A theoretical value for von Karman's constant

The physical principles supporting the entity-entrainment model of turbulent processes in the planetary boundary layer (Telford and Presley, 1978; Telford, 1980) are elaborated to derive a formula for von Karman's constant (k) in terms of the entrainment constant, the turbulent-decay constant, and the height ratio of the successive self-similar layers of the model. The steps of the derivation are discussed in detail, and a k value of 0.369 is obtained. This result is found to be in agreement with observations of neutral-boundary-layer motion on large scales but somewhat smaller than that of laboratory experiments; the possible reasons for this discrepancy are explored.