A theoretical value for von Karman's constant

This paper extends the theory of the entity and entrainment model of turbulence to obtain a numerical value of von Karman's constant,k=0.37. The formula is, $$k = (2a^3 /A)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \ln \beta $$ where,a=1/12 is the entrainment constant,A=1 is the turbulent decay constant, and β is the ratio in height of the successive self-similar layers of the theory, where β is evaluated as β=e ². These new values fork and β improve the surface roughness length estimates derived from this theory.