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.
W ang, The time averaged energy dissipation rates for shear flows, Physica D, 99 (1997) 555-563
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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.