In the context of flow visualization a triple decomposition of the velocity gradient  was proposed by Kolat in 2007 who demonstrated the technique in two dimensions, which was later realized in three dimensions by Nagata et al. in 2020.  The triple decomposition opens for a refined energy stability analysis of the Navier-Stokes equations, with implications for the mathematical analysis of the structure, computability and regularity of turbulent flow. We here perform an energy stability analysis of turbulent incompressible flow, which suggests a scenario where  any exponentially unstable irrotational  flow structures rapidly evolve towards linearly unstable shear flow and stable rigid body rotational flow , which dissipates to heat . In contrast to worst case energy stability estimates, this refined stability analysis reflects the existence of stable flow structures in turbulence over extended time , and the robustness of average quantities .
In the context of flow visualization a triple decomposition of the velocity gradient into irrotational straining flow, shear flow and rigid body rotational flow was proposed by Kolar in 2007 V. Kolar, International journal of heat and fluid flow, 28, 638, (2007) , which has recently received renewed interest. The triple decomposition opens for a refined energy stability analysis of the Navier-Stokes equations, with implications for the mathematical analysis of the structure, computability and regularity of turbulent flow. We here perform an energy stability analysis of turbulent incompressible flow, which suggests a scenario where at macroscopic scales any exponentially unstable irrotational straining flow structures rapidly evolve towards linearly unstable shear flow and stable rigid body rotational flow . This scenario does not rule out irrotational straining flow close to the Kolmogorov microscales, since there viscous dissipation stabilizes the unstable flow structures . In contrast to worst case energy stability estimates, this refined stability analysis reflects the existence of stable flow structures in turbulence over extended time .
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into irrotational straining flow, shear flow and rigid body rotational flow
R
Kolat
Kolar
R
who demonstrated the technique in two dimensions, which was later realized in three dimensions by Nagata et al. in 2020.
V. Kolar, International journal of heat and fluid flow, 28, 638, (2007)
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, which has recently received renewed interest.
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at macroscopic scales
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straining
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, which dissipates to heat
. This scenario does not rule out irrotational straining flow close to the Kolmogorov microscales, since there viscous dissipation stabilizes the unstable flow structures
D
, and the robustness of average quantities