Clouds of bubbles are generated at the sea surface by breaking wind waves or by heavy rain. Rows of subsurface bubble clouds have been detected by a bottom-mounted side-scan sonar, and are possibly formed by the effects of Langmuir circulation. A simple equation is devised to describe the effects of the turbulent diffusion of bubbles from the free surface, bubble rise and dissolution, and advection by Langmuir circulation. The equation is solved analytically using a series expansion in which advection is supposed small in comparison with diffusion. The solution provides a quantitative measure of the principal effects produced by the circulation, in particular the distortion of the bubble field, and estimates of the advective flux.
A random-walk numerical model, in which changes occurring in individual bubbles are followed, is tested against the analytical model in the range for which the latter is valid. There is good agreement. The numerical model is useful in extending the solutions to more complex cases which include a broad distribution of bubble sizes, and to ranges in which the analytic solution is invalid. The model is used to quantify the effect of the circulation on the acoustic scattering cross-section of the bubble clouds and to explore differences between the conclusions of earlier models and observations by Johnson & Cooke (1979).
In the appendices an estimate is made of the depth to which bubbles can be carried by the vertical velocities observed below wind rows, and this is found to agree reasonably well with the maximum depth to which bubbles are observed to penetrate. Estimates of mean vertical diffusion coefficients based on observations of bubbles are compared with some calculated solely from the advective flux in Langmuir circulation. The latter are, as expected, smaller than those representing the sum of all the contributions to the flux, but are a significant fraction, of the order of 0.2–0.4. A method of deriving the vertical diffusion coefficient from observations of the vertical distribution of the acoustic scattering cross-section of bubbles appears not to be very sensitive to circulation and may provide estimates within about 25% of the actual values.