This thesis is devoted to the study of unsteady energy exchanges in the vicinity of a
phase change or between two different phases explored in three scenarios. First, the transfer
function of the supersonic quasi-one dimensional flow of a single-phase non-ideal gas in
a nozzle is investigated using linear and non-linear approaches. The possibility of exploiting
near thermodynamic critical point (TCP) shock properties to confer a low-pass-filter
behaviour to the nozzle on pressure and velocity fluctuations when prescribing an inlet
entropy fluctuation is revealed. This is illustrated with siloxane D6 gas employing a multiparameter
Span-Wagner equation of state to compute equilibrium properties and evaluate
nozzle transfer functions which are contrasted with ideal gas predictions. Secondly, the
interaction of an entropy perturbation with a two-dimensional bow shock, formed when
a single-phase supersonic flow encounters a semi-circular obstacle, is investigated, with a
van der Waals model representing a dense gas operating near the TCP, and compared to
linear interaction analysis (LIA) for an isolated shock. Variations of refraction properties
along the shock are shown to be exploitable for flow control and a noted departure from
LIA prediction for incoming perturbation amplitudes greater than 5% of the base flow
values is observed. Thirdly, energy exchanges between two different phase shallow-layers,
representing the atmosphere and ocean, are investigated in the context of the 2022 Hunga
Tonga-Hunga Ha’apai volcano eruption using a two-way coupled isentropic model. The
linear properties are derived and show the disappearance of the ‘Proudman resonance’,
occurring when atmospheric wave speed and oceanic gravity wave speed match, resulting
in a finite atmosphere-to-ocean energy transfer and providing a low-cost predictive tool.
Two-dimensional global numerical simulations show the predictive nature of the two-layer
model for the Tonga event when simulating the atmospheric wave propagation provoked
by the shock-induced energy injection in the atmosphere.