Adrian Matei edited observations.tex  about 10 years ago

Commit id: dbf18235bf181c5a536b4c034f5bc129d235965d

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Next, we will assess how variability in bubble plumes depth affects the whitecap time decay. For instance, we will be able to check if a fast decrease in bubble plumes depth influences the longevity of whitecap fractions. To support this correlation between whitecap fractions time decay and bubble plumes dynamics we will use data collected by the sonar and the foam camera. \par  There was already mentioned that the primary source for whitecap production and variabily is the existence of bubble plumes, therefore our intention is to make direct correlations between bubble plumes and other factors like wind speed and sea state. If we can verify and understand these direct correlations, than we will check the validity of a dynamical relation between bubble plumes and whitecap production. Considering this fact, we want to see how the depth of bubble plumes change with sea state. Thus, we will correlate these changes in bubble plumes depth with different wave states, like wave frequency spectrum and wave amplitude. We want to analyze this bubble plumes dynamics during wind driven waves, which are slower than the environmental wind speed, have higher frequencies and lower amplitudes. For comparison, we will make the analysis during swells as well, which are affected by wind history, are faster than the environmental wind speed, have lower frequencies and higher amplitudes. As a result, we will be able to determine how swells, because of low magnitude wave energy dissipation, shape whitecap coverage variability. \par   Conditions that maximize the effect of swells are weak to moderate wind at sea surface, waves (swells) are usually coming from the south \cite{Callaghan_Deane_Stokes_Ward_2012}, and low frequency waves (around 0.1 Hz). A good way to estimate the effect of swells would be to observe them after the storm passes, during post-storm lower winds. We can perform this by using the wind speed ship data and Wave Rider data. \par  As discussed above, wave energy dissipation is a determinant factor of whitecap production. Going to the direct relation between whitecap coverage and bubble plumes, wave energy dissipation can be considered as a function of bubble plumes depth. Significant bubble plumes depth translates into large magnitude wave energy dissipation. We must include the whole environmental set when it comes to wave energy dissipation. Therefore, we must consider wind speed, wave frequency and wave height. On the open ocean, winds faster than waves extract energy from the waves by reducing their height, enlarging their slope (having higher frequency), and, thus, leading to wave energy dissipation. The presence of this phenomena sustaines a strong correlation between bubble plumes depth and wave state. Accounting for the fact that wave energy dissipation is proportional to wind speed and bubble plume depth, and inversely proportional to wave amplitude and wave speed (wave phase velocity), we can infer that whitecaps have the same properties. We can show this complex relation of wave energy dissipation with the other parameters  through the following relation: equation:  \begin {equation}  \epsilon = \frac{{u}_{\ast}{d}_{bp}}{{a}_{w} c},  \end{equation} where ${u}_{\ast}$ is wind speed (wind stress), ${d}_{bp}$ is bubble plume depth, ${a}_{w}$ is wave amplitude, and $c$ is wave phase speed.