  A new type of wave-mean flow interaction is identified and studied in which a
small-amplitude, linear, dispersive modulated wave propagates through an
evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction)
wave or a dispersive shock wave (undular bore). The Korteweg-de Vries (KdV)
equation is considered as a prototypical example of dynamic wavepacket-mean
flow interaction. Modulation equations are derived for the coupling between
linear wave modulations and a nonlinear mean flow. These equations admit a
particular class of solutions that describe the transmission or trapping of a
linear wave packet by an unsteady hydrodynamic state. Two adiabatic invariants
of motion are identified that determine the transmission, trapping conditions
and show that wavepackets incident upon smooth expansion waves or compressive,
rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic
reciprocity recently described in Phys. Rev. Lett. 120, 144101 (2018) in the
context of hydrodynamic soliton tunnelling. The modulation theory results are
in excellent agreement with direct numerical simulations of full KdV dynamics.
The integrability of the KdV equation is not invoked so these results can be
extended to other nonlinear dispersive fluid mechanic models.
