We focus on adaptive wave motion suppression of fluid flows in the presence of unknown parameters. The suppression problem is addressed by low-dimensional adaptive nonlinear output feedback controller synthesis. We employed adaptive proper orthogonal decomposition to recursively compute the set of empirical basis functions needed by the Galerkin projection to derive updated reduced order models that can be used as the basis for Lyapunov-based adaptive output feedback controller design. A static observer is applied to estimate the state modes of the system required by the adaptive controller. The effectiveness of the proposed adaptive wave motion suppression method is illustrated on a generalized form of the Korteweg-de Vries-Burgers (KdVB) equation which can adequately describe the wave motions in a wide range of fluid flow processes.