Luc Deike

Accurate parameterizations of ocean wave spectra are necessary in a wide array of disciplines including coastal, ocean, and naval engineering as well as in the study of wave interactions and ocean-atmosphere momentum flux. Many such applications use spectrum parameterizations based on temporal data collected well over a half century ago. The development of spatial wave measurement techniques that can accurately capture a larger range of scales allows us to revisit the question of how best to represent an ocean wave spectrum in a variety of ocean wave conditions. We discuss two commonly used wave spectrum parameterizations through a comparison to data collected in field campaigns studying fetch-limited, fully-developed, and mixed sea conditions. We discuss a spectrum parameterization for fully-developed seas that has a $k^{-2.5}$ (or $ω^{-4}$) dependence on the wavenumber (or angular frequency) in the tail as opposed to the $k^{-3}$ (or $ω^{-5}$) dependence seen in other frequently-used parameterizations. With knowledge of the peak wavenumber $k_p$ and significant wave height $H_s$, alongside the wind speed, fully-developed conditions can be well-represented. We then compare the impact of using different wave spectrum parameterizations through a Large Eddy Simulation (LES) study of Marine Atmospheric Boundary Layers (MABLs) over the sea surface and find that changing the parameterization used results in variations in the equivalent roughness akin to significant changes in wave conditions.

Accurate parameterizations of ocean wave spectra are necessary in a wide array of disciplines including coastal, ocean, and naval engineering as well as in the study of wave interactions and ocean-atmosphere momentum flux. Many such applications use spectrum parameterizations based on temporal data collected well over a half century ago. The development of spatial wave measurement techniques that can accurately capture a larger range of scales allows us to revisit the question of how best to represent an ocean wave spectrum in a variety of ocean wave conditions. We discuss two commonly used wave spectrum parameterizations through a comparison to data collected in field campaigns studying fetch-limited, fully-developed, and mixed sea conditions. We discuss a spectrum parameterization for fully-developed seas that has a $k^{-2.5}$ (or $ω^{-4}$) dependence on the wavenumber (or angular frequency) in the tail as opposed to the $k^{-3}$ (or $ω^{-5}$) dependence seen in other frequently-used parameterizations. With knowledge of the peak wavenumber $k_p$ and significant wave height $H_s$, alongside the wind speed, fully-developed conditions can be well-represented. We then compare the impact of using different wave spectrum parameterizations through a Large Eddy Simulation (LES) study of Marine Atmospheric Boundary Layers (MABLs) over the sea surface and find that changing the parameterization used results in variations in the equivalent roughness akin to significant changes in wave conditions.

Characterizing the Marine Atmospheric Boundary Layer (MABL) requires understanding the coupling between ocean waves and the turbulent atmospheric boundary layer above them. This coupling controls momentum exchange between the atmosphere and the ocean; it is of practical importance in the global climate, flow of ocean currents, ocean engineering, and offshore wind energy. Computational study of the MABL is complex because it must resolve the coupled physics of waves and turbulence over a wide range of spatial and temporal scales. This study expands on approaches for representing dynamic, local waves in Large Eddy Simulations (LES) of the MABL by developing a subfilter wave drag model to be local and scale-invariant. It explores the effects of different wave parameters (significant wave height and peak frequency of the wave energy spectrum) on the resulting momentum flux beyond monotonic relationships between surface stress through friction velocity $u_\ast$ and wind velocity above the surface $U_{10}$. Results are compared to field data and in a discussion on how representation of the MABL and associated momentum flux need to account for both wind and wave effects.

Characterizing the Marine Atmospheric Boundary Layer (MABL) requires understanding the coupling between ocean waves and the turbulent atmospheric boundary layer above them. This coupling controls momentum exchange between the atmosphere and the ocean; it is of practical importance in the global climate, flow of ocean currents, ocean engineering, and offshore wind energy. Computational study of the MABL is complex because it must resolve the coupled physics of waves and turbulence over a wide range of spatial and temporal scales. This study expands on approaches for representing dynamic, local waves in Large Eddy Simulations (LES) of the MABL by developing a subfilter wave drag model to be local and scale-invariant. It explores the effects of different wave parameters (significant wave height and peak frequency of the wave energy spectrum) on the resulting momentum flux beyond monotonic relationships between surface stress through friction velocity $u_\ast$ and wind velocity above the surface $U_{10}$. Results are compared to field data and in a discussion on how representation of the MABL and associated momentum flux need to account for both wind and wave effects.

Liquid interfaces appear throughout nature and engineering and are typically contaminated by surface active agents (surfactants), which are characterized by a wide range of solubility. We demonstrate that solubility enhances by an order of magnitude surfactant-induced flow in air-liquid-air films, in contrast to previously studied geometries where solubility dampens the flow. The enhancement is described by a single parameter comparing the depletion length to the film thickness. Our experiments are well described by an asymptotic theory of the Navier-Stokes equations with surfactant kinetics.

Liquid interfaces appear throughout nature and engineering and are typically contaminated by surface active agents (surfactants), which are characterized by a wide range of solubility. We demonstrate that solubility enhances by an order of magnitude surfactant-induced flow in air-liquid-air films, in contrast to previously studied geometries where solubility dampens the flow. The enhancement is described by a single parameter comparing the depletion length to the film thickness. Our experiments are well described by an asymptotic theory of the Navier-Stokes equations with surfactant kinetics.

We perform direct numerical simulations of continuously growing broadband surface waves forced by a turbulent atmospheric boundary layer coupled with a developing underwater current. We resolve and analyse the multiscale space–time evolution of the waves by considering the wave spectrum in frequency and wavenumber space and describe the kinematics of nonlinear gravity–capillary waves under a current initially described by a viscous boundary layer and transitioning to turbulence at later times under the wind-wave forcing. The wave speed experiences a scale-dependent Doppler shift, with shorter waves shifted by currents closer to the surface, in agreement with the framework from Stewart & Joy (1974 Deep Sea Res. Oceanogr. Abstracts 21(12), 1039–1049). At low wave slopes, the wave energy concentrates along the linear dispersion relation. When the wave slope is high enough, we observe wave energy located in multiple branches associated with nonlinear bound harmonics travelling at the speed of a carrier mode. These nonlinear branches are well described by a generalized nonlinear dispersion relation that links each harmonic to the effective velocity of the carrier mode to which they are bound, and are found to be Doppler shifted with the carrier mode. The generalized Doppler-shifted nonlinear dispersion relation remains valid as the underwater current becomes turbulent, and the depth-varying mean current profile can be systematically reconstructed from the measured phase velocities from waves at different scales.

We use a newly commissioned rapid expansion aerosol chamber (REACh) facility to study the homogeneous nucleation of water vapor to form liquid droplets. We perform high-speed measurements to track the partitioning of water into vapor and droplets throughout the expansion process, including tunable diode laser absorption spectroscopy (TDLAS) to access the vapor concentration and in-line holography to track the size and concentration of nucleating droplets. We retrieve the peak saturation ratio achieved in each expansion from the TDLAS measurements in combination with adjusted thermocouple temperature readout. We monitor the number of nucleated droplets and their subsequent growth as a function of saturation ratio, and observe the onset of homogeneous nucleation of water vapor occurring at a threshold saturation ratio near $S=5$, in agreement with prior literature and classical nucleation theory. The trends we observe in average diameter and droplet concentration suggest that warm air pockets near the chamber walls inhomogeneously mix with cold air at the center of the chamber following expansion. Active forced mixing with fans yields more spatially uniform temperature readings across the chamber, but also significantly broadens the droplet size distribution. Our results demonstrate the capability of TDLAS and holography techniques to track both water vapor and liquid water in the high saturation ratio environments necessary for the homogeneous nucleation of droplets. Our findings also reveal that droplet nucleation and growth dynamics are highly sensitive to turbulence.

We use a newly commissioned rapid expansion aerosol chamber (REACh) facility to study the homogeneous nucleation of water vapor to form liquid droplets. We perform high-speed measurements to track the partitioning of water into vapor and droplets throughout the expansion process, including tunable diode laser absorption spectroscopy (TDLAS) to access the vapor concentration and in-line holography to track the size and concentration of nucleating droplets. We retrieve the peak saturation ratio achieved in each expansion from the TDLAS measurements in combination with adjusted thermocouple temperature readout. We monitor the number of nucleated droplets and their subsequent growth as a function of saturation ratio, and observe the onset of homogeneous nucleation of water vapor occurring at a threshold saturation ratio near $S=5$, in agreement with prior literature and classical nucleation theory. The trends we observe in average diameter and droplet concentration suggest that warm air pockets near the chamber walls inhomogeneously mix with cold air at the center of the chamber following expansion. Active forced mixing with fans yields more spatially uniform temperature readings across the chamber, but also significantly broadens the droplet size distribution. Our results demonstrate the capability of TDLAS and holography techniques to track both water vapor and liquid water in the high saturation ratio environments necessary for the homogeneous nucleation of droplets. Our findings also reveal that droplet nucleation and growth dynamics are highly sensitive to turbulence.

Bubbles entrained by breaking waves rise to the ocean surface where they cluster and burst, emitting sea spray aerosols into the atmosphere. Bubble bursting thereby links seawater biogeochemistry and aerosol chemistry, influencing the ability of emitted aerosols to serve as cloud condensation nuclei or ice nucleating particles. The mechanisms of film drop and jet drop production are modulated by organic material present in seawater, which may affect the size, number, and composition of resulting aerosols. We disentangle the effect of surfactant on collective bursting processes using laboratory experiments with detailed bubble and aerosol measurements down to small sizes, multiple bubble size configurations, and measurements of bubble lifetime. Submicron aerosol emission, linked to film drop production, increased with surfactant up to an optimal concentration, while production of supermicron aerosols emitted through jet drop production was shut down. Our work paves the way to integrate organic composition into sea spray emission functions.

Bubbles entrained by breaking waves rise to the ocean surface where they cluster and burst, emitting sea spray aerosols into the atmosphere. Bubble bursting thereby links seawater biogeochemistry and aerosol chemistry, influencing the ability of emitted aerosols to serve as cloud condensation nuclei or ice nucleating particles. The mechanisms of film drop and jet drop production are modulated by organic material present in seawater, which may affect the size, number, and composition of resulting aerosols. We disentangle the effect of surfactant on collective bursting processes using laboratory experiments with detailed bubble and aerosol measurements down to small sizes, multiple bubble size configurations, and measurements of bubble lifetime. Submicron aerosol emission, linked to film drop production, increased with surfactant up to an optimal concentration, while production of supermicron aerosols emitted through jet drop production was shut down. Our work paves the way to integrate organic composition into sea spray emission functions.

Abstract Bubble-mediated exchange during wave breaking is an essential pathway for oxygen transfer at the ocean–atmosphere interface. Conventional wind-dependent gas transfer velocity formulations generally ignore wave-bubble effects and use local wind speed alone to determine the air–sea gas exchange rate. Here, we quantify the influence of waves and bubbles using a generalised wind-wave-bubble gas transfer formulation that accounts for symmetric (diffusive flux through the unbroken ocean and large bubble surface) and asymmetric (pressurised large and small bubbles that dissolve completely) contributions. We contrast it with a widely used wind-dependent formulation using simulations from a global ocean circulation model over the historical period (1959–2020). Including waves and bubbles reduces the model–observation mismatch with quality-controlled biogeochemical Argo float oxygen concentrations in key mode and deep water mass formation regions by ∼70% to 90% and captures observed episodes of bubble-induced supersaturation. This addresses the systematic oxygen undersaturation bias simulated by the wind-dependent simulation. These surface changes propagate into the interior, raising oxygen concentrations by +2 to +10 µ mol kg −1 across most water mass layers. The wind-wave-bubble formulation also enhances flux variability across timescales, and amplifies the climatological seasonal amplitude of the global air–sea oxygen flux by ∼30% relative to the wind-dependent formulation. These results establish bubbles as a first-order, global-scale control on ocean oxygen, resulting in a closer match to observed oxygen saturation and enhancing interior oxygen ventilation.

Surfactants at the air–sea interface are known to alter surface wave dynamics by modifying surface tension and Marangoni stresses. In this study, we perform two-dimensional direct numerical simulations of gravity-capillary waves with insoluble surfactants using a coupled phase field and volume-of-fluid method. We consider a nonlinear equation of state for surface tension and resolve Marangoni stresses induced by surfactant concentration gradients. We explore a broad parameter space characterised by initial wave steepness $ak$ , Bond number $\textit{Bo}$ (comparing gravity and surface tension), Reynolds number $\textit{Re}$ (comparing inertia and viscosity), and the importance of surfactant concentration and strength of the gradient, characterised by a surfactant parameter $\beta$ . We analyse the impact of surfactants on wave patterns, surface roughness, wave breaking, energy dissipation and surface vorticity. Our results reveal a non-monotonic dependence of wave shape, roughness, vorticity and energy dissipation on $\beta$ , which is found to be governed by Marangoni effects that peak at intermediate surfactant concentrations. Wave regime transition at high $\textit{Bo}$ is governed by an effective $\textit{Bo}$ , which accounts for the reduction in surface tension induced by surfactants. We further introduce a rescaled parameter $\textit{Bo}\,\textit{Re}^{-1/2}\,(ak)^{-1}$ based on force balance, which collapses the transition boundaries across different $\textit{Re}$ . These findings provide a systematic understanding of surfactant-modulated wave dynamics for both laboratory and geophysical applications.

Abstract We investigate the energy growth and dissipation of wind‐forced breaking waves at high wind speed using direct numerical simulations of the coupled air–water Navier–Stokes equations. A turbulent wind boundary layer drives the growth of a pre‐existing narrowband wave field until it breaks, transferring energy into the water column. Under sustained wind forcing, the wave field resumes growth. We separately analyze energy transfers during wave growth and breaking‐induced dissipation. Energy transfers are dominated by pressure input during growth and turbulent dissipation during breaking. Wind input during growth is balanced with dissipation during breaking over an entire growing‐breaking cycle. The wave growth rate scales with , modulated by the wave steepness due to sheltering, and the energy dissipation follows the inertial scaling with wave slope at breaking, confirming the universality of the process. Following breaking, near‐surface vertical turbulence dissipation profiles scale as , with their magnitude controlled by the breaking‐induced dissipation.

When a large air cavity breaks in a turbulent flow, it goes through very large deformations and cascading events of new interface formation, including elongated filaments and bubbles over a wide range of scales, with their rate of formation controlled by turbulence and capillary processes. We experimentally investigate the effects of surfactants and salt on the fragmentation, and observe an order of magnitude increase of the number of bubbles being produced in some cases. For bubbles larger than the Hinze scale $d_H$ (defined as the balance between surface tension and turbulence stresses), we observe that bubble size distributions remain unchanged for all solutions tested. For bubbles below $d_H$, however, we observe an increase of the number of bubbles produced and an associated steepening of the bubble size distribution upon the addition of surfactant or salt. This later effect is only visible for some of the surfactants tested when their adsorption timescale is fast enough compared to the rate at which new interfaces are being generated by turbulence.

When a large air cavity breaks in a turbulent flow, it goes through very large deformations and cascading events of new interface formation, including elongated filaments and bubbles over a wide range of scales, with their rate of formation controlled by turbulence and capillary processes. We experimentally investigate the effects of surfactants and salt on the fragmentation, and observe an order of magnitude increase of the number of bubbles being produced in some cases. For bubbles larger than the Hinze scale $d_H$ (defined as the balance between surface tension and turbulence stresses), we observe that bubble size distributions remain unchanged for all solutions tested. For bubbles below $d_H$, however, we observe an increase of the number of bubbles produced and an associated steepening of the bubble size distribution upon the addition of surfactant or salt. This later effect is only visible for some of the surfactants tested when their adsorption timescale is fast enough compared to the rate at which new interfaces are being generated by turbulence.

The coalescence and breakup of drops are classic examples of flows that feature singularities. The behaviour of viscoelastic fluids near these singularities is particularly intriguing – not only because of their added complexity, but also due to the unexpected responses they often exhibit. In particular, experiments have shown that the coalescence of viscoelastic sessile drops can differ significantly from that of their Newtonian counterparts, sometimes resulting in a sharply distorted interface. However, the mechanisms driving these differences in dynamics, as well as the potential influence of the contact angle are not fully known. Here, we study two different flow regimes effectively induced by varying the contact angle and demonstrate how that leads to markedly different coalescence behaviours. We show that the coalescence dynamics is effectively unaltered by viscoelasticity at small contact angles. The Deborah number, which is the ratio of the relaxation time of the polymer to the time scale of the background flow, scales as $\theta ^3$ for $\theta \ll 1$ , thus rationalising the near-Newtonian response. On the other hand, it has been shown previously that viscoelasticity dramatically alters the shape of the interface during coalescence at large contact angles. We study this large contact angle limit using two-dimensional numerical simulations of the equation of motion. We show that the departure of the coalescence dynamics from the Newtonian case is a function of the Deborah number and the elastocapillary number, which is the ratio between the shear modulus of the polymer solution and the characteristic stress in the fluid.

The coalescence and breakup of drops are classic examples of flows that feature singularities. The behaviour of viscoelastic fluids near these singularities is particularly intriguing – not only because of their added complexity, but also due to the unexpected responses they often exhibit. In particular, experiments have shown that the coalescence of viscoelastic sessile drops can differ significantly from that of their Newtonian counterparts, sometimes resulting in a sharply distorted interface. However, the mechanisms driving these differences in dynamics, as well as the potential influence of the contact angle are not fully known. Here, we study two different flow regimes effectively induced by varying the contact angle and demonstrate how that leads to markedly different coalescence behaviours. We show that the coalescence dynamics is effectively unaltered by viscoelasticity at small contact angles. The Deborah number, which is the ratio of the relaxation time of the polymer to the time scale of the background flow, scales as $\theta ^3$ for $\theta \ll 1$ , thus rationalising the near-Newtonian response. On the other hand, it has been shown previously that viscoelasticity dramatically alters the shape of the interface during coalescence at large contact angles. We study this large contact angle limit using two-dimensional numerical simulations of the equation of motion. We show that the departure of the coalescence dynamics from the Newtonian case is a function of the Deborah number and the elastocapillary number, which is the ratio between the shear modulus of the polymer solution and the characteristic stress in the fluid.

Surface bubbles in the ocean are critical in moderating several fluxes between the atmosphere and the ocean. In this paper, we experimentally investigate the drainage and lifetime of surface bubbles in solutions containing surfactants and salts, subjected to turbulence in the air surrounding them modelling the wind above the ocean. We carefully construct a set-up allowing us to repeatably measure the mean lifetime of a series of surface bubbles, while varying the solution and the wind speed or humidity of the air. To that end, we show that renewing the surface layer is critical to avoid a change of the physical properties of the interface. We show that the drainage of the bubbles is well modelled by taking into account the outwards viscous flow and convective evaporation. The mean lifetime of surface bubbles in solutions containing no salt is controlled by evaporation and independent on surfactant concentration. When salt is added, the same scaling is valid only at high surfactant concentrations. At low concentrations, the lifetime is always smaller and independent of wind speed, owing to the presence of impurities triggering a thick bursting event. When the mean lifetime is controlled by evaporation, the probability density of the lifetime is very narrow around its mean, while when impurities are present, a broad distribution is observed.

Surface tension gradients of air–liquid–air films play a key role in governing the dynamics of systems such as bubble caps, foams, bubble coalescence and soap films. Furthermore, for common fluids such as water, the flow due to surface tension gradients, i.e. Marangoni flow, is often inertial, due to the low viscosity and high velocities. In this paper, we consider the localised deposition of insoluble surfactants onto a thin air–liquid–air film, where the resulting flow is inertial. As observed by Chomaz (2001 J. Fluid Mech . 442 , 387–409), the resulting governing equations with only inertia and Marangoni stress are similar to the compressible gas equations. Thus, shocks are expected to form. We derive similarity solutions associated with the development of such shocks, where the mathematical structure is closely related to the Burgers equation. It is shown that the nonlinearity of the surface tension isotherm has an effect on the strength of the shock. When regularisation mechanisms are included, the shock front can propagate and late-time similarity solutions are derived. The late-time similarity solution due to regularisation by capillary pressure alone was found by Eshima et al. (2025 Phys. Rev. Lett. 134 , 214002). Here, the regularisation mechanism is generalised to include viscous extensional stress.

Surface bubbles in the environment or engineering configurations, such as the ocean-atmosphere interface, sparkling wine, or during volcanic eruptions typically live on contaminated surfaces. A particularly common type of contamination is surface active agents (surfactants). We consider the effect of insoluble surfactant on jet drop formation by bubble bursting. Contrary to the observed trend that surfactants decrease the ejected drop radius for bubbles with precursor capillary waves, we find that surfactants increase the ejected drop radius for bubbles without precursor capillary waves—a regime characteristic of small bubbles. Consequently, the results have fundamental implications for understanding aerosol distributions in contaminated conditions. We find that the trend reversal is due to the effect of Marangoni stresses on the focusing of the collapsing cavity. We demonstrate quantitative agreement on the jet velocity and drop size between laboratory experiments and numerical simulations by using the measured surface tension dependence on surfactant concentration as the equation of state for the simulations.

Shocks due to hyperbolic partial differential equations (PDEs) appear throughout mathematics and science. The canonical example is shock formation in the inviscid Burgers' equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=0$. Previous studies have shown that when shocks form for the inviscid Burgers' equation, for positions and times close to the shock singularity, the dynamics are locally self-similar and universal, i.e., dynamics are equivalent regardless of the initial conditions. In this paper, we show that, in fact, shock formation is self-similar and universal for general first-order strictly hyperbolic PDEs in one spatial dimension, and the self-similarity is like that of the inviscid Burgers' equation. An analytical formula is derived for the self-similar universal solution.

Bubbles bursting at the surface of the ocean produce drops that heavily influence ocean-atmosphere interactions. One of the mechanisms through which drops are formed is called jet drop production, where the collapse of the bubble cavity leads to the formation of a fast upwards jet that breaks to form drops. While isolated bubble bursting has been extensively studied, bubbles are often found in rafts (for instance in the ocean surface or a sparkling wine glass) and the understanding of collective effects remains more limited. We investigate experimentally how jet drop formation is modified by the presence of neighboring bubbles during the collapse. With the help of multiple high speed views of the collapsing bubble, we show how a change of cavity shape during collapse leads to the selection of smaller, faster, and more numerous drops. The size of the emitted drops is monotonically reduced with increasing number of neighboring bubbles (up to six for hexagonal packing) with the size reduction reaching a factor 5. The drop size distribution associated with bubbles arranged in rafts of various sizes is therefore much wider than in the case of isolated bubbles, and with a peak shifted to smaller sizes.

Bubble-mediated gas exchange associated with wave breaking is a critical pathway for ocean-atmosphere exchange of low solubility gases such as oxygen. Yet, ocean and climate models, as well as observation-based products, usually rely on wind-only air-sea flux formulations derived from carbon constraints that ignore the asymmetric nature of the bubble flux, contributing to discrepancies between estimates of oxygen inventories and their response to climate change. Without bubbles, gas exchange is controlled by a symmetric wind-driven exchange, with the ocean-atmosphere gas partial pressure difference controlling whether outgassing or uptake occurs. Bubbles entrained by wave breaking can enhance this symmetric turbulent exchange, and contribute an additional asymmetric flux, always leading to an uptake, as they get squeezed by hydrostatic pressure (large bubbles) or collapse and fully dissolve (small bubbles). We present an observation-constrained theoretical framework of the air-sea flux accounting for air entrainment due to wave breaking and symmetric and asymmetric bubble exchange. The combined evidence from theory, laboratory, and field measurements of carbon dioxide fluxes, oxygen concentration, and noble gas supersaturation yields a universal formulation of gas exchange which we implement into a global ocean biogeochemical model. We discuss the resulting oxygen fluxes and demonstrate that our wind-wave-bubble formulation better reproduces observed in situ oxygen concentrations in water mass formation regions, where air-sea exchange is high, than a commonly used wind-only formulation. We show that the asymmetric bubble flux is essential for evaluating air-sea oxygen fluxes and estimating the magnitude of the ocean oxygen loss associated with global warming.

Despite its importance in both geophysical and industrial contexts, the inertial fragmentation of gas filaments has received much less attention than their liquid counterparts. Yet, gas filaments produce the smallest bubble sizes, which drive gas dissolution, critical to ocean-atmosphere exchange such as carbon dioxide and oxygen, as well as marine aerosols emission, serving as nuclei for cloud condensation and ice particle production. Here, we unravel the fundamental physics governing the splitting of a single filament in a model geometry by combining numerical simulations, laboratory experiments and theory. We show that the splitting of a single filament generates a power-law bubble size distribution following $d^{-3/2}$ with $d$ the volume equivalent bubble diameter, suggesting the existence of a self-similar breakup mechanism, absent in liquid ligament fragmentation. We propose a deterministic model, based on the capillary fragmentation of a filament with power-law shape, which quantitatively captures the bubble size distribution. We demonstrate that the filament shape at breakup sets the size distribution of a first generation of bubbles. This distribution is then reproduced at smaller and smaller scales by latter breakups in a self-similar manner. The $d^{-3/2}$-distribution coincides with the size distribution of small bubbles observed in dilute turbulent flow, such as below breaking waves. We argue that the turbulent bubble size distribution observed in nature arises as the superposition of many individual filament splittings. The turbulence nature of the flow only sets the initial conditions of each splitting dynamics, and play no role in the bubble size selection.

Bubbles entrained by breaking waves rise to the ocean surface, where they cluster before bursting and release droplets into the atmosphere. The ejected drops and dry aerosol particles, left behind after the liquid drop evaporates, affect the radiative balance of the atmosphere and can act as cloud condensation nuclei. The remaining uncertainties surrounding the sea spray emissions function motivate controlled laboratory experiments that directly measure and link collective bursting bubbles and the associated drops and sea salt aerosols. We perform experiments in artificial seawater for a wide range of bubble size distributions, measuring both bulk and surface bubble distributions (measured radii from $30\,\unicode{x03BC} \mathrm{m}$ to $5\,\mathrm{mm}$ ), together with the associated drop size distribution (salt aerosols and drops of measured radii from $50\,\mathrm{nm}$ to $500\,\unicode{x03BC} \mathrm{m}$ ) to quantify the link between emitted drops and bursting surface bubbles. We evaluate how well the individual bubble bursting scaling laws describe our data across all scales and demonstrate that the measured drop production by collective bubble bursting can be represented by a single framework integrating individual bursting scaling laws over the various bubble sizes present in our experiments. We show that film drop production by bubbles between $100\,\unicode{x03BC} \mathrm{m}$ and $1\,\mathrm{mm}$ describes the submicron drop production, while jet drop production by bubbles from $30\,\unicode{x03BC} \mathrm{m}$ to $2\,\mathrm{mm}$ describes the production of drops larger than $1\,\unicode{x03BC} \mathrm{m}$ . Our work confirms that sea spray emission functions based on individual bursting processes are reasonably accurate as long as the surface bursting bubble size distribution is known.

Abstract Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multilayer numerical solver resolving upper-ocean dynamics over scales from O (50) cm to O (1) km, including a broadbanded wave field and wave breaking. The present numerical study isolates the effect of wave breaking and allows us to study the surface layer in wave-influenced and wave-breaking-dominated regimes. Following our previous work showing wave-breaking statistics in agreement with field observations, we extend the analysis to underwater breaking-induced turbulence and related dissipation (in freely decaying conditions). We observe a rich field of vorticity resulting from the turbulence generation by breaking waves. We discuss the vertical profiles of dissipation rate, which are compared with field observations, and propose an empirical universal shape function. Good agreement is found, further demonstrating that wave breaking can dominate turbulence generation in the near-surface layer. We examine the dissipation from different angles: the global dissipation of the wave field computed from the decaying wave field, the spectral dissipation from the fifth moment of the breaking front distribution, and a turbulence dissipation estimated from the underwater strain-rate tensor. Finally, we consider how these different estimates can be understood as part of a coherent framework.

Surface bubbles in the environment or engineering configurations, such as the ocean-atmosphere interface, sparkling wine, or during volcanic eruptions typically live on contaminated surfaces. A particularly common type of contamination is surface active agents (surfactants). We consider the effect of insoluble surfactant on jet drop formation by bubble bursting. Contrary to the observed trend that surfactants decrease the ejected drop radius for bubbles with precursor capillary waves, we find that surfactants increase the ejected drop radius for bubbles without precursor capillary waves - a regime characteristic of small bubbles. Consequently, the results have fundamental implications for understanding aerosol distributions in contaminated conditions. We find that the trend reversal is due to the effect of Marangoni stresses on the focusing of the collapsing cavity. We demonstrate quantitative agreement on the jet velocity and drop size between laboratory experiments and numerical simulations by using the measured surface tension dependence on surfactant concentration as the equation of state for the simulations. *Jun Eshima and Tristan Aurégan contributed equally to this work.

We perform Direct Numerical Simulations of broadband surface waves forced by a turbulent atmospheric boundary layer coupled with a developing underwater current. We analyze the spatio-temporal evolution of the wave spectrum and describe the kinematics of nonlinear gravity-capillary waves under a current transitioning to turbulence. The wave speed experiences a scale-dependent Doppler shift, with shorter waves shifted by currents closer to the surface, aligning with the framework from Stewart and Joy (1974). At low wave slope, the wave energy concentrates along the linear dispersion relation. When the wave slope is high enough, we observe wave energy located in multiple branches associated with nonlinear bound harmonics traveling at the speed of a carrier mode. These nonlinear branches can be described by resonant three-wave interactions. We obtain a generalized nonlinear dispersion relation accounting for both the influence of various wave modes and the effect of the depth-varying current.

We investigate experimentally the effect of salinity and atmospheric humidity on the drainage and lifetime of thin liquid films motivated by conditions relevant to air–sea exchanges. We show that the drainage is independent of humidity and that the effect of a change in salinity is reflected only through the associated change in viscosity. On the other hand, film lifetime displays a strong dependence on humidity, with more than a tenfold increase between low and high humidities: from a few seconds to tens of minutes. Mixing the air surrounding the film also has a very important effect on lifetime, modifying its distribution and reducing the mean lifetime of the film. From estimations of the evaporation rate, we are able to derive scaling laws that describe well the evolution of lifetime with a change of humidity. Observations of the black film, close to the top where the film ruptures, reveal that this region is very sensitive to local humidity conditions.

Abstract High‐frequency wind and wave variability influence air‐sea gas fluxes by modulating the gas transfer velocity at the interface. Traditional gas transfer velocity formulations scale solely with wind speed and neglect wave effects, including wave breaking and bubble‐mediated transfer. In this study, we quantify the influence of wave effects on the air‐sea flux and ocean carbon storage using a wind‐wave‐bubble gas transfer velocity formulation in an ocean general circulation model (MOM6‐COBALTv2). Wave effects introduce strong variability in global air‐sea fluxes at high‐frequency and seasonal timescales (+15–40%). Compared to a traditional wind‐dependent formulation, local fluxes can be modified by 2–20 mmol (i.e., 20–50% flux difference), with the largest differences occurring during storms. The wind‐wave‐bubble formulation yields a modest global increase in ocean carbon storage (+0.07 PgC , 3%) due to regional and seasonal compensations, as well as the p feedback that limits the flux response to a faster exchange velocity. Yet, wave effects lead to an enhancement of carbon storage within the ocean interior, with the largest gain in mode and intermediate waters and a wave‐induced hemispheric asymmetry in carbon storage. Notably, the southern hemisphere, where wave activity is consistently high, gains more carbon than the more sheltered northern hemisphere. These results highlight the need to account for wave‐induced variability to capture local and seasonal carbon dynamics, which are essential, for instance, to high‐frequency in situ observational deployments and regional marine carbon dioxide removal assessment efforts.

The thinning of liquid sheets and the resulting capillary waves due to surfactant deposition are relevant to understanding how bubbles burst, with implications for the environment, health, and industry. Here, a similarity solution is obtained, which describes the sheet thinning and capillary waves. The final rupture mechanism of a bubble is explored, suggesting that insoluble surfactant deposition alone does not cause finite-time rupture; instead, sufficient thinning may allow other physical mechanisms to do so. Comparisons to an existing experiment and suggestions for measurements are given.

Surface bubbles in the ocean are critical in moderating several fluxes between the atmosphere and the ocean. In this paper, we experimentally investigate the drainage and lifetime of surface bubbles in solutions containing surfactants and salts, subjected to turbulence in the air surrounding them modelling the wind above the ocean. We carefully construct a setup allowing us to repeatably measure the mean lifetime of a series of surface bubbles, while varying the solution and the wind speed or humidity of the air. To that end, we show that renewing the surface layer is critical to avoid a change of the physical properties of the interface. We show that the drainage of the bubbles is well modelled by taking into account the outwards viscous flow and convective evaporation. The mean lifetime of surface bubbles in solutions containing no salt is controlled by evaporation and independent on surfactant concentration. When salt is added, the same scaling is valid only at high surfactant concentrations. At low concentrations, the lifetime is always smaller and independent of wind speed, owing to the presence of impurities triggering a thick bursting event. When the mean lifetime is controlled by evaporation, the probability density of lifetime is very narrow around its mean, while when impurities are present, a broad distribution is observed.