Bubble transport theory with application to the upper ocean

Abstract

The formalism of transport theory is adapted to a general description of bubble populations in a moving fluid. The bubble distribution, as a function of position, velocity, radius and time, satisfies a Boltzmann-type transport equation that is derived and then formally solved by the method of characteristics. In order to apply this new analytical tool to the specific problem of gas bubble transport in the upper ocean, an ocean model and a bubble dynamics model must be chosen. For the purpose of illustration, explicit solutions are written, for distributed sources in a stationary ocean with simple expressions for bubble gas diffusion and drag. Calculated results clarify the relations between observed bubble distributions at sea, proposed bubble source mechanisms and known models of single-bubble dynamics.