Extension of the Eulerian–Lagrangian description to nonlinear perturbations in an arbitrary inviscid flow

A new theoretical formulation is proposed to describe the propagation of large amplitude perturbations in an arbitrary flow of inviscid fluid. This formulation relies on the mixed Eulerian–Lagrangian description, for which exact nonlinear equations are derived. Using properties of Hamiltonian formalism, generalized expressions are found for the acoustic pseudo-energy density and flux. They verify a conservative energy balance. All these expressions only depend on the reference flow variables and the displacement vector of the fluid particles due to the perturbation. When the small perturbation assumption is added, the linear expressions from the literature are retrieved.

► Mixed Eulerian–Lagrangian description of nonlinear waves in arbitrary inviscid flows. ► Derivation of the propagation equation. ► Derivation of a conservative acoustic energy balance through Hamiltonian formalism. ► Comparison with linear equations for small perturbations.