Buoyant Motion in a Turbulent Environment

Abstract

Solutions are given of the simultaneous equations for the vertical velocity and temperature of an element of fluid moving under buoyancy and subject to continuous mixing of heat and momentum with its environment. Three distinct modes of behaviour result: (A) ascent followed by damped oscillations, (B) asymptotic ascent to an equilibrium level, (C) absolute buoyancy in which the ascent rate increases indefinitely. For an environment in which the lapse rate is subadiabatic the motion is of type A for sufficiently large elements but may become B for the smaller elements; in super-adiabatic lapse rates the mode is C for sufficiently large elements, and B for the smaller elements, which are in no way unstable. The mode of motion is independent of the initial conditions but the scale of the motion is not.