UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The stability of body centered polygonal vortex line configurations Mertz, Gordon J.


This thesis is concerned with the stability of rectilinear vortex line configurations. A method for consideration of stability problems, using the equations of motion for small perturbations about equilibrium, is developed; and the free energy criterion for stability stated. The former method is used in analyzing the stability of the body centered polygonal configuration, which is a Thomson polygon centered by a vortex of arbitrary relative circulation; the latter criterion is applied to the Thomson heptagon stability question. The main results are that a Thomson polygon of any order can be stabilized by a large enough central circulation and that the Thomson heptagon is stable.

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.