Dear EFDC users, In efdc.inp fire, they are described as: * AHO: CONSTANT HORIZONTAL MOMENTUM AND MASS DIFFUSIVITY m*m/s* AHD: DIMESIONLESS HORIZONTAL MOMENTUM DIFFUSIVITY (ONLY FOR ISHDMF>0)* AVO: BACKGROUND, CONSTANT OR EDDY (KINEMATIC) VISCOSITY m*m/s* ABO: BACKGROUND, CONSTANT OR MOLECULAR DIFFUSIVITY m*m/sIn EFDC interface, they are described as:* AHO: Background/Constant Horizontal Eddy Viscosity m*m/s* AHD: Eddy Diffusivity (dimensionlees) * AVO: BACKGROUND or CONSTANT vertical EDDY VISCOSITY m*m/s* ABO: BACKGROUND or CONSTANT vertical MOLECULAR DIFFUSIVITY m*m/s1) For AHO, is HORIZONTAL MOMENTUM AND MASS DIFFUSIVITY exactly the same as horizontal eddy viscosity? I’m confused about the coexistence of diffusivity and viscosity. 2) Is the difference between AVO and ABO that AVO is assumed in turbulent flow and ABO in laminar flow? 3) If so, why don’t we consider EDDY viscosity and molecular diffusivity in a horizontal scale? 4) I have seen that molecular diffusivity is the same as dynamic viscosity. If it’s right, why does ABO have a unit [m*m/s], which is for not dynamic but kinematic viscosity? Thank you. Minjeong

We will certainly work on cleaning up the definitions so that this is a little more clear. I have discussed these questions with the lead developer of EFDC+, and have tried to represent his answers as closely as possible. Please let me know if there are any points of confusion.1) Both AHO and AHD are used in the computation of horizontal eddy viscosity using the Smagorinsky (1963) method. The value which is set in EE is the background value. Inclusion of mass diffusivity is optional and can be turned on by the user with the ISHDMF = 1 or 2 flags. By default, this flag is set to zero. The background values set by the user in EFDC_Explorer for AHO and AHD are terms which are added to the computed values. This is a slight variation on the original method.2) That is not the case. Both AVO and ABO impact momentum and mass flux only in the vertical direction. These terms are always used if you have a multi-layer model.3) Both AHO and AHD are used to compute horizontal eddy viscosity following the Smagorinsky (1963) method, again the inclusion of the mass diffusivity in the water column is optional. AVO and ABO only impact vertical momentum and mass diffusion following the Mellor Yamada 2.5-level turbulence closure (1974).4) ABO is the vertical diffusion term used to compute diffusion of mass in the vertical. It is not a property of the fluid itself, like dynamic and kinematic viscosity.

Hi Tom, thanks for your kind answer but I still have some points of confusion. 1) I understand AHD is an optional parameter to compute horizontal eddy viscosity; however, I’m not sure about the definition of AHO. AHO is described as both ‘horizontal momentum and mass diffusivity’ and ‘horizontal eddy viscosity’. Do you mean ‘diffusivity’ is the same term as ‘viscosity’? 2) What is the physical difference between AVO (vertical EDDY VISCOSITY) and ABO (vertical MOLECULAR DIFFUSIVITY)? 3) Are eq(2.13) and eq(2.19) for calculating AVO and ABO, respectively in EFDC+ Theory? Here, A_v is defined as ‘vertical turbulent momentum diffusion coefficient’ and A_b is defined as ‘vertical mass diffusion coefficient’ that is different from what I mentioned in the 2nd question. Are A_v in eq(2.13) and A_v in eq (2.2) same? 4) Could you check the attached figure describing each term of the x-momentum equation whether it’s correct that the momentum equation doesn’t consider the turbulence term? I found that the Mellor Yamada equation calculates the turbulent intensity (q) and turbulent length scale (l) which relate to the vertical turbulent viscosity and diffusivity. How does EFDC calculate turbulence with ‘q’ and ‘l’ and associate turbulence with momentum equations? 5) When I have a single-layer model, is there no vertical movement? Is that model just a 2-D one (x and y)? In the case of a multi-layer model, is vertical movement only possible by turbulence because EFDC assumes hydrostatic?Thank you. Minjeong

- Not at all, but depending on how the user configures the model several options are available. Let me describe exactly what happens with AHO and AHD when different options are selected for horizontal momentum diffusion:ISHMDF = 0: This option computes no horizontal momentum diffusion, in this case AHO and AHD are not used.ISHMDF = 1: Horizontal Momentum diffusion is computed. Case 1 for this is when the user provides both an AHO and AHD value, in which case AHO added as background values to the Horizontal Eddy Viscosity following the Smagorinsky method. Case 2 here is when the user provides an AHO value but not an AHD value, in which case the AHO value provided by the user becomes the constant Horizontal Eddy Viscosity used in the model.ISHMDF = 2: Horizontal Momentum and Mass Diffusion are computed, and the effects of wall drag are included. If the user has provided values for both AHO and AHD, then those values will be used to compute both momentum and mass diffusion. If AHD is not provided, then again the AHO value is used as the constant Horizontal Eddy Viscosity.2) Just as in the horizontal direction, these are background values which are added to the computed A_v following Mellor and Yamada. AVO influences momentum diffusion in the vertical, while ABO impacts mass diffusion in the vertical.3) Those are the equations used to compute A_v and A_b. Again the background value specified in the user interface gets added to these computed values to give the user more control.4) We use the Mellor Yamada method for q2 and l. In the figure, you provided the Coriolis term is only the second term you’ve identified (f is the Coriolis parameter). These methods haven’t been modified since the early development of EFDC. Turbulence is accounted for using horizontal eddy viscosity, and vertical turbulence closure following Smagorinsky (1963) and Mellor and Yamada (1982).5) 1 layer models are just 2-D models and should yield similar results to a model using the Saint Venant equations rather than the full RANS equations. In a multilayer model the vertical momentum and mass transport are facilitated by way of turbulence closure following Mellor and Yamada (1982). EFDC uses the Boussinesq approximation.Thank you for your detailed questions on this topic. We will be working towards developing more detailed documentation on this process to help users understand.