# [MITgcm-support] initial W caused by bathymetry?

Martin Losch Martin.Losch at awi.de
Wed Jan 7 10:55:26 EST 2009

```Hi David,

I was not thinking when I replied to you this morning. You are right
of course, and a uniform horizontal flow-field on a C-grid is
automatically divergent near topography (because by definition there
is no flow into topography), so that everything is OK and you should
get the effects that you described. Your interpolated 3D solutions
are already nearly non-divergent (save the errors introduced by
interpolation) and you don't see the pronounced w-effects.

I guess you'll have to specify a non-divergent field as initial
conditions.

Martin
On 7 Jan 2009, at 16:13, David Hebert wrote:

> Hi Martin,
>
> The scale of W is about 10% of U. So I specify U=0.1m/s, and those
> stripes are +- 0.0137m/s.  The value of 0.0137m/s agrees with
> continuity computations when comparing with my grid...
>
> dx = 14.5m
> dz = 1m
> u=0.1m/s
>
> Thus, du/dx would be 0.1/14.5 = 0.0069. Using hfac's, dx could be
> half near bathymetry, which would yield 0.1/7.25 = 0.0138.
>
> I also wonder if this were a simulation with variable dz, and the
> bottom dz was larger (say 100m), would that manifest the magnitude
> of w since we now are integrating over a large z?
>
> Anyway, the stripes persist for quite some time in the simulation.
> Admittedly, if I were to start this simulation with u,v from
> larger, mesoscale simulation then W might not stretch through the
> domain.  Often here we will start with a large mesoscale simulation
> and interpolate to simulate sub-mesoscale with higher resolution
> bathymetry. It would seem we need to be carefull that non-divergent
> free horizontal motions are created.
>
> Thanks,
>
> David
>
> Martin Losch wrote:
>> David,
>>
>> what is the scale of the w-values? The only thing I can think of
>> is that this is the round-off error showing up. This would not be
>> visible with a non-uniform u-field, because other ("real") effects
>> would dominate.
>>
>> Martin
>> On 7 Jan 2009, at 03:12, David Hebert wrote:
>>
>>> Hi Everyone,
>>>
>>> I would like to conduct a 3D, nonhydrostatic simulation with a
>>> barotropic flow over a seamount. In the past I have typically
>>> started these simulation with a U velocity throughout the domian.
>>> In this case, U=10cm/s. Since U=10cm/s everywhere (and V=0) at
>>> t=0, I would expect continuity to be satisified and W=0. However,
>>> I get several vertical "stripes" for W at t=0 (see attached
>>> vertical cross-sections for U,W at t=0).  These "stripes" seem to
>>> be caused because the model is using areas where there is
>>> bathymetry to compute continuity. i.e., where there is land, U=0,
>>> and the adjacent point U=10cm/s, resulting in a nonzero value of
>>> du/dx. Furthermore, since du/dx is zero above the bathymetry, the
>>> induced W is manifested vertically.
>>>
>>> My question is has anyone come across this issue where bathymetry
>>> seems to cause velocity gradients? How do I get around it? I
>>> should note I see similar stripes in W when I initialize U and V
>>> from a larger domain simulation.
>>>
>>>
>>> David
>>>
>>> <Ut0.png>
>>> <Wt0.png>
>>> <Ut0.png><Wt0.png>
>>> _______________________________________________
>>> MITgcm-support mailing list
>>> MITgcm-support at mitgcm.org
>>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>>
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```