A Small Question about the Equations of LINCOM

[paulharrison]

Hi, I am new to CFD, and trying to understand. I am reading the nice review of the mathematics behind LINCOM at: RIS_R_900.pdf. I take Eqs. (8) and (9) with the substitution (10), and we clearly have 4 equations in 4 unknowns. Very good. We expand according to (11) and (12). Here I understand that we have doubled the number of unknowns to 8. But some magic (presumably Reynolds averaging) gives the extra equations (13)-(15), which seem to be 5 equations, probably with some redundancy. So let us say 4, and we still have enough constrains. Still good.

At this point, however, I notice that Eq. (14) looks like a typing error. Since the right hand side is a vector zero, I have to assume that on the LHS here, we mean Curl(\bold v), (the curl symbol has been omitted). But I am anyway mystified at this point, since if I look to Eq. (2), I find that

\bold V = (cos th, sin th, 0) (U*0/kappa)ln(z/z_0)

Now, it seems to me that the curl of this "background flow" is not zero at all. In fact, it is a rotational flow.

So, is the notation \bold V intended to mean different things in eqs. (2) and (14), or is Eq.(14) meant to mean something other than curl (\bold V)=\bold 0?

Thanks in advance for any clarification.

Best Wishes,

Paul Harrison.

[Morten]

Hi Paul,


You are right, the background flow is not irrotational, but I just think Eqn. 14 states that the flow field has no gradient. This is true for the two horizontal dimensions, since the background flow is the same everywhere. It is also true for the vertical direction, since its vertical component is zero.


Report Risø-R-900 focussed on roughness-change perturbations. The model for effects of variable terrain elevation was revised in Risø-R-1356.


Cheers,
Morten


References:

https://backend.orbit.dtu.dk/ws/portalfiles/portal/7766601/RIS_R_900.pdf
https://backend.orbit.dtu.dk/ws/portalfiles/portal/7726842/ris_r_1356.pdf

[paulharrison]

Dear Morten,

Thanks for your kind answer. I will think a little more about it. Thanks also for the later reference, which I had not seen. I have just downloaded it and will read it with interest.

Cheers, Paul.