The first application of theory of the rise of line thermals was to understand the rise of turbulent smoke plumes emitted from smoke stacks into a cross-wind. Initial solutions required numerical calculations. In this article analytical solutions are found, and these are used here to explore solutions for the rise of buoyant line wakes from submarine vehicles. Solutions cater for wakes in both neutral and stable environments, and for sources which have either negative or positive initial buoyancy. Account is also taken of sources with differing size and initial momentum. Practical examples of submarine thermal wake flows are given using neutral and typical stably stratified upper ocean conditions and a range of source conditions. A key result is that small-diameter submarine wakes with high temperatures produced in weakly stratified ocean waters will have a large height of rise, and may easily reach the surface. By contrast, large-source-diameter wakes, with temperatures close to ambient and emitted into strongly stratified oceans, will have very small heights of rise.
Jason H. Middleton (Thu,) studied this question.