Edward A. Cox
Dept. of Math. Phys., Univ. College Dublin, Belfield, Dublin 4, Ireland
Inst. of Fluid Dynam. and Heat Transfer, Technical Univ., Vienna, Austria
Current studies indicate that fluids with high specific heats may prove useful in a number of technological applications. These fluids have been shown to exhibit a range of new phenomena---the most prominent example probably being the existence of negative shocks (shocks across which the normal stresses decrease). Of particular theoretical interest is the possibility of propagating waves with mixed nonlinearity where for example positive and negative shocks propagate as stable structures within a single wave pulse. Here existing results for essentially plane waves are extended to include the effects of signal variations in directions transverse to the propagation direction. An extended Khoklov--Zabolotskaya--Kuznetsov (eKZK) is derived which models a propagating finite-amplitude sound beam. The extension to mixed nonlinearity predicts the formation of postitive and negative shocks and the existence of sonic shocks (where the shock speed is equivalent to the convected sound speed upstream or downstream of the shock). Numerical results are presented illustrating the combined effects of nonlinearity and diffraction for both time harmonic and pulsed radiators. An analysis of these results is given in terms of propagating characteristic surfaces.