Flow Laminarization and Acceleration by Suspended Particles

In [Comm. Appl. Math. Comput. Sci., 4(2009), pp. 153-175], Barenblatt presents a model for partial laminarization and acceleration of shear flows by the presence of suspended particles of different sizes, and provides a formal asymptotic analysis of the resulting velocity equation. In the present paper we revisit the model. In particular we allow for a continuum of particle sizes, rewrite the velocity equation in a form which involves the Laplace transform of a given function or measure, and provide several rigorous asymptotic expansions for the velocity. The model contributes to a better insight to the extreme velocities in hurricanes, fire storms, and dust storms, and the analysis confirms Barenblatt's conclusion that often the smallest suspended particles are responsible for the extreme flow acceleration at large altitudes.