Calculation of eddy viscosity and eddy diffusivity
According to Garcia et al. (2013), vertical eddy diffusivity is
eddy_diffusivity = beta * eddy_viscosity
Eddy viscosity in a parabolic profile is calculated as
eddy_viscosity = von_karman_constant * shear_velocity * vertical_location * (1 - vertical_location/depth)
.
However, the code in calculateKz.m calculates the eddy diffusivity (I'm assuming Kz
) as
eddy_diffusivity = beta * von_karman_constant * shear_velocity * Zprime * (1 - Zprime/depth)
where Zprime
is vertical_location + (0.5 * Kprime * Dt)
, and Kprime
is calculated as
Kprime = beta * von_karman_constant * shear_velocity * (1 - 2*vertical_location/depth)
.
The vertical gradient of eddy viscosity is von_karman_constant * shear_velocity * (1 - 2*vertical_location/depth)
, so this make sense.
A few questions:
- Is my interpretation of the code correct?
- Can we verify that FluEgg calculates eddy diffusivity differently than the paper describes?
- If so, what is the reference?
- Why is
Zprime
used instead ofvertical_location
to calculate eddy viscosity?
Most relevant to the current issue:
From the code, it doesn't seem that Zprime
is a property that's independent of the eggs because the equation for beta
contains the settling velocity of the eggs (which in turn is dependent on the diameter and density of the eggs), which makes the eddy diffusivity and viscosity dependent on properties of the eggs.
- Is this correct, or can we make eddy viscosity a property independent of the eggs?
- What is
Zprime
and the term0.5 * Kprime * Dt
?
Also, how is the calculation for ZR
working?
If H
is the cell depth, and Z
is the vertical location of the egg from the water surface
- When the egg is at the top and
Z
is 0,ZR
would beH
- When the egg is at the bottom and
Z
is equal toH
,ZR
will be2H
Is this accurate?
Edit: Added link to Garcia et al. (2013)
Edit: Added questions about calculation of ZR
Edit: Changed question from eddy diffusivity to viscosity