ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
In this paper the instability of infinitely long cylindrical structures submerged in a uniform inviscid flow is investigated. When the flow velocity is zero, two families of hydroelastic waves exist, with phase velocities that are equal in magnitude and have opposite signs. Positive values of the fluid velocity increase the magnitude of the phase velocity of the waves that propagate in the same direction as the flow, and decrease the magnitude of the phase velocity of the waves propagating opposite to the flow. It is shown by constructing an energy conservation law for the linearized equations of motion that both types of waves have initially positive energy, in the sense that they both require an energy source to be sustained. After a critical value of fluid velocity is exceeded the slow waves acquire negative energy, in the sense that they require an energy sink to be sustained. Coalescence between the "fast'' (positive energy) and the "slow'' (negative energy) waves creates waves with zero energy which do not require neither an energy source nor a sink to be sustained, and grow exponentially in time. It is further shown that the front end of any initially localized disturbance will propagate with a speed equal to the minimum group velocity of the fast waves and the back end will propagate with speed equal to the maximum group velocity of the slow waves. Consequently, if those two characteristic speeds have opposite signs, the instability is absolute, whereas if they have the same sign the instability is convective. It is shown that this simple physical criterion applies to a more general class of instabilities that involve the interaction of positive and negative energy waves.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.858326
