Some observations on the simple exponential function as a Lagrangian velocity correlation function in turbulent diffusion

Abstract In view of the repeated statements that a function of the form e −t L (t = traveltime, L = Lagrangianintegraltimescaleofturbulenceinthevelocitycomponentofconcern) provides a good approximation to the Lagrangian velocity correlation functions R(t) in turbulent flow, a check is made how well does the expression for crosswind spread ensuing from the assumption R(t) = e −t L represent the data embodied in the recently published updated Hosker-Briggs-Gifford-Pasquill graphs for spread. The comparisons are made with the graphs for horizontal crosswind spread σ J for Pasquill's stability categories A to F and for the vertical spread σs for category D (neutral). The agreement is excellent. Since the above graphs include the effect of dry deposition and since the long-travel distance ends of the graphs show close agreement with Taylor's prediction for spread at large travel times (strictly, for a homogeneous and stationary turbulence), based on a theory that does not account for the deposition process, it is pointed out that the assumption of a constant fractional depletion by deposition along any horizontal crosswind line renders Taylor's theory valid also for the case where dry deposition is in operation.