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Abstract In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000Nonlinearity13249–55) and Eyink (2003Nonlinearity16137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s $\frac{4}{5}$, $\frac{4}{3}$, $\frac{4}{15}$laws. We apply these computations to improve a recent result of Hofmanovaet al(2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruèet al(2023Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giriet al(2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.