[MITgcm-support] Friction velocity ustar in S/R exf_wind.F

[Stanislav Martyanov]

Hi Martin!

Thank your for your reply. Yes, I understand that some optimization
was made for the computational reasons. But I still have some doubts
about the used formula for ustar in s/r exf_wind. I'll try to explain
what I mean in detail.

So, let's see the code in exf_wind.f with my brief comments:

Line 146-153: We calculate usSq = (ustress*ustress) +
(vstress*vstress). Both ustress and vstress have units [N/m^2] because
they are the wind stress vector's components along X and Y axes. After
that we obtain variable usSq which has unit [ (N/m^2)^2 ]. It is OK.

Line 156: wStress = SQRT(usSq). So wStress is now in [N/m^2]. That is
OK too, because wStress is just a module of wind vector.

Line 157: c            ustar = SQRT(usSq/atmrho). This is a correct
statement, but it is commented.

Line 176: recip_sqrtRhoA = 1. _d 0 / SQRT(atmrho). That is OK, we are
optimizing the code for the further computations.

Line 179: ustar = wStress*recip_sqrtRhoA.    Now that is a problem, as
I think. Because after that, ustar has units (N/m^2) / (kg/m^3)^0.5.
But it has to have units as friction velocity - [m/s]. The problem is
that we have not taken another one SQRT.

If we rewrite, adding additional SQRT, as:
ustar = SQRT(wStress)*recip_sqrtRhoA,

then the units of ustar will be [m/s] as it should be. Friction
velocity is basically determined as SQRT(stress/density).

Best regards,
Stanislav





> Hi Stanislav,
>
> I am no expert on this, but did you see lines 156/157:
>              wStress(i,j,bi,bj) = SQRT(usSq)
> c            ustar = SQRT(usSq/atmrho)
>
> so ustar should be sqrt(usSq/atmrho). for algorithmic reasons wstress=sqrt(usSq) is computed first and then divided by sqrt(atmrho) later in lin 179. To this makes sense, although it’s not very easy to read.
>
> Martin

> On 4. Mar 2018, at 13:58, Stanislav Martyanov <martyanov.sd at gmail.com> wrote:
>
> Hello!
>
> I think it should be
>
> ustar = SQRT (wStress(i,j,bi,bj) / atmrho)
>
> rather than
>
> ustar = wStress(i,j,bi,bj)*recip_sqrtRhoA
>
> in exf package in S/R exf_winf.F (line 179)?
>
> In the current version wStress is not affected by the function SQRT,
> but should be, in my opinion.
>
> Best regards,
> Stanislav