A general method is presented to investigate the hydrodynamic stability of ideal incompressible or barotropic flows described in a Lagrangian representation. Based on the theory of short-wavelength instabilities, the problem is reduced to a transport equation which involves only the distortion matrix of the equilibrium flow. The theory is applied to Gerstnerʼs rotational free-surface gravity waves. It is shown that they are three-dimensionally unstable when their steepness exceeds 1/3.