Reduction of air-sea momentum flux due to whitecap residual foam observed during a laboratory experiment

Abstract

Whitecap foam, created by breaking waves, is a ubiquitous ocean surface feature. Full understanding of its role in the air-sea interaction is crucial for precise momentum flux parameterization which directly influences forecast accuracy, especially in hurricanes where whitecaps are pervasive. Despite its importance, the role of whitecap foam in air-sea interaction remains largely unexplored. This study uses a wind-wave tank and an artificial foam generator to study the impact of whitecap residual foam on air-sea coupling. We find that foam reduces momentum flux, indicative of a smoothed surface roughness, and reduces wave form stress across all wind speeds, with a more pronounced effect in surfactant-rich water. Foam also alters wave characteristics and airflow separation. These findings offer new insights into whitecap residual foam’s role in air–sea coupling and have implications for modelling hurricanes and other wind driven processes.

Introduction

Our capacity to accurately predict hurricane intensity is intimately tied to our understanding of air-sea coupling, especially wind-wave coupling¹. Wind-wave coupling has enormous implications for momentum transfer across the air-sea interface^2,3,4. It impacts wave dynamics and upper ocean mixing⁵ and alters hurricane development and intensification^6,7,8,9.

Within the air-sea boundary layer, the friction velocity ($u_{*}$) can be calculated from the wind stress ($\tau$) via Eqs. (1 and 2),

$$\tau = \rho u_{*}^{2}$$

(1)

$$u_{*} = \left[ {\left( {\overline{{ - u^{\prime}w^{\prime}}} } \right)^{2} + \left( {\overline{{ - v^{\prime}w^{\prime}}} } \right)^{2} } \right]^{\frac{1}{4}} .$$

(2)

Here, $u^{\prime},v^{\prime},w^{\prime}$, are wind fluctuations in the along, cross, and vertical directions, and overbar is the time average. In laboratory experiments, $v$ can be neglected, because of assumed uniformity in the lateral direction¹⁰, as shown in Eq. (3),

$$u_{*} = \left[ {\left( {\overline{{ - u^{\prime}w^{\prime}}} } \right)^{2} } \right]^{\frac{1}{4}} .$$

(3)

In ocean, weather, and climate modelling, the wind stress is typically parameterized by the product of the drag coefficient ($C_{D}$) and 10-m wind speed ($U_{10}$) following Eq. (4),

$$\tau = \rho_{a} C_{D} U_{10}^{2} .$$

(4)

$C_{D}$ quantifies the transfer rate of momentum across the air-sea interface. Many observational studies have worked to improve $C_{D}$ parameterization by quantifying the impacts of environmental factors, such as wind speed¹¹, waves^12,13, gustiness¹⁴, and atmospheric stability¹⁵. Fundamentally, $C_{D}$ approximately linearly increases with wind speed^16,17. This relationship is widely utilized in ocean and climate modelling^3,18. However, Powell, et al.¹⁹, Donelan, et al.²⁰ and others^5,21,22 found that $C_{D}$ reaches a plateau when $U_{10}$ is around 30 m/s. However, the precise mechanism that causes this is not understood.

One explanation is airflow separation resulting from steeper waves at high wind speeds²⁰. This theory posits that as waves become steeper the wind detaches from one crest and reattaches at the next, having limited interaction with the wave trough which reduces momentum exchange²³. Reul, et al. ²⁴ observed flow separation in a 1-D wave tank where waves had effectively infinite width, making this condition unrealistic of the open ocean. Potter et al.²⁵ attributed the C_D roll-off during a typhoon above 22 m s⁻¹ to flow separation. At the time, the waves were very large, strongly forced, and aligned with the wind, meaning that the conditions were unique and unlikely to regularly occur in the field, especially at lower wind speeds. As such, it remains uncertain whether flow separation is the primary mechanism leading to the leveling of $C_{D}$ at high wind speeds.

Another theory for the limiting nature of the drag coefficient is the slip-layer^1,19,26, which is caused by an amalgamation of bubbles, foam, spray, and streaks at the air-sea interface during highly forced conditions²⁷. Whitecap foam is distinguished as either an actively generated (stage A) that forms along the crest of a breaking wave, or decaying (stage B) foam left on the surface²⁸. For this study, we used a foam generator to simulate whitecap residual foam analogous to the lingering stage B foam. This foam is thought to dampen the capillary waves that give the sea its apparent roughness, synonymous with reduced friction velocity observed in the presence of oil film²⁹. Holthuijsen et al.³⁰ suggests that whitecap residual foam produces a frothy surface that blurs the atmosphere–ocean transition, dampens short waves, and encumbers momentum transfer. In the surf zone, foam may have the opposite effect. Two studies found that surf zone foam, generated through bathymetrically induced wave breaking, increased surface roughness^31,32.

In our study, we investigated whitecap residual foam’s effect on air-sea interaction over a range of wind speeds in a wind-wave tank. The experiment was conducted in the Air-Sea Interaction Salt-Water Tank (ASIST) at the University of Miami. This facility has a rich history of supporting air-sea interaction research^10,20,33,34. ASIST is 15-m long, 1-m high, and 1-m wide, with a porous beach at the far end (Fig. 1a). Its fan can generate winds up to 30 m/s. The water depth was set to 0.475 m. The tank was equipped with one TSI Constant Temperature Anemometer (CTA, or “hot-film”) at fetch of 4.9 m and 0.27 m above the water surface, operating at 1000 Hz for horizontal and vertical wind speeds (Fig. 1b). Hot-film anemometers measure wind speed based on the dependence of sensor temperature to fluid velocity³⁵. Two Pitot anemometers were deployed at fetches of 4.9 and 9 m to measure the along-tank pressure gradient and calibrate the hot film’s wind speeds measurements. Two Senix Toughsonic Ultrasonic Distance Meters (UDM) were deployed at fetches of 4.9 and 9 m for use when running the experiment with seawater, while in freshwater, two HR Wallingford wave probes were used at these fetches to collect wave elevation. To record the foam, we also set up two side-view cameras at 3 and 4 m fetches. The momentum flux and wave form stress were measured over the foam patch at 5 m fetch. The specific flux and wave measurement methodology is listed in the Methods section.

Fig. 1

(a) Overview of the experiment setup showing the placement of two hot-film anemometers, two ultrasonic distance meters (UDMs), and two wave probes. The foam maker is positioned at the base of the tank near the inlet. (b) A side perspective of ASIST, highlighting the foam maker’s location at the bottom. (c) A snapshot capturing the foam coverage on the surface.

Results

Momentum flux and wave form stress.

For each of the conditions shown in Table 1, we determined $u_{*}$ and $z_{0}$. These are shown in Fig. 2, subplots (a) & (b), (c) & (d), respectively as a function of $U_{10}$. In each subplot, the water types are distinguished by color and have a quadratic fit with shaded areas denoting the 95% confidence intervals. The experiments were repeated under multiple conditions: Freshwater (FW), freshwater-foam (FW-F), seawater (SW), seawater-foam (SW-F), and Triton-X water-foam (TX-F). The suffix “F” represents the foam maker turned on. TX-100 is used to simulate the effect of soluble surfactants in the ocean and results in more stable, longer-lived bubbles. This, in turn, causes the bubbles (foam patch) to travel further down the tank before popping. For all water types, there is a clear trend showing $u_{*}$ increases with $U_{10}$, consistent with previous tank experiments^20,36. Figure 2a shows that there is a foam-induced reduction in $u_{*}$ between FW and FW-F, reaching approximately 10–20% with greater difference at higher wind speeds. The introduction of surfactants further decreases $u_{*}$ about 5%. Similarly, Fig. 2b shows that foam and surfactants cause a decrease in $u_{*}$ compared to seawater. Under foam-free conditions, $u_{*}$ approximately equals the prediction from Couple Ocean–Atmosphere Response Experiment (COARE) algorithm^18,37, while in foamy conditions, $u_{*}$ falls below COARE. Shown by the blue, orange, and green solid lines in subplot (a), our findings differ from those of who reported an increase in momentum flux due to foam (addressed under Discussion). In freshwater, subplot Fig. 2c clearly demonstrates that $z_{0}$ increases with wind speed but decreases when foam is added. Similarly, subplot Fig. 2d shows that foam also decreases $z_{0}$ in seawater.

Table 1 Experiment conditions: actual wind speed ($U_{z}$) & wind speed extrapolated onto 10 m height ($U_{10}$) under different fan speeds.

Fig. 2

(a & b) $u_{*}$ vs $U_{10}$ under different conditions. The shaded area represents the standard errors of the mean of $u_{*}$ at each wind speeds. Each data point corresponds to one three-minutes run. The black dashed line is the prediction from COARE. The blue, orange, and green lines show the results from Troitskaya, et al. 38 (T19). (c & d) $z_{0}$ vs $U_{10}$ under different conditions (FW, FW-F, SW, SW-F, and TX-F). The crosses in each subplot are the observations.

Wave form stress and significant wave height

We next explore the wave form stress ($\tau_{f}$) under different conditions. Figure 3a and b show the form stress quadratically increases with $U_{10}$. In freshwater, the form stress is decreased by about 20–30% with foam. The addition of surfactants further reduces the form stress to ~ 50% below foam-free conditions. For seawater, form stress is also significantly reduced by foam. Reduced wave form stress represents reduced wave energy and suppressed air-sea interaction.

Fig. 3

(a & b) Form stress vs $U_{10}$ under different conditions. The gray points are observation, and the error bars denote the errors of the means.

We have shown that foam reduces the momentum transfer, surface roughness, and form stress. This highlights foam’s role in modulating air-sea interaction, and it follows that wave properties should also be altered by foam. In Fig. 4, we show the significant wave height H_s (subplots a & b). Foam is associated with a reduction in H_s for $U_{10}$ below ~ 15 m/s in freshwater and seawater. This is expected because $u_{*}$ and $\tau_{f}$ were reduced. This discovery mirrors³⁹, who showed that waves do not commence growth until a certain threshold of wind speed is attained. The introduction of foam appears to influence this threshold, necessitating a higher wind speed for wave initiation. Above 15 m/s the significant wave height is expected to decrease when foam is present because of reduced form stress, as shown in Fig. 3a and b. However, at higher wind speeds, the foam patch travelled further down the tank and reached the wave gauges (this was not the case at lower speeds). The foam accumulated on wave crests (Figs. 1c and 5), and contributed to an apparent increase in wave height in the TX-F and SW-F conditions. However, in the case of FW-F, even when the foam maker was activated, the wave height remained largely consistent with the FW condition. This is attributed to the limited bubble lifetime and quantity in unadulterated freshwater. This means that foam can reshape the wave form which has potential implications for airflow over the surface.

Fig. 4

(a & b) Significant wave height $\left( {H_{s} } \right)$ vs wind speed ($U_{10}$) under different foam conditions. The error bars denote the standard errors of the mean.

Fig. 5

Snapshot of the water surface when the foam is present shows foam accumulating on the wave crest. The orange lines marks the boundaries among wind, water and foam layer. Top: the boundary between wind and foam. Bottom: the boundary between foam and water surface. The foam accumulates most at the wave crest.

Discussion

We have demonstrated that both wave form stress and wave height are modified under foam conditions. Next, we analyze the wave spectrum at fan speeds of 30 Hz and 40 Hz (~ 18 and 24 m/s), as shown in Fig. 6. The corresponding wave steepness, listed in Supplementary Table S1, exceed 0.05, which indicates the waves were approaching the breaking limit 0.14⁴⁰. Regrettably, we are only able to show spectra for freshwater because of measurement errors associated with the UDM used to measure spectra in seawater. Figure 6 reveals that as foam coverage increases, the peaks waves shift to progressively to lower frequencies. The shift is approximately the same for both wind speeds shown. Because foam decreases the momentum flux, the effective fetch is decreased. Were this the open ocean, reduced effective fetch would shift the wave spectra to higher frequencies, as has been demonstrated many times. Here we find the opposite impact. When foam is present and the effective fetch is reduced, the wave spectra is redshifted. This is the same result observed by Troitskaya et al.³⁸, at wind speeds like those plotted here. Consequently, both laboratory studies found something akin to reduction in effective fetch. There are at least four distinct effects of foam on gravity waves. First, the surface tension and water density modulation by foam change the dispersion of waves, especially in the capillary range. Foam decreases both the surface tension and the liquid density; however, these quantities have opposing effects on the dispersion. More importantly, the surface tension and density affect waves at scales of $k^{3}$, so their effects are important for capillary waves but not otherwise. Second, reduced water density should lead to increased wind input⁴¹. Third, the presence of foam introduces a more gradual transition from air to water density and surface waves to some extent can be considered as reduced gravity waves, with reduced gravity $g^{\prime} = \rho ^{\prime}/\rho *g$. The presence of foam in this case would then be expected to reduce the frequency, and thus also phase speed, of waves, qualitatively consistent with the redshift observed here. Finally, it is also possible that the suppression of shorter waves by foam means that the momentum from wind, which would otherwise go into shorter waves via form stress, would be available for the growth of longer waves, also in support of the redshift shown in Fig. 6. Present laboratory measurements are insufficient to more precisely quantify the contribution of each of these effects on the frequency shift due to the presence of foam and should be investigated more thoroughly in the future.

Fig. 6

Wave spectrum under different foam conditions.

Figure 7 illustrates the influence of foam on the mean square slopes of waves. For freshwater (FW, FW-F, and TX-F), the introduction of foam corresponds to a reduction in the mean square slopes. The colored lines are MSS from ³⁸, who also found the foam reduces the mean square slopes. This trend aligns with the reduced momentum flux observed in Figs. 2 and 3, highlighting the role of foam in damping wave energy and altering surface dynamics.

Fig. 7

Mean square slopes (MSS) vs wind speeds ($U_{10}$) under different foam conditions.

To investigate the impact of foam on momentum transfer across the water surface in greater detail, we present uw cospectra in the scaling of⁴². For tank experiments, cospectra scaled this way are typically shifted to higher frequencies compared to those recorded in the open ocean. This discrepancy arises because the measurement height, z, in the tank (0.27 m) is significantly smaller than the open ocean (typically around 3–10 m) and so changes of wave elevation in the tank substantially alter the surface-relative measurement height. To account for this, we normalized the frequency using z = 0.135 m (half of the actual measurement height) which resulted in observed frequency peak approximately aligned with the peak in the Miyake cospectra. This adjustment only shifts the normalized frequency of the cospectra but has no effect on its magnitude. Cospectra are plotted in Fig. 8, which were recorded with and without foam for $U_{10}$ ≈ 11, 17, and 23 m/s and averaged over 15 min. Under non-foam conditions, the cospectra follows the Miyake curve, demonstrating that the momentum transfer adheres to a well-established form. This highlights the validity of the tank experiment in capturing the natural dynamics of wind-driven momentum exchange, as previously demonstrated by^20,41. When foam is introduced, momentum transfer is reduced at all frequencies. This suggests foam, acting as a viscoelastic medium at the water’s surface, influences how the wind interacts with the underlying water by creating a buffer that dampens the momentum exchange across the interface. It has previously been demonstrated that reduction in friction velocity can be linked to decrease in the flux at both isolated and broad frequencies due to gustiness⁴³, wind-waves angle^44,45, and flow separation²⁵ but never before has this been linked to surface foam.

Fig. 8

Mean $uw$ cospectrum in the scaling of Miyake, et al. 40 for wind speeds, 11, 17, and 23 m/s. The purple line is the universal curve from of Miyake, et al. 40. The shaded area marks the standard errors of the mean.

Our results show that foam alters wave elevation by reducing air-to-water momentum exchange. However, we also discovered that foam can increase the apparent wave height by accumulating on the crests. Therefore, we now examine the influences of foam on wave form stress and airflow separation. Airflow separation is estimated using the wind-steepness index developed by³.

$${\text{WS }} = ak\left( {U_{{\frac{\lambda }{2}}} /c_{p} - 1} \right)^{2} ,$$

(5)

Here, $k$ is the peak wave number which is calculated from the dispersion relationship, $a$ is the amplitude of the surface elevation ($\eta$), i.e., $\sqrt 2 rms\left( \eta \right)$, $U_{\lambda /2}$ is the wind speed at the height of half a wavelength ($\lambda$), and $c_{p}$ is wave speed at peak frequency. $U_{\lambda /2}$ is calculated from the wind speed profile using equations shown in Methods and represents a distance of ~ 3–6 cm above the mean water level, depending on the wind speeds. The ratio between $U_{\lambda /2}$ and $c_{p}$ is used to estimate the detachment of wind flow. A larger wind-steepness means increased airflow separation which decreases air–sea coupling and reduces the momentum flux.

In Fig. 9a and b, we show the percentage contribution of form stress to total stress, $R = \tau_{f} /\tau$, as a function of $U_{10}$. R of 2 m/s is not shown because $\tau$ is very low resulting in large variability. Results show that form stress becomes more dominant at higher wind speeds, consistent with Donelan et al.³, but is reduced when foam is present. Under foam-free conditions, R is above the black dashed line, but with foam, R generally falls below the line. This indicates that the reduced momentum flux in the presence of foam is due to reduced form stress. This may be related to the alteration of the surface due to foam, which in turn mediates the momentum transfer. To explore this further, Fig. 9c and d shows the wind-steepness as a function of $U_{10}$. Results indicate a low level of airflow separation in the presence of foam at wind speeds below 15 m/s. However, at wind speeds exceeding 15 m/s, foam significantly intensifies the airflow separation, surpassing the levels observed in non-foam conditions.

Fig. 9

(a–b) Wave form stress contribution (R) vs wind speed ($U_{10}$). (c-d) wind-steepness vs $U_{10}$. Colors represent different experiment conditions: FW (black solid), FW-F (red), TX-F (blue). Shaded area marks the confidence interval of the fit. The black line is the prediction from Donelan et al.³.

During our experiment we encountered two mechanisms that play distinct and important roles in modulating wave growth and momentum exchange. When the wind was slow (U₁₀ < 15 m/s), the waves were recorded outside the foam patch and reduced wave height is attributed to reduction in the air-to-water momentum transfer because the foam decreased $z_{0}$. Under these conditions, airflow separation was low, as expected. At higher wind speeds (U₁₀ > 15 m/s), the waves were measured inside the foam patch (which had travelled down the tank). In this case, the apparent wave height increased because it was a combination of the wave height and the foam height with foam accumulating on the wave crests. This occurred because the wavy surface has convergence on the front face of the wave and divergence on the rear face of the wave. This resulted in maximum concentration of material on the crest which elevated air flow separation. Hence, two spatially non-uniform mechanisms are revealed: a decrease in momentum flux due to the lower roughness of foam compared to water, and a decrease in momentum flux due to airflow separation over waves inside a foam patch. There is nothing physically meaningful about the wind speed this transition occurred, it’s simply an artifact of the experimental set-up.

Translation of our results to the field is tricky because much remains unknown about whitecaps at high wind speeds. However, we can make a few generalizations to quantify the potential effect. Holthuijsen, et al.³⁰ compiled 19 previous studies to show that whitecaps cover a little over 50% of the ocean at 24 m/s, the highest wind speed measured during our experiment. Callaghan et al.^46,47 and Potter et al.⁴⁸ show the lifetime of stage B residual foam can be 5–10 times longer than stage A foam generated during breaking. Hence, the theoretical maximum residual foam coverage is 45% at 24 m/s. At this wind speed, we have shown the friction velocity decreases about 17% in the presence of residual foam. Therefore, the spatially averaged friction velocity is expected to be reduced by 8%. We expect this number to double at hurricane force winds when whitecaps may approach full coverage, as predicted by some studies (refer to Fig. 1 in Anguelova and Webster⁴⁹).

Until now the existence of a slip-layer, as hypothesized by^1,19,26,30, has not been experimentally proven. However, the theorized slip-layer is not just whitecap residual foam, but a frothy mix of foam, spray, streaks, and bubbles that blur the atmosphere–ocean transition. We have only explored one of the elements that are thought to contribute to this layer, and while our results are unequivocal, it is likely that at hurricane wind speeds, the reduction in momentum flux due to the slip layer is even greater than seen here. The precise implications of this research depend upon the prevalence of whitecap foam inside hurricanes which is poorly understood. At higher winds, more whitecaps exist but atmospheric stability, currents, wind fetch and duration, temperature, salinity and surfactants, and waves are also important to whitecap formation and lifetime⁴⁹. Furthermore, whitecap generation may change based on the angle between the wind and swell. Holthuijsen et al.³⁰ suggested that crossing-swell can postpone whitecap formation resulting in higher wind stress, whereas whitecaps are more readily formed for opposing and following swell. The interaction of wind, wind sea, and swell inside hurricanes is complex¹³ meaning the impact of whitecaps on momentum flux must be spatially nonuniform. Conceivably, when conditions are favorable to foam generation it follows that reduction in wind stress and wave growth would constrain breaking and reduce foam formation insomuch that conditions become cyclic. In addition to offering observational evidence of a slip layer, our experiment suggests that foam may also contribute to air flow separation. Donelan et al.²⁰ showed airflow separation reduces surface stress at high winds over steep waves, because they create a shelter on their leeward side where momentum exchange is significantly reduced. Previously, the slip-layer and airflow separation were considered distinct mechanisms in the context of the momentum flux. However, our study suggests an interconnection between them. The proliferation of waves breaking at high wind speeds results in patches of foam that smooth the ocean surface, reducing the momentum transfer. This foam then accumulates at wave crests increasing the apparent wave height amplifying the opportunity for flow separation. The increase in apparent wave height due to foam relative to the height of open ocean waves will likely be far smaller than observed here.

Our results are comparable to Troitskaya et al.³⁸ who completed a similar experiment to ours. Estimating momentum flux from velocity profiles, they found that foam increases the drag coefficient for wind approximately below 22–25 m/s, (i.e., over our wind speed range). They determined that while foam itself has higher roughness than the water, it decreased the peak wave frequency by damping the short waves, resulting in a reduced mean square slope. This is somewhat counterintuitive since MSS is a measure of surface roughness and so a decrease would typically imply reduced momentum exchange. However, using a quasi-linear model, they determined that, below ~ 25 m/s, the roughness-enhancing effect of the foam was greater than the damping effect on short waves, resulting in a higher drag coefficient. Hence, like our study, Troitskaya found wave frequency and MSS are reduced in the presence of foam, but unlike ours, they found the momentum flux increases. The reason our results diverge in this way is unknown, but we suggest this may be related to the foam location and characteristics. Whereas Troitskaya generated patchy foam in the middle of the tank, ~ 3 m fetch (cf. their Fig. 1), we generated full foam coverage at the wind inlet. Furthermore, the properties of the foam (e.g., size distribution and lifetime) were assuredly different. In their case the wind travelled down the tank before interacting with the foam. Troitskaya’s model defined the foam-free surface to be aerodynamically smooth and the foam roughness length equal to the average radius of the foam bubble. Hence, the difference in height equates to rapidly elevated roughness, which would increase the momentum flux. In our experiment, the wind passed over the foam before interacting with the water. Furthermore, our experiment was designed so that the flux footprint (i.e., the source location of the measured flux) was within the foam patch resulting in a direct measurement of momentum at the air-foam interface. Meanwhile, they do not mention footprint, but their experimental set-up suggests the footprint included both water and foam. Finally, we note that the quasi-linear model used by Troitskaya assumes no flow separation, whereas in our study we find that flow separation is a critical component of the momentum flux reduction when foam is present. Nonetheless, together these studies highlight the nuanced impact of foam on air-sea interaction and suggest that the real-world implication of foam will depend on the environmental conditions and foam characteristics.

Finally, we must acknowledge the limitations in our study. First, we did not measure the bubble size spectrum, so it is not known how characteristic they are of bubbles produced in open water, (i.e., the artificial foam may not precisely replicate real ocean foam). Furthermore, in our experiment the bubbles were perpetually replenished in place, which is not true in the field. A static foam patch may have a greater impact downwind than transient open water whitecaps. We also recognize that our study is limited by a finite tank width and unidirectional wind and waves, neither of which are seen in the ocean, especially under hurricane conditions. Therefore, the precise results of our study may not translate directly to open water prediction. Nonetheless, our broad findings, that whitecap residual foam reduces friction velocity and alters wave properties downwind, still stand. Furthermore, the artificial foam helps to maintain controllable and reproducible experimental conditions in our experiment. While there are some differences in bubble properties, the key physical mechanisms including stress modulation and change in wave properties related to natural surfactants are still represented well.

Summary

In this study, we used an air-sea interaction tank to investigate the impact of foam on air-sea coupling. Our investigation focused on the momentum flux and wave properties under varying foam conditions and wind speeds. Our results reveal a consistent reduction in momentum flux due to foam at all wind speeds due to a decrease in energy across all frequencies. The addition of surfactants, which increase bubble formation and prolong foam lifetime, further amplifies this effect, decreasing both momentum flux and wave form stress. Our study also shows that wave frequency and MSS are reduced in the presence of foam when compared to foam-free conditions. Under low winds ($U_{10} < 15$ m/s), wave height is reduced when foam is present. At higher wind speeds ($U_{10} >$ 15 m/s), foam increased the apparent wave height because it accumulated on the wave crests and drifted downwind to the wave probes (i.e., H_s = H_wave + H_foam). Moreover, foam’s accumulating tendency enhances airflow separation as evidenced by an increase in wind-steepness for $U_{10} > 15$ m/s.

Our research emphasizes the important role of foam in air-sea interaction. Foam influences the momentum flux, waves, and airflow at high winds, a domain where direct flux measurements are scarce, and the complexities of wave breaking are profound. Our findings clarify the elusive impact of foam on momentum exchange and offer insights that fill a critical gap in understanding the nuanced interplay of foam in air-sea processes. The results are expected to help foster a significant step forward in hurricane modeling accuracy.

Methods

Momentum flux

Following Donelan et al.²⁰, we calculated $u_{*}$ and $U_{10}$ using Eqs. (6 and 7).

$$U_{10} = U_{z} + \frac{{u_{*} }}{k}ln\left( \frac{10}{z} \right)$$

(6)

$$u_{z}^{2} = u_{z*}^{2} - \frac{\partial \tau }{{\partial z}}z.$$

(7)

Here, $u_{z*}$ is the friction velocity at measurement height z using equation Eq. (3), and $k$ = 0.42 is the Von-Karman constant. Runs are averaged over three minutes. $\partial \tau /\partial z$ is estimated via the horizontal air-pressure gradient using the momentum budget approach²⁰. Further details about this methodology, which is widely used in other tank experiments, can also be found in Curcic and Haus¹⁰. We also calculated the surface roughness $z_{0}$ using Eq. (8) ⁵⁰:

$$z_{0} = \frac{10}{{exp\left( {kU_{10} /u_{*} } \right)}}$$

(8)

For wave elevation measurements in seawater, we deployed a Senix ultrasonic distance meter (UDM) at fetch of 5 m, operating at a frequency of 20 Hz. For freshwater, we used a wave probe (WP) mounted at the same fetch, operating at a frequency of 100 Hz. Each wave sensor was only reliable for its given water type. At fetches of 3 and 4 m, we mounted two 1-megapixel Basler Pylon Ace, side-view cameras which recorded at 30 Hz. Foam was produced using two 1 × 1 m rigid frames laced with aeration tubing mounted at the tank bottom at fetch between 0.5–2.5 m. This allowed the wind to travel the maximum possible distance over foam before reaching the anemometer. The foam patch was located at the wind input so there was no opportunity for waves to develop before reaching the foam. As such, there was no opportunity for the turbulent plumes generated by the bubble maker to dampen preexisting waves. This configuration ensured that wind-wave interaction observed in the experiment originated downstream of the foam generator, whereby eliminating any interference the bubble generator may have had.

Each frame was connected to three EcoPlus air7 pumps which provided air at 600 L/minute (200 L/minute per pump × 3). When on, the pumps continuously blew air through the aeration tubes which generated bubbles that rose to form whitecap residual foam effectively mimicking stage B foam. A similar technique was employed in Chesapeake Bay to investigate foam emissivity⁵¹. The resulting foam patch was 1 m wide, with a length between ~ 3.0 and 5 m (depending on foam migration) as shown in Fig. 1c. This ensured substantial foam coverage over the flux footprint so that the fluxes recorded were sourced over the foam. We did not directly measure the surface current generated by the foam maker, which could decrease the relative velocity at measurement height. However, we were able to estimate the surface current using videos of the foam as it traversed down the tank. From this we found the surface current was approximately 10 cm/s near the generator and dissipated rapidly downstream. When we account for this (using Eq. 6) we find the effect of the surface current on $U_{10}$ is less than 5% for wind speed exceeding 10 m/s.

Wave form stress

The wave form stress, $\tau_{f}$, was estimated using Eq. (9).

$$\tau_{f} = \tau - \tau_{v} = \rho_{a} u_{*}^{2} - \rho_{a} u_{v}^{2} .$$

(9)

Here, $\rho_{a}$ is air density, (1.12 $kg/m^{3}$ ) and $u_{v}$ is calculated using Eqs. (10 and 11) following^3,52, which assumes that the law of wall with a pure laminar flow can be applied to the viscous stress.

$$U\left( z \right) = \frac{{u_{v} }}{k}ln\left( {\frac{z}{{z_{0v} }}} \right)$$

(10)

$$R = \frac{{z_{0v} u_{v} }}{\nu },$$

(11)

where $u_{v}$ and $z_{0v}$ are the viscous friction velocity and roughness length of the viscous layer, respectively. The Reynolds number (R) was set to 0.11. Although waves or foam can result in a non-smooth surface, their effects were similarly neglected here, consistent with other studies using this tank³³.

We conducted experiments across various water types and foam conditions, as detailed in Table 1. In cases 1 & 2, we used freshwater (FW). In case 3 we added 2 ml of Triton-X 100 in freshwater (TX). Triton X-100 is routinely used to simulate the effect of soluble surfactants in the ocean. The presence of surfactants limits the coalescing of surface bubbles, which keeps them separate and makes them more stable, whereby increasing their lifetime. The result is smaller, longer-lived bubbles. The addition of Trinton X-100 resulted in a concentration of approximately 240 $\mu g/L$. Following Kamalanathan and Martin ⁵³, we estimate the surface tension of the TX water was 70 $mN/m$. The surface tension of seawater is normally about 74 $mN/m$. In cases 4 & 5, we used seawater (SW). In each scenario, the experiment was run first with no foam and then with the foam generator turned on, as indicated by suffix “F” in Table 1. Whenever we changed the wind speed, we gave the tank one minute to reach stationarity as previously demonstrated^10,20. By design, when the fan is 0 Hz, there is still a calm wind flowing through the tank, resulting in a wind speed of about 2 m/s.

For each wind speed, the experiment lasted sixteen minutes. Following the one-minute initialization period, the data was segmented into five three-minute intervals. In each, wind fluctuations were calculated using Reynolds decomposition and any measurements exceeding five standard deviations from the mean were removed, accounting for <  < 0.1% of data. There were several gaps in the UDM data, likely caused by moisture collecting on sensor head, consequently, we segmented the wave data into three separate five-minute intervals, to increase the number of data points for each averaging period. Within each segment, we detrended the data and removed the spikes as with the wind, we also used a two-second high-pass filter to remove noise.