© 1983 by Oxford University Press
ON THE WAVETRAINS ASSOCIATED WITH ELASTIC JUMPS ON FLUID-FILLED ELASTIC TUBES
( Department of Engineering Sciences and Applied Mathematics, Northwestern University Evanston, Illinois 60201, USA )
Small-amplitude elastic jumps on fluid-filled, axisymmetrically deformed, tethered elastic tubes are studied. In the case of elastic jumps across which flow force is conserved, we show that while there must be some turbulent energy loss for a jump to exist, energy can also be radiated from the jump through a cnoidal wavetrain. If the turbulent energy loss is small, the wavetrain consists of almost solitary waves, while the maximum permissible energy loss corresponds to a transition between uniform flows. Whether the wavetrain occurs up- or down-stream of the jump depends on the elastic properties of the tube wall, the pre-stretch and the mean radius of the tube.
By means of the numerical integration of a viscosity-modified Korteweg-de Vries equation, solutions are also obtained for the time development of weak laminar elastic jumps propagating into fluid at rest. The shape of the jump profile depends on the same parameters as govern the profile of a weak turbulent jump. Calculation of these governing parameters using typical work functions suggests that each of the four types of jump profile predicted should be observable. When viscous effects are relatively small, we show that at large times the solution for the leading waves of a jump tends to the quasi-steady solution proposed by Byatt-Smith (10).