This Letter presents nontrivial stochastic identities for random isotropic second-rank tensor fields. They can be considered as markers of statistical isotropy in turbulent flows of any nature. The case of axial symmetry is also considered. We confirm the validity of the identities using different direct numerical simulations of turbulent flows.

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• Isotropic turbulence
• Turbulent mixing
• Random matrix theory
• Statistical hydrodynamics