Question about the surface stress

[mathieulandreau]

Hi,

I am looking for the exact equation of the surface stress used in the first cell. In module_diffusion_em, I found

CASE (1,2) ! ustar computed from surface routine
    DO j = j_start, j_end
    DO i = i_start, ite
       V0_u=0.
       tao_xz=0.
       V0_u=    sqrt((u_2(i,kts,j)**2) +         &
                        (((v_2(i  ,kts,j  )+          &
                           v_2(i  ,kts,j+1)+          &
                           v_2(i-1,kts,j  )+          &
                           v_2(i-1,kts,j+1))/4)**2))+epsilon
       ustar=0.5*(ust(i,j)+ust(i-1,j))

       tao_xz=ustar*ustar*u_2(i,kts,j)/V0_u
       ru_tendf(i,kts,j)=ru_tendf(i,kts,j) +   g*tao_xz*0.5*(rho(i,kts,j)+rho(i-1,kts,j))/dnw(kts)
       IF ( (config_flags%m_opt .EQ. 1) .OR. (config_flags%sfs_opt .GT. 0) ) THEN
          nba_mij(i,kts,j,P_m13) = -tao_xz
       ENDIF
    ENDDO
    ENDDO

I suppose that g, rho and dnw are the different terms of $\mu_d$. $\Delta z$ is missing however so is the equation :
$\partial_t (u) = ... - u^{*2} . \frac{u}{\sqrt{u^2 + v^2}} \frac{1}{\Delta z}$
By the way, according to Skamarock et al. (2019), $U = \mu_d u /m_y$. Isn't there a $m_y$ missing ?

Thank you,
Mathieu

[dudhia]

Quick answer, as I have limited time. ru_tendf contains a mu. mu*dnw is dp and rho*g/dp is 1/dz.

…

On Fri, Apr 25, 2025 at 4:25 AM mathieulandreau ***@***.***> wrote: *mathieulandreau* created an issue (wrf-model/WRF#2209) <#2209> Hi, I am looking for the exact equation of the surface stress used in the first cell. In module_diffusion_em, I found CASE (1,2) ! ustar computed from surface routine DO j = j_start, j_end DO i = i_start, ite V0_u=0. tao_xz=0. V0_u= sqrt((u_2(i,kts,j)**2) + & (((v_2(i ,kts,j )+ & v_2(i ,kts,j+1)+ & v_2(i-1,kts,j )+ & v_2(i-1,kts,j+1))/4)**2))+epsilon ustar=0.5*(ust(i,j)+ust(i-1,j)) tao_xz=ustar*ustar*u_2(i,kts,j)/V0_u ru_tendf(i,kts,j)=ru_tendf(i,kts,j) + g*tao_xz*0.5*(rho(i,kts,j)+rho(i-1,kts,j))/dnw(kts) IF ( (config_flags%m_opt .EQ. 1) .OR. (config_flags%sfs_opt .GT. 0) ) THEN nba_mij(i,kts,j,P_m13) = -tao_xz ENDIF ENDDO ENDDO I suppose that g, rho and dnw are the different terms of $\mu_d$. $\Delta z$ is missing however so is the equation : $\partial_t (u) = ... - u^{*2} . \frac{u}{u^2 + v^2} \frac{1}{\Delta z}$ By the way, according to Skamarock et al. (2019), $U = \mu_d u /m_y$. Isn't there a $m_y$ missing ? Thank you, Mathieu — Reply to this email directly, view it on GitHub <#2209>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AEIZ77CJSMCW3RUPRZP5YY323IERPAVCNFSM6AAAAAB33IQH5KVHI2DSMVQWIX3LMV43ASLTON2WKOZTGAYTSNRUG44DINY> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[mathieulandreau]

Thank you for this answer.
This means indeed that for the uncoupled-u :
$\partial_t (u) = ... - u^{*2} . \frac{u}{\sqrt{u^2 + v^2}} \frac{1}{\Delta z}$
Mathieu