This study examines the turbulent stress anisotropy tensor based on the Lumley triangle technique and eigenvalues in wave–current combined flows. The invariant functions are also presented at a different vertical location from the bed to comprehend the level of anisotropy in the combined flow. The spectral variation of the ratio of momentum flux to the turbulent kinetic energy is examined and discussed in comparison to the canonical value. The combined wave–current data display spectral variation considerably smaller than the canonical value (≈ 0.3) through the spectral frequencies domain. To characterize the behaviors of eddies in the wave–current turbulent flow, the Taylor and Kolmogorov length and time scales were analyzed and discussed. Furthermore, to enumerate the degree of organization of complex eddy motions in the combined flow, the normalized Shannon entropy is also evaluated using a discrete probability distribution.