Abstract <p> We embed the covariant, gauge-invariant gravitational radiation criteria of Fernández-Álvarez and Senovilla, based on conformal geometry and the Bel–Robinson tensor, into the hydrodynamic framework of gauge/gravity duality. This construction uncovers a direct correspondence between bulk gravitational waves and dissipative processes in the boundary fluid, from which a natural notion of entropy production emerges. We further analyze a smooth flat-space limit in which the dual fluid becomes Carrollian, with dissipation governed by Carroll-covariant tensors. As an example, we apply our framework to the Robinson–Trautman family of solutions. </p>