The logarithmic bottom drag coefficient "Cd" = {k/(log[dz/Zob])}^2 where dz is the height of the first rho-point above the ocean bottom z=-H is "clipped" in set_vbc.F as "Cd"=min[A,max(B,"Cd")] where A=0.5, B=1.0 x 10^(-6).

For highly tidally active regions such as AK, dz will have a large variation in value (at a single location) due to the large tidal range in elevation (e.g. +/- 3.5 m). Furthermore, when there is wetting and drying, dz can become really small (leading to large "Cd" values) locally before these places actually become dry. These could introduce prohibitively small time-step restrictions in order to achieve numerical stability.

I have a couple of questions :

(1) For regions with large tides and/or wetting-drying, when using the Log bottom drag formulation in ROMS, is some special treatment necessary?

(2) The A, B values given in the above formula are the ROMS default values. Are there corresponding "optimal" values for say the shelf and the estuary which give physically more realistic solutions?

Thank you.

## ROMS Logarithmic bottom drag, tides and wetting-drying

### Re: ROMS Logarithmic bottom drag, tides and wetting-drying

Unless I've done the math wrong, I don't see how one could ever trigger those limits on Cd.

For a fixed bottom stress, the effective drag coefficient and reference depth, zref, are related by:

zref = z0 * exp ( k/sqrt(Cd) )

As zref decreases when the boundary layer is better resolved, u(zref) decreases so the effective Cd required to maintain the same stress increases.

The maximum allowed Cd of A=0.5 corresponds to a zref of 1.76*z0. Since the roughness scale z0 is of order 2 mm, zref would need to fall below 4 mm to be limiting. Only at the very limit of the typical Dcrit for wetting/drying (10 cm) used in the default ocean.in, with 10 s-levels, would the height of the velocity point above the bed 1/20*Dcrit be 5 mm. For any water depth greater than Dcrit you presumably would not be close to the realm of the limiting maximum Cd.

Conversely, an absurdly high zref would implied by the lower bound on Cd of B=1e-6.

So isn't it unlikely these parameters are controlling the way the logdrag option impacts the effective bottom stress?

Are you proposing the stress itself limits time-step? If you believe this is happening, perhaps you could report on the Forum for everyone's consideration the time-step, stresses being reached, and the vertical resolution at the time of your instability problems.

For a fixed bottom stress, the effective drag coefficient and reference depth, zref, are related by:

zref = z0 * exp ( k/sqrt(Cd) )

As zref decreases when the boundary layer is better resolved, u(zref) decreases so the effective Cd required to maintain the same stress increases.

The maximum allowed Cd of A=0.5 corresponds to a zref of 1.76*z0. Since the roughness scale z0 is of order 2 mm, zref would need to fall below 4 mm to be limiting. Only at the very limit of the typical Dcrit for wetting/drying (10 cm) used in the default ocean.in, with 10 s-levels, would the height of the velocity point above the bed 1/20*Dcrit be 5 mm. For any water depth greater than Dcrit you presumably would not be close to the realm of the limiting maximum Cd.

Conversely, an absurdly high zref would implied by the lower bound on Cd of B=1e-6.

So isn't it unlikely these parameters are controlling the way the logdrag option impacts the effective bottom stress?

Are you proposing the stress itself limits time-step? If you believe this is happening, perhaps you could report on the Forum for everyone's consideration the time-step, stresses being reached, and the vertical resolution at the time of your instability problems.

John Wilkin: DMCS Rutgers University

71 Dudley Rd, New Brunswick, NJ 08901-8521, USA. ph: 609-630-0559 jwilkin@rutgers.edu

71 Dudley Rd, New Brunswick, NJ 08901-8521, USA. ph: 609-630-0559 jwilkin@rutgers.edu