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Erratum
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Journal of Fluid Mechanics , Volume 1035 , 25 May 2026 , E1
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
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© The Author(s), 2026. Published by Cambridge University Press

The publisher apologises that, upon publication of this article (Scapin et al. Reference Scapin, Wu, Farrar, Chapron, Popinet and Deike2025), several typographical errors were introduced by the typesetters during the production process. These affect Figure 8 (specifically panel b and the caption), Figure 9 (specifically the caption), and Figure 11 (specifically panel b). The correct versions of Figures 8, 9, and 11 are reported in figures 1, 2, and 3, respectively.

Figure 1.

Reynolds shear stress normalized by the square of the nominal friction, $-\langle u'w'\rangle /u_\ast ^2$ , as a function of the vertical wave-following coordinate $\zeta$ for: (a) $u_\ast /c=0.5$ and (b) $u_\ast /c=0.9$ . The Reynolds shear stress is averaged over the same time windows as in figure 7 of the published article Scapin et al. (Reference Scapin, Wu, Farrar, Chapron, Popinet and Deike2025). The dot-dashed curves represent the instantaneous values during the breaking stage, i.e. $\omega t\in [58\,{-}\,98]$ for $u_\ast /c=0.5$ and $\omega t\in [22\,{-}\,42]$ for $u_\ast /c=0.9$ . The dashed green curve represents the Reynolds stress on a flat stationary surface at $Re_\ast =720$ .

Figure 2.

Streamwise velocity profile normalized by the friction velocity, $\langle u_a^+\rangle =\langle u_a\rangle /u_\ast$ , as a function of vertical wave-following coordinate (in wall units) $\zeta ^+=\zeta u_\ast /\nu _a$ with $\nu _a=\mu _a/\rho _a$ : (a) $u_\ast /c=0.5$ and (b) $u_\ast /c=0.9$ , both at $Re_{\ast ,\lambda }=214$ ( $Re_\ast =720$ ). The velocity profiles are averaged over the same time windows as in figure 7 of the published article Scapin et al. (Reference Scapin, Wu, Farrar, Chapron, Popinet and Deike2025). The dotted black lines refer to the fitted log law employed to estimate the intercept for each case. The continuous black line represents the mean velocity profile at $Re_\ast = 720$ for a flat stationary surface.

Figure 3.

Drag coefficient $C_D$ evaluated at $\overline {z}=10$ $\textrm {m}$ using equation 5.3 of the published article Scapin et al. (Reference Scapin, Wu, Farrar, Chapron, Popinet and Deike2025) as a function of $u_\ast /c$ (top) and $a_{{rms}}k$ (bottom) with $a_{{rms}}=a/\sqrt {2}$ . The figure includes the calculation of $C_D$ with the data generated in this work and the one retrieved from Wu et al. (2022). For all the cases, the reported $C_D$ is an average value between the first growing cycle, $G_1$ , and a fraction of the second growing cycle, $G_{2,a}$ (immediately after the breaking event). Whenever available, the data pertaining to the second growing cycle $G_{2,b}$ and the final stage $F$ are displayed. The employed time window to define $C_D$ follows the convention given in figure 3(b) of the published manuscript (Scapin et al. Reference Scapin, Wu, Farrar, Chapron, Popinet and Deike2025). For the cases at $u_\ast /c=[0.4\,{-}\,0.5\,{-}\,0.7\,{-}\,0.9]$ at $Re_{\ast ,\lambda }=214$ with $(L_0-h_W)/\lambda =3.36$ , we separate between these two stages (blue and red dots). The green symbols display the experimental datasets from Buckley et al. (2020) up to $u_\ast /c\approx 0.71$ and from Curcic & Haus (2020) up to $u_\ast /c\approx 2.25$ .

References

Scapin, N., Wu, J., Farrar, J.T., Chapron, B., Popinet, S. & Deike, L. 2025 Momentum fluxes in wind-forced breaking waves. J. Fluid Mech. 1009, A20.10.1017/jfm.2025.77CrossRefGoogle Scholar
Figure 0

Figure 1. Reynolds shear stress normalized by the square of the nominal friction, $-\langle u'w'\rangle /u_\ast ^2$, as a function of the vertical wave-following coordinate $\zeta$ for: (a) $u_\ast /c=0.5$ and (b) $u_\ast /c=0.9$. The Reynolds shear stress is averaged over the same time windows as in figure 7 of the published article Scapin et al. (2025). The dot-dashed curves represent the instantaneous values during the breaking stage, i.e. $\omega t\in [58\,{-}\,98]$ for $u_\ast /c=0.5$ and $\omega t\in [22\,{-}\,42]$ for $u_\ast /c=0.9$. The dashed green curve represents the Reynolds stress on a flat stationary surface at $Re_\ast =720$.

Figure 1

Figure 2. Streamwise velocity profile normalized by the friction velocity, $\langle u_a^+\rangle =\langle u_a\rangle /u_\ast$, as a function of vertical wave-following coordinate (in wall units) $\zeta ^+=\zeta u_\ast /\nu _a$ with $\nu _a=\mu _a/\rho _a$: (a) $u_\ast /c=0.5$ and (b) $u_\ast /c=0.9$, both at $Re_{\ast ,\lambda }=214$ ($Re_\ast =720$). The velocity profiles are averaged over the same time windows as in figure 7 of the published article Scapin et al. (2025). The dotted black lines refer to the fitted log law employed to estimate the intercept for each case. The continuous black line represents the mean velocity profile at $Re_\ast = 720$ for a flat stationary surface.

Figure 2

Figure 3. Drag coefficient $C_D$ evaluated at $\overline {z}=10$$\textrm {m}$ using equation 5.3 of the published article Scapin et al. (2025) as a function of $u_\ast /c$ (top) and $a_{{rms}}k$ (bottom) with $a_{{rms}}=a/\sqrt {2}$. The figure includes the calculation of $C_D$ with the data generated in this work and the one retrieved from Wu et al. (2022). For all the cases, the reported $C_D$ is an average value between the first growing cycle, $G_1$, and a fraction of the second growing cycle, $G_{2,a}$ (immediately after the breaking event). Whenever available, the data pertaining to the second growing cycle $G_{2,b}$ and the final stage $F$ are displayed. The employed time window to define $C_D$ follows the convention given in figure 3(b) of the published manuscript (Scapin et al.2025). For the cases at $u_\ast /c=[0.4\,{-}\,0.5\,{-}\,0.7\,{-}\,0.9]$ at $Re_{\ast ,\lambda }=214$ with $(L_0-h_W)/\lambda =3.36$, we separate between these two stages (blue and red dots). The green symbols display the experimental datasets from Buckley et al. (2020) up to $u_\ast /c\approx 0.71$ and from Curcic & Haus (2020) up to $u_\ast /c\approx 2.25$.