Long‐Term Statistics of Observed Bubble Depth Versus Modeled Wave Dissipation

Abstract

Air bubble penetration depths are investigated with a bottom‐mounted echosounder at a seabed observatory in northern Norway. We compare a 1‐year time series of observed bubble depth against modeled and estimated turbulent kinetic energy flux from breaking waves as well as wind speed and sea state. We find that the hourly mean and maximum bubble depths are highly variable, reaching 18 and 38 m, respectively, and strongly correlated with wind and sea state. The bubble depth is shallowest during summer following the seasonal variations in wind speed and wave height. Summertime shallowing of the mixed layer depth is not limiting the penetration depth. A strong relationship between bubble depth and modeled turbulent kinetic energy flux from breaking waves is found, similar in strength to the relationship between bubble depth and wind speed. The wind sea is more strongly correlated with bubble depth than the total significant wave height, and the swell is only weakly correlated, suggesting that the wave model does a reasonable separation of swell and wind sea.

Scaling the Bubble Penetration Depth in the Ocean

“…. This is consistent with previous results (e.g., Derakhti et al, 2023;Graham et al, 2004;Strand et al, 2020;Wang et al, 2016). The Γ −1 parameter adds weight to relevant wave field statistics and suggests a clear link between penetration depths and TKE injection mediated by wave breaking.…”

“…Assuming a balance between the wind energy input and the wave‐breaking dissipation rates (e.g., Thomson et al., 2016), then a means to quantify wave‐breaking enhancement of TKE relative to a rigid‐wall‐scaling can defined through the ratio of the wind energy input to the depth integrated TKE dissipation given by: $$${{\Gamma }=E}_{\mathrm{i}\mathrm{n}}/{\varepsilon }_{D},$$$ with the expectation that through the wave‐affected layer (in terms of the TKE dissipation rate enhancement) Γ » 1 with the wave breaking driven enhancement constraint to this layer (e.g., Drennan et al., 1992, 1996). Previous work suggests that stronger forcing leads to deeper penetration depths (e.g., Derakhti et al., 2023; Graham et al., 2004; Strand et al., 2020). However, evaluating the behavior of observed penetration depths as a function of wind speed and wind energy input alone exhibits a low index of agreement.…”

“…Efforts have been largely focused on building a robust relationship between observed bubble plume characteristics and atmospheric and sea state conditions. Bubble penetration depths appeared to be proportional to the 10‐m wind speed ( U 10 ), with penetration depths increasing with wind magnitude (e.g., Derakhti et al., 2023; Strand et al., 2020; Vagle et al., 2010; Wang et al., 2016). Thorpe (1992) used the wavelength and significant wave height to scale the depth of the bubble injection, showing dependence on the inverse wave age and suggesting deeper penetration depths under strong forcing conditions.…”

Gas Fluxes and Steady State Saturation Anomalies at Very High Wind Speeds

“…While the wind‐wave tank provides an excellent closed system that can be tightly monitored, and that enables very high wind speeds to be experimentally studied, questions remain on how applicable these results are to an open ocean setting. In particular, the water depth in the SUSTAIN tank (0.8 m) is much shallower than the maximum depth of bubble plumes in the ocean, which can extend to 38 m deep (Strand et al., 2020) though mean bubble penetration depth is likely to be within the depth of the SUSTAIN tank (estimated at less than 0.5 m [Callaghan, 2018; Callaghan et al., 2012]). Additionally, although features of the tank such as the sloping beach reduce limitations due to the short fetch in the tank, the tank certainly is not the same as the real ocean.…”

Current shear and turbulence during a near-inertial wave

“…We used a 3 = 5 and additional calibration coefficients for T 1 and T 2 as proposed in (Rapizo et al, 2017). The wave dissipation F ds can be derived by integrating the 1D variance spectrum (Strand et al, 2020) 16) exceeds the classical parametrization (i.e. S ds = T 1 + T 2 from Eq.…”