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Here is a video of windrows forming on Sheepscot Lake. The white streaks of foam are the windrows. The formation of windrows is described in Dommermuth, D.G., Lewis, C.D., Tran, V.H., and Valenciano, M.A. (2014) “Simulations of wind-driven breaking ocean waves with data assimilation,” Proceedings of the 30th Symposium on Naval Hydrodynamics, Hobart, Tasmania, Australia. The paper is available at http://tinyurl.com/y79sm9rp. Videos associated with the paper are available at http://tinyurl.com/y8madvbw. Animations of windrows forming are available at these links: https://youtu.be/6r9JbrykUcE, https://youtu.be/JnLGxS3c4dA, https://youtu.be/IhrHRJSYfPE, and https://youtu.be/Sbn23QN3jD4.

This animation shows a numerical simulation of windrows forming.  Among other things, Dommermuth, Lewis, Tran, and Valenciano (2014) discuss the formation of windrows under the action of wind. The paper is available at http://tinyurl.com/y79sm9rp. Videos associated with the paper are available at http://tinyurl.com/y8madvbw. Dommermuth, et al. (2014) use Lagrangian particles to illustrate the formation of windrows. Animations of windrows forming using Lagrangian particles are available at these links: https://youtu.be/6r9JbrykUcE, https://youtu.be/JnLGxS3c4dA, https://youtu.be/IhrHRJSYfPE, and https://youtu.be/Sbn23QN3jD4. A video of windrows forming on a lake is available at https://youtu.be/iL0wb00Y4es.

As discussed by Dommermuth, et al. (2014), surfing and swirling jets are key mechanisms in the formation of windrows. Pizzo (2017) and Deike, Pizzo, and Melville, W. K. (2017) also study surfing using Lagrangian particles.

Dommermuth, et al.’s (2014) studies are three-dimensional. Pizzo’s (2017) studies are two-dimensional. As shown by Dommermuth, et al. (2014), the formation of windrows is strongly tied to the formation of Langmuir circulations in the upper ocean and wind streaks in the lower atmosphere. Pizzo discusses implications of surfing in the upper ocean, but since his simulations are two-dimensional, some key mechanisms associated with the formation of windrows and Langmuir circulations are missing. Furthermore, most of the surfing events that are observed in Dommermuth, et al. (2014) are due to spilling breaking, whereas Pizzo’s (2017) analysis is focused on plunging.

Dommermuth, et al. (2014) study the formation of windrows as a result of surfing wind-driven waves. Pizzo (2017) studies Lagrangian transport using analytical solutions for plunging breaking waves, and Deike, et al. (2017) use dispersive focusing to model Lagrangian transport. Pizzo (2017) and Deike, et al. (2017) need to get off the computer and out of the laboratory and visit Sheepscot Lake on a windy day (see https://youtu.be/iL0wb00Y4es) to see how foam surfs waves.

Pizzo (2017) does not cite Dommermuth, et al. (2014). Whether or not Deike, et al. (2017) cite Dommermuth, et al. (2014) is unknown.

References:

Dommermuth, D.G., Lewis, C.D., Tran, V.H., and Valenciano, M.A. (2014) “Simulations of wind-driven breaking ocean waves with data assimilation,” Proceedings of the 30th Symposium on Naval Hydrodynamics, Hobart, Tasmania, Australia.

Pizzo, N.E. (2017) Surfing surface gravity waves, J. Fluid Mech., 823, 316–328.

Deike, L., Pizzo, N. E. and Melville, W. K. (2017) Lagrangian transport by breaking surface waves. J. Fluid Mech. (submitted).

 

Energy dissipation, air entrainment, and statistical analyses of plunging breaking waves based on the Numerical Flow Analysis (NFA) code are discussed in Brucker, O’Shea, Dommermuth, and Adams (2010) “Three-dimensional simulations of deep-water breaking waves,” Proceedings of the 28th Symposium on Naval Hydrodynamics, Pasadena, California, USA. The paper is available at http://tinyurl.com/y8eava8e. Videos associated with the paper are available at http://tinyurl.com/yc38hk5u.

Volumetric energy and air entrainment analyses are made by Chen, Kharif, Zaleski, and Li (1999), Brucker, et al. (2010), Deike, Popinet, and Melville (2015), and Deike, Melville, and Popinet (2016). Brucker, et al. (2010) and Deike, et al. (2016) analyze the spatial variation in air entrainment. Brucker, et al. (2010) analyze the spatial variation in the mean kinetic energy balance using Reynolds and Favre averaging.

Dommermuth, Lewis, Tran, and Valenciano (2014) discuss wind-driven breaking waves. The paper is available at http://tinyurl.com/y79sm9rp. Videos associated with the paper are available at http://tinyurl.com/y8madvbw.

A formulation is developed to assimilate ocean-wave data into the Numerical Flow Analysis (NFA) code. NFA is a Cartesian-based implicit Large-Eddy Simulation (LES) code with Volume of Fluid (VOF) interface capturing. The sequential assimilation of data into NFA permits detailed analysis of ocean-wave physics with higher bandwidths than is possible using either other formulations, such as High-Order Spectral (HOS) methods, or field measurements. A framework is provided for assimilating the wavy and vortical portions of the flow. Nudging is used to assimilate wave data at low wavenumbers, and the wave data at high wavenumbers form naturally through nonlinear interactions, wave breaking, and wind forcing. Similarly, the vertical profiles of the mean vortical flow in the wind and the wind drift are nudged, and the turbulent fluctuations are allowed to form naturally. As a demonstration, the results of a HOS of a JONSWAP wave spectrum are assimilated to study short-crested seas in equilibrium with the wind. Log profiles are assimilated for the mean wind and the mean wind drift. The results of the data assimilations are (1) Windrows form under the action of breaking waves and the formation of swirling jets; (2) The crosswind and cross drift meander; (3) Swirling jets are organized into Langmuir cells in the upper oceanic boundary layer; (4) Swirling jets are organized into wind streaks in the lower atmospheric boundary layer; (5) The length and time scales of the Langmuir cells and the wind streaks increase away from the free surface; (6) Wave growth is very dynamic especially for breaking waves; (7) The effects of the turbulent fluctuations in the upper ocean on wave growth need to be considered together with the turbulent fluctuations in the lower atmosphere; and (8) Extreme events are most likely when waves are not in equilibrium.

The above animation is described in the paper “Three-Dimensional Simulations of Deep-Water Breaking Waves.” The paper is available for download at http://tinyurl.com/y8eava8e. Videos associated with the paper are available at http://tinyurl.com/yc38hk5u.

The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully non- linear progressive waves are generated by applying a normal stress to the free surface. Precise control of the forcing allows for a systematic study of four types of deep-water breaking waves, characterized herein as weak plunging, plunging, strong plunging, and very strong plunging.

The three-dimensional isocontours of vorticity exhibit intense streamwise vorticity shortly after the initial ovular cavity of air is entrained during the primary plunging event. An array of high resolution images are presented as a means to visually compare and contrast the major events in the breaking cycles of each case. The volume-integrated energy shows 50% or more of the peak energy is dissipated in strong and very strong plunging events. The volume of air entrained beneath the free surface is quantified. For breaking events characterized by plunging, strong plunging and very strong plunging, significant quantities of air remain beneath the free surface long after the initial breaking event. The rate at which the air beneath the free surface degasses is linear and the same in all cases. The use of volume-weighted (Reynolds) and mass-weighted (Favre) averages are compared, and it is found that statistics obtained by Favre averaging show better agreement with respect to the position of free surface than do those obtained by Reynolds averaging. The average volume fraction plotted on a log scale is used to visually elucidate small volumes of air entrained below the free surface. For the strong plunging and very strong plunging cases significant air is also entrained after the initial plunging event at the toe of spilling breaking region. Improvements to the Numerical Flow Analysis code, which expand the types of problems it can accurately simulate are discussed, along with the results of a feasibility study which shows that simulations with 5-10 billion unknowns are now tractable.