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:
a9 a+ 8 = ( air -X X &U1+ ý U - 2% $in(*u I a + - -- a - x-(j N 5 (W-9) (B-10) (B-11) 3 D. W. Pritchard, "Threedimenional Models," in Estuarine Modelb. An Asmigt, Eurkoumsatal Protection Aency, Water Pollution Control Resewah Series. 16070 DZV, 1971. 4.4-11 + 6P X, + VV2u, -k 'po) a5+-G2 +213 sin(CO 1 a- , 1 P 0 F ,2 v 'U au3 .1 . a at Jaxi I aF Po ax3 interpreted as the nine components of the turbulent stres tensor Rj RiI = -pulul (3.12) P g + -V-2g3 + -1 (u-'a ,) ((&13) P0 uj) The momentum equations have been written in component form for a Cartesian sytem with x 3 positive upward. The qutntities 0 and [13 are, respectlily, the latitude and the locally vertical component of the earth's rotation vector. Rotational effects are negligible in the vertical momentum equation, and the corresponding terms have been dropped for simplicity. Coeevastion of enealy aT + jL V2T - a(u7) (B_14) Equations (B-9) through (B-14) differ in form from their instantaneous counterparts only through inclusion of the terms representing time average of products of fluctuating quantities. These terms represent turbulent diffusion of heat and momentum and arise from those stochastic components of the motion that have time scales shorter than the averaging period. These equations, together -'ith appropriate boundary conditions, are the fundamental relationships governing thermal dispersion in a turbulent incompressible medium and form the basis for any subsequent deterministic mathematical models. 4. Approximutions to the Basic Eqemo The conservation equations cannot be solved in their complete forms as shown. The actual formulation of any given model depends upon the simpllficatlom nd assumptions invoked consistent with the time and space scales of interest in the dispersion proces, plant design parameters, and the flow field and gpometry of the receiving waters. For highly simplfied gpometo' and flow conditions, analytical solutions am polble in some instances. In general, however, mom