A kinematic choice l(x,t) = √2 k^{1/2}(x,t) τ makes the 1-equation URANS model satisfy the time-window, wall, bounded-energy, and statistical-equilibrium conditions without model adjustments.
Saint-Venant (Barré) , Note à joindre au Mémoire sur la dynamique des fluides, CRAS 17(1843), 1240-1243
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On URANS Congruity with Time Averaging: Analytical laws suggest improved models
A kinematic choice l(x,t) = √2 k^{1/2}(x,t) τ makes the 1-equation URANS model satisfy the time-window, wall, bounded-energy, and statistical-equilibrium conditions without model adjustments.