Supercavitating body dynamics, bifurcations and control

Numerical investigations conducted into the dive-plane dynamics of supercavitating bodies, which are described by a non-smooth system, are discussed. For a selected set of system-parameter values, a fundamental understanding of the solution structure obtained in terms of equilibrium and periodic solutions is presented. After carrying out smoothing approximations, bifurcations of solutions of the resulting smooth system are studied by using the cavitation number as a control parameter. Supercritical Hopf bifurcations of fixed points and period-doubling bifurcations are found, and the use of feedback control to suppress or delay the onset of Hopf bifurcation is presented. The present work provides a basis for interpreting the tail-slap phenomenon of a supercavitating body as a limit-cycle motion and controlling it.