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Hi folks. I'm trying to run a simple 2D model of a tidal creek. Upland water sources to the creek are negligible, so the only boundary condition is time-varying water surface elevation at the creek mouth (see attached image). The problem is that velocity does not smoothly vary in the creek during a tidal cycle (see attached time series). Water is generally flowing in the correct direction on ebb and flood, but velocity magnitude is very noisy throughout the domain in an unphysical way. It seems that there is some high-frequency numerical sloshing going on that could be the problem, but I'm not sure. Here are some details of the simulation (more in attached case file):

• channel length ~ 4km
• grid resolution = 10m
• time step = 1s
• constant eddy visc = 0.1 m2/s
• Mannings roughness = 0.025 (0.05 on boundaries)
• TREATMENT OF THE LINEAR SYSTEM = 2
• FREE SURFACE GRADIENT COMPATIBILITY = 0.9

I've tried reducing the time step to 0.1s, but the fluctuations persist.

Any insights on my setup would be much appreciated!

Thanks,
Ben

Hi
As I can see the oscillations are small so it could be hard to find a solution
By the way, I think this could be related to the imposed boundary condition as there is only one and you impose the water level.
I think it could be improved if you add a part of the downstream creek in you model.
In my opinion, the velocity at the actual downstream boundary would be better controlled and I hope this will limit the BC effect in your model

Hope this helps

Thanks, Christophe. Yes the fluctuations are small but are noisy enough to invalidate the results (given the relatively low true velocity). It seems that the fluctuations are imposed upon the physical velocity signal and muddling it. Take a look at the last bit of the time series (previous post) where I've held the water level constant - you can see the fluctuations persist and have a regular frequency (actual velocity should be zero). You can also see regular non-physical fluctuations in the water level which should be constant.

Yes, there is only the d/s boundary. Unfortunately, that boundary is very near the d/s end of the creek (at the confluence with the estuary; see attached image). I've tried extending the model slightly into the estuary, but I still get the numerical noise in depth and velocity.

Is there anything I can change with the numerical settings to dampen the noise?





Thanks,
Ben

Hi Ben,

I would check if it's not an initial condition. Is the BC held constant the last 12h in your graph? What is the amplitude at the BC?

Good luck,

Patrick

Hi Patrick. Thanks for responding. The initial condition is constant elevation. The d/s BC starts at this same elevation, so there is no miss-match there initially.

Yes, the d/s level is held at 0.99 m for the last bit (~7.5 hrs) of my simulation - you can see the numerical noise lingers during that period. The velocity noise seems to die out faster than the water level noise.

It is also worth noting that I ran this same exact model with a different boundary condition which is purely sinusoidal and with slightly larger amplitude (more characteristic of a "typical" tide at my site; the simulation I'm having trouble with is of a storm surge scenario). The "typical" scenario yields a much smoother water level and velocity signal at the sample point (see attached figure with time series for both the problematic "surge" simulation and the smoother "typical" simulation). Weird...

Finally, switching TREATMENT OF THE LINEAR SYSTEM from 2 to 1 had no effect (except slowing the simulation way down). Nor did switching SCHEME FOR ADVECTION OF VELOCITY from 14 (yes tidal flats) to 1 (no tidal flats).

Thoughts? Thanks.

Even if water levels are the same you still 'shock' the system as your initial velocities are zero at mean water levels. You can see oscilationtions in the first tidal cycle of your typical simulation.
Maybe run your 'surge' with using the typical as initial condition.

Patrick

Thanks for the clarification.
Maybe you could try to start your simulation from the high level with eventually a first constant part where you could check every thing stay without oscillation in the result...
Otherwise, even if it's not realistic, I think you could omit the lateral roughness (the velocities are low...)
And maybe increase the eddy viscosity...

Hope this helps

Thanks, guys.

Patrick, we're on the same wavelength! I tried spinning up the simulation using the smooth "typical" timeseries for the first 24 hours then smoothly transitioning to the surge timeseries. The velocity signal is OK for the first 24 hrs, then gets noisy again as the BC transitions to the surge timeseries. Note that the "typical" timeseries is a smooth sine curve, while the surge timeseries was pulled from historical data and, therefore, is not quite as smooth. I'm wondering if the lack of smoothness in the surge timeseries at the boundary is causing little "shock waves" to ripple through the system. I'm going to fit a smooth synthetic curve to the surge timeseries and use that instead to see if the noise goes away.

Christophe - good idea with the steady first part of the timeseries...I'll try that too. If modifying the d/s BC does not help, I'll start playing with friction.

Thanks,
Ben

Hi again,

So for my case, smoothing out the time series of water level prescribed at the d/s boundary indeed reduced noise in the velocity signal. See the attached plot; the "smooth fit" synthetic time series was defined using a modulated sine function and resulted in much less velocity noise than did the "historic" time series which was pulled from a nearby gauge.

I think this issue may be related to the fact that my creek is quite small and short. Also, the low velocity in the creek makes a little bit of numerical noise problematic (low signal:noise ratio).

Cheers,
Ben