What is observable from measurements downstream of an oblique shock?

The interaction of incident disturbances with an oblique shock can lead to the transmission, generation, and reflection of acoustic, entropic, and vortical waves. The classical work by McKenzie & Westphal [Phys. Fluids, vol. 11, 1968, 2350-2362] provides explicit expressions that describe this interaction. The dual to this forward perspective is one of an observer downstream of the oblique shock. Starting from observations of the downstream waves, our interest is to determine their dependence on the incident disturbances. The notion of the domain of dependence of a measurement in compressible flow, in absence of shocks, was introduced by Wang & Zaki [J. Fluid Mech., vol. 1009, 2025, A67], using adjoint variational techniques. The adjoint field released from a sensor position at the measurement time defines the space of earlier-in-time disturbances that can influence the sensor. The present work focuses on the modifications to the adjoint fields due to an oblique shock, and we derive analytical expressions that describe these effects. We compare the analytical predictions to numerical simulations, and discuss the implications for data assimilation in compressible flows with shock.