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A wave equation, that governs finite amplitude acoustic disturbances in athermoviscous Newtonian fluid, and includes nonlinear terms up to second order,is proposed. In contrast to the model known as the Kuznetsov equation, theproposed nonlinear wave equation preserves the Hamiltonian structure of thefundamental fluid dynamical equations in the non-dissipative limit. An exacttraveling front solution is obtained from a generalized traveling waveassumption. This solution is, in an overall sense, equivalent to the Taylorshock solution of the Burgers equation. However, in contrast to the Burgersequation, the model equation considered here is capable to describe wavespropagating in opposite directions. Owing to the Hamiltonian structure of theproposed model equation, the front solution is in agreement with the classicalRankine-Hugoniot relations. The exact front solution propagates at supersonicspeed with respect to the fluid ahead of it, and subsonic speed with respect tothe fluid behind it, similarly to the fluid dynamical shock. Linear stabilityanalysis reveals that the front is stable when the acoustic pressure belongs toa critical interval, and is otherwise unstable. These results are verifiednumerically. Studies of head-on colliding fronts demonstrate that the frontpropagation speed changes upon collision.

Analytical and numerical modeling of front propagation and interaction of fronts in nonlinear thermoviscous fluids including dissipation