Lognormal bubble size distributions

Abstract

In the study of oceanic bubbles based on empirical acoustics, the distributions among the sizes are typically represented by power laws with negative slopes as convenient descriptors of data in log/log format. However, power laws do not address the fact that as bubble sizes approach zero their numbers must approach zero. Multiple power laws, including a horizontal segment preceded by a positive power-law segment and followed by the expected negative power-law segment, have been used to recognize and mitigate this problem. Although not universally adopted as yet, several acoustic researchers have suggested that at least some oceanic bubble distributions are more appropriately represented by lognormal distributions. In 1941, A. N. Kolmogorov used the 1922 work of L. R. Richardson concerning a stochastic downward cascade of random sizes of turbulent vortices that asymptotically result in lognormal distributions of vortices. This current paper uses such a cascade of vortices to begin a downward cascade of bubbles sizes causing cascading shear forces on large bubbles that were created by breaking waves. In combination with this decreasing effect of turbulent shear on these fragmenting bubbles, the downward cascade of bubbles sizes overlaps and continues with a strengthened partial-pressure effect on ever increasing surface tension caused by their diminishing sizes. Issues associated with this approach, such as summing lognormal generators and intermittency, will be discussed.