Energy Cascades,” ResearchGate preprint, Jan 2021. https://www.researchgate.net/publication/348419601
- Dommermuth, D.G., “Knots and Streaks – Where to Find Them,” ResearchGate preprint, Jan 2021. https://www.researchgate.net/publication/348578523
- Dommermuth, D.G., “Whitecaps, Inverse Energy Cascades, and Energy Budgets,” ResearchGate preprint, April 2021. https://www.researchgate.net/publication/350874498
- Dommermuth, D.G., “An Annotated Bibliography of the Ocean’s Heartbeat,” ResearchGate preprint, April 2021. https://www.researchgate.net/publication/351234250
- Dommermuth, D.G., “Modeling the Ocean’s Heartbeat,” ResearchGate preprint, April 2021. https://www.researchgate.net/publication/352410045
- Dommermuth, D.G., “The Ocean’s Heartbeat,” 27th WISE Meeting, Bergen, Norway, September 5-9, 2021. https://www.researchgate.net/publication/354152802
- Dommermuth, D.G., “The Ocean’s Heartbeat,” Poster presentation, 27th WISE Meeting, Bergen, Norway, September 5-9, 2021. https://www.researchgate.net/publication/354151421
- Dommermuth, D.G., “The Ocean’s Heartbeat: An Inverse Energy Cascade that Mixes the Lower Atmosphere and Upper Ocean,” PowerPoint presentation, Air-Sea Interactions and Implications for Offshore Wind Energy, virtual event, February 10-11, 2022. https://www.researchgate.net/publication/358510653
- Dommermuth, D.G., “An Overview of the Ocean’s Heartbeat,” WISE 2022 Meeting, Brest, France, May 29-June 2, 2022. https://www.researchgate.net/publication/358228366
- Dommermuth, D.G., “An Overview of the Ocean’s Heartbeat,” PowerPoint presentation, WISE 2022 Meeting, Brest, France, May 29-June 2, 2022. https://www.researchgate.net/publication/360978580
- Dommermuth, D.G., “The Ocean’s Heartbeat: An Inverse Energy Cascade that Mixes the Lower Atmosphere and Upper Ocean,” 34th Symposium on Naval Hydrodynamics, Washington, D.C., USA, June 26 – July 1, 2022. https://www.researchgate.net/publication/361556689
- Dommermuth, D.G., “Frameworks for Studying the Ocean’s Heartbeat,” 35th Symposium on Naval Hydrodynamics, Nantes, France, July 8-12, 2024. https://www.researchgate.net/publication/381128147
- Dommermuth, D.G., “Frameworks for Studying the Ocean’s Heartbeat,” PowerPoint presentation, 35th Symposium on Naval Hydrodynamics, Nantes, France, July 8-12, 2024. https://www.researchgate.net/publication/382268957
Electric and Magnetic Fields of Meandering Flows
- Dommermuth, D. G., “Magnetic Induction due to the Effects of Breaking Ocean Waves,” ResearchGate preprint, Oct 2020.
https://www.researchgate.net/publication/344482876 - Dommermuth, D. G., “The Generation of Electric Fields by Meandering Flows,” ResearchGate preprint, Oct 2020. https://www.researchgate.net/publication/344787449 (Please see more recent technical reports on the electric field that is induced by the transport of space charge density by the meandering wind.)
- Dommermuth, D. G., “The Electric and Magnetic Fields due to the Transport of Space Charge Density by the Meandering Wind over the Ocean Surface,” ResearchGate preprint, Sep 2021. https://www.researchgate.net/publication/354665883 (Please see more recent technical reports on the electric field that is induced by the transport of space charge density by the meandering wind.)
- Dommermuth, D.G., “The Electric and Magnetic Fields due to the Transport of Space Charge Density by the Meandering Wind over the Ocean Surface: New Evidence of an Inverse Energy Cascade in the Lower Atmosphere,” ResearchGate preprint, Sep 2021. https://www.researchgate.net/publication/354935485
- Dommermuth, D.G., “The Electric and Magnetic Fields due to Magnetic Induction by Meandering Flows in the Oceanic and Atmospheric Boundary Layers: New Evidence of an Inverse Energy Cascade in the Upper Ocean,” ResearchGate preprint, Oct 2021. https://www.researchgate.net/publication/355215804
- Dommermuth, D.G., “The Magnetic Fields due to Magnetic Induction by Meandering Drift Currents,” ResearchGate preprint, Oct 2021. https://www.researchgate.net/publication/355651651
- Dommermuth, D.G., “A Parametric Study of the Electric Field in the Atmosphere due to the Transport of Space Charge Density by the Meandering Wind over the Ocean Surface,” ResearchGate preprint, Nov 2021. https://www.researchgate.net/publication/356002487
Maxima Scripts for Meandering Flows
- Dommermuth, D.G., “Maxima Coding for Solving the Electric and Magnetic Fields due to the Transport of Space Charge Density over the Ocean Surface: New Evidence of an Inverse Energy Cascade in the Lower Atmosphere,” ResearchGate code, Sep 2021. https://www.researchgate.net/publication/354935522
- Dommermuth, D.G., “A Maxima Script for Solving the Electric and Magnetic Fields due to Magnetic Induction by Meandering Flows in the Oceanic and Atmospheric Boundary Layers: New Evidence of an Inverse Energy Cascade in the Upper Ocean,” ResearchGate code, Oct 2021. https://www.researchgate.net/publication/355209396
Fortran Codes for Meandering Flows
- Dommermuth, D.G., “A Fortran Code for Calculating Electric and Magnetic Fields due to the Transport of Space Charge Density by the Meandering Wind over the Ocean Surface: New Evidence of an Inverse Energy Cascade in the Lower Atmosphere,” ResearchGate code, Sep 2021. https://www.researchgate.net/publication/354935467
- Dommermuth, D.G., “A Fortran Code for Calculating the Electric and Magnetic Fields due to Magnetic Induction by Meandering Flows in the Oceanic and Atmospheric Boundary Layers: New Evidence of an Inverse Energy Cascade in the Upper Ocean,” ResearchGate code, Oct 2021. https://www.researchgate.net/publication/355209298
- Dommermuth, D.G., “F90 Coding for Calculating the Magnetic Fields due to Magnetic Induction by Meandering Drift Currents,” ResearchGate code, Oct 2021. https://www.researchgate.net/publication/355651566
- Dommermuth, D.G., “F90 Coding for a Parametric Study of the Electric Field in the Atmosphere due to the Transport of Space Charge Density by the Meandering Wind over the Ocean Surface,” ResearchGate code, Nov 2021. https://www.researchgate.net/publication/356002311
The Effect of the Wind Drift on Wave Growth, Wave Breaking, and the Production of Turbulence
- Dommermuth, D. G., “Comments on the Wave Energy Cascade, Part 3,” ResearchGate preprint, 2018. https://www.researchgate.net/publication/325036393
- Dommermuth, D. G., “The Effect of Wind-Drift Currents on the Production of Turbulent Kinetic Energy During Wave Breaking,” ResearchGate preprint, 2018.
https://www.researchgate.net/publication/325139479 - Dommermuth, D. G., “The Effect of Wind-Drift Currents on Near-Breaking Waves,” ResearchGate preprint, 2018. https://www.researchgate.net/publication/325273964
- Dommermuth, D. G., “Breaking Waves and Wind in Equilibrium,” ResearchGate preprint, 2018. https://www.researchgate.net/publication/325883021
The Effect of Standing Waves on the Wave Energy Cascade
- Dommermuth, D. G., “Comments on the Wave Energy Cascade,” arXiv:1710.09361v2[physics.ao-ph], 2017. https://arxiv.org/abs/1710.09361v2
- Dommermuth, D. G., “Comments on the Wave Energy Cascade, Part 2,” ResearchGate preprint, 2018. https://www.researchgate.net/publication/324994196
Helmholtz Decompositions into Wavy and Vortical Portions
- Dommermuth, D. G., “The laminar interactions of a pair of vortex tubes with a free surface,” J. Fluid Mech., Vol. 246, 1993, pp. 91–115. https://doi.org/10.1017/S0022112093000059
- Mui, R. C. and Dommermuth, D. G., “The vortical structure of a near-breaking gravity-capillary wave,” Journal of Fluids Engineering, Vol. 117, 1994,355–361. https://doi.org/10.1115/1.2817269
- Dommermuth, D. G., Novikov, E.A., and Mui, C.Y., “The Interaction of Surface Waves with Turbulence,” The Proceedings of the Symposium on Free-Surface Turbulence, ASME Fluids Engineering Division Summer Meeting, Lake Tahoe, California, USA, 1994. https://www.researchgate.net/publication/271527603
Entrainment and Mixing due to Plunging Breaking Waves
- Brucker, K. A., O’Shea, T. T., Dommermuth, D. G., and Adams, P., “Three-dimensional simulations of deep-water breaking waves,” Proceedings of the 28th Symposium on Naval Hydrodynamics, Pasadena, California, USA, 2010. https://www.researchgate.net/publication/266619197
- Dommermuth, D. G., “The Entrainment and Mixing of Air due to a Rectilinear Vortex Moving Parallel to a Free Surface,” ResearchGate preprint, Jun 2020. https://www.researchgate.net/publication/342247893
Numerical Methods
- Dommermuth, D. G., “PID control of numerical simulations of breaking ocean waves,” ResearchGate preprint, Jan 2023. https://www.researchgate.net/publication/367569374
Windrows
https://www.researchgate.net/publication/344943225
Dommermuth et al. (2014); Dommermuth (2020b) show that windrows form due to the action of breaking waves. Foam, biological material, flotsam, and jetsam surf the fronts of breaking waves. The surfing action of the breaking waves scrubs the free surface clean like a wedge plow on a train clears snow. Dommermuth et al. (2014); Dommermuth (2020b) hypothesize that each successive pass of a breaking wave increases the length of the windrows. There is a sweet spot for forming long rectilinear windrows whereby there is surfing followed by spilling of foam, flotsam, jetsam, etc. off to the sides of the whitecaps. Dommermuth (2020c) shows that windrows are less likely to persist if the whitecaps are long crested. When whitecaps are too long transverse to the wind, successive passes of breaking waves tend to break up the windrows. Conversely, if whitecaps are too narrow transverse to the wind, there is no surfing to line up foam, flotsam, jetsam, etc. Here, numerical simulations confirm that successive surfing and scrubbing events lead to the formation of windrows. For Type 1 Windrows, successive spilling breaking waves progress down the middle of the breaking wave that proceeded them, whereas for Type 2 Windrows, successive spilling breaking waves progress down the middle of the windrow band of the breaking wave that proceeded them. The windrows that are formed by Type 1 interactions are thick and rectilinear. The windrows that are formed by Type 2 interactions are thinner, clumpy, and serpentine. Type 2 Windrows have twice as many bands as Type 1. Random fluctuations to the lateral positions of the spilling breakers show that Type 1 and Type 2 Windrows are persistent over a broad range. However, windrows will not form if the lateral positions of spilling breaking waves are uniformly distributed relative to each other.
Further Observations on how Wave Breaking Affects the Formation of Windrows
https://www.researchgate.net/publication/344482865
Dommermuth et al. (2014) shows that windrows form due to the action of breaking waves. Foam, biological material, flotsam, and jetsam surf the fronts of breaking waves. The surfing action of the breaking waves scrubs the free surface clean like a wedge plow on a train clears snow. Each successive pass of a breaking wave increases the length of the windrows. This surfing mechanism differs from Langmuir (1938)’s original hypothesis that the “seaweed accumulated in streaks because of transverse surface currents converging toward the streaks.” There is a sweet spot for forming long rectilinear windrows whereby there is surfing followed by spilling of foam, flotsam, jetsam, etc. off to the sides of the whitecaps. Windrows are less likely to persist if the whitecaps are long crested. When whitecaps are too long transverse to the wind, successive passes of breaking waves tend to break up the windrows. Conversely, if whitecaps are too narrow transverse to the wind, there is no surfing to line up foam, flotsam, jetsam, etc.