Remarks on turbulent transfer across of plane zero momentum‐exchange

Abstract

Despite the advances in the statistical theory of turbulence, the PRANDTL [see 1 of “References” at end of paper] concept of mixing‐length still affords the most convenient method of evaluating momentum‐transfer from velocity‐profiles in turbulent flow. In symmetrical conduits, eddy‐diffusivity is known directly from the BOUSSINESQ quotient of shear‐stress and velocity‐gradient. Hence mixing‐length is not essential for the expression of eddy‐diffusivity in pipe‐flow, but is convenient when the distribution of shear‐stress is not known, as in most flow‐problems in meteorology and hydrology.

Investigation of Energy and Mass Transfers Near the Ground Including the Influences of the Soil Plant-Atmosphere System

“…The essential mathematical requirement for indicating finite eddy viscosity here is simply that the velocity gradient and the shear stress both approach zero at proportional rates. This is substantially true for the parabola deduced for laminar flow and is also satisfied sufficiently by the error function (Brooks & Berggren 1944). The latter yielding a wide shallow dip at velocity maximum has since been found to explain satisfactorily the cross-midstream distribution of fine # A glass of tritiated water standing uncovered in a laboratory (where the dew point is near the water temperature) will lose its tracer quality in a week without change in water level.…”

Implementation of a Model for Predicting the Size Distribution of Coal Particles in a Horizontal Fluid Pipeline

“…This is because, the flow velocity is much closer to the transition velocity, 3.4 m/s; the velocity which determines whether the root mean square velocity fluctuation will be calculated from equation (18) or equation (22). The original Karabelas model with 𝜉 = 0.25 could not predict the concentration profile of Roco and Shook's, [48] experimental data. This is because, 𝜉 is not varying with the parameters influencing the concentration profile (Eq 1).Validation with Schaan et al [52] experimental data is presented in Fig.…”

“…𝐶 𝑣𝑓 =efflux concentration, 𝜖 1 =Liquiddiffusivity which was also shown to be varying with vertical coordinate and partly with friction velocity [48].…”

THE EFFECT OF ICE COVER ON VERTICAL TRANSFER IN STREAM CHANNELS1

“…Brooks and Berggren (1944) show that a slight change in fitting the velocity profile can result in an appreciable difference 1432 dY in values of e*. approach zero near the plane of zero shear it is difficult to justify the validity of Equations (10) in the central region.…”

“…approach zero near the plane of zero shear it is difficult to justify the validity of Equations (10) in the central region. Brooks and Berggren (1944) show that a slight change in fitting the velocity profile can result in an appreciable difference 1432 dY in values of e*. By considering that the zero shear stress is due t o the balanced exchange of considerable momentum, Brooks and Berggren suggested an error function fitting for the central region of pipe flow.…”