Document: NRC Regulatory Guide
Document ID: f4c5fb1d-efb9-4168-9804-5ad3f6f64d06
Document Type: regulatory_guide
Title: Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in Natural Water Bodies
Source: NRC Regulatory Guide Division 4
Source URL: https://www.nrc.gov/docs/ML0037/ML003739535.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-4.4
CFR Part: 
CFR Title: 

Content:
s the mean temperature gradient, and D, is the eddy diffusion coefficient. All quantities are defined relative to the s direction. The definition for eddy diffusion given in Eq. (A-6) is analogous. to that for molecular diffusion in a Fickian substance. Because turbulent diffusion is scaled to eddies, the magnitude of the eddy diffusion coefficient depends directly upon eddy size, which in turn determines the size of a diffusing plume. As a result, an empirical 4/3 power law of plume width is often applied to estimate horizontal eddy diffusion. The 4/3 law apparently holds only for a semi-infinite water body such as an ocean; for finite systems such as lakes and rivers, a constant horizontal eddy diffusion coefficient may be preferable at large distances from the effluent source.' Furthermore, since the eddy spectrum is limited by the size of the system, boundary effects may appreciably diminish horizontal dispersion in near-shore or shallow areas. Similarly, the typical vertical turbulence structure, 6 G. T. Csanady, "Dispersal of Effluents in the Great Lakes," Water Research, Vol. 4, No. 1, 1970. 4.4-8 with a maximum near the water surface due to wind stress, usually results in decreasing horizontal diffusion with depth. Whereas horizontal eddy diffusion varies with the scale of horizontal turbulence, eddy diffusion in the vertical direction can be constrained by shallowness of the water body and the interaction between turbulence. and buoyancy. Buoyant forces result from ambient thermal stratification and/or heated discharge, and they impose a density stability on the water column which wind-induced turbulence must overcome. The interaction between turbulence and buoyancy is often expressed by the Richardson number, g dp p dz R i - p(A-7) ldU\ 2 k\dz/) where g represents the acceleration of gravity, dp/dz is the vertical density gradient, and dU/dz is the vertical gradient of the horizontal mean velocity. The quantity (l/p)(dp/dz) represents buoyancy or density