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.
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.