mathematician needed

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Oh, ok I see you've let it stew for 3 months ...

Here is the link:

Everyone needs a solution to the Navier Stokes equation.

The reason we have wind tunnels and not computers is because there isn't one. The only people who claim to have a solution are the climate change alarmists.

Beat me to it!

We don't have a solution to the n-body problem. And yet planets, satellites etc generally end up where predicted by numerical methods. Quite a lot of people seem to think numerical methods can similarly provide useful results for river modelling.

Turbulence. Chaotic behaviour.

It is interesting to see from the complex shapes of F1 car front wings, etc. that computational fluid dynamics is now able to model very hard problems. Because of the combinatorial explosion there will always be limits in how far chaotic and turbulent processes can be predicted.

With climate change, the problem is not so much solving the equations, it is knowing what assumptions to make.

Weather forecasting has made amazing progress (greatly helped by ensemble averaging). Some way off doing 30 year predictions though.

I think Manning's equation is your friend....

Numerical integration works reasonably well for planets, where the action of the sun predominates, and there is only one first order linear differential in play.

Navier stokes are non linear partial derivatives. These are not really amenable to numerical integration.

1. Mathematical modelling is not necessarily helpful. During a severe storm, trees and boulders get washed into the river, significantly impeding flow. There's no point calculating for a near-perfect scenario, if that isn't going to happen.

The vegetation can also form a dam further upriver, and when that eventually gives way an awful lot more water than predicted arrives in a short space of time.

1. This website seems to answer the question, without reinventing the wheel.
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2. The Flow rate, during a storm, is 2m/s, width is 9m, and water depth is 'thigh-deep'= say 0.6m. So, that's say 10 cu.m/s.

The OP says "the worst case flow past it would be 41.2 cu.m/sec". So, if that happens, it will obviously flood if the height of the banks is close to 0.6m. And it obviously won't flood if the banks are at least say 2.5m high. Sorry to be trite, but the Op did not mention how high the banks are.

How likely is the 'worst case' said to be?

What are the consequences if it overflows? Is the house uphill of the river, as the insurers won't be bothered if the OP's roses get inundated?

1. The OP only talks about his section of the river, but he is on a hill, and, if it overflows higher up, no amount of calculations of his stretch will help him.

No, it is interesting to see from the fact that F! car designers still employ massive and expensive wind tunnels, that computational fluid dynamics is still not able to model very hard problems.

Because of the combinatorial explosion there will always be

No, it is both. The reason assumptions are made is because otherwise the equations are insoluble and the data sets are sparse. And because otherwise the results don't fit the primary assumption that while the earths temperature has, over aeons, varied wildly, the only possible cause to day is human activity of one specific sort.

Actually it hasn't. And ensemble averaging is bollocks. Generally one ensemble is right and the rest are plain wrong.

It is scarcely better than 50 years ago except we know more about what is happening now.

Don't forget the re-introduced beavers.

Only in the short term. Model far enough into the future and you won't know where on their orbits the planets are.

Yes but those wings don't always work 100% if there is a cross wind, the camber on the road is not perfect or the car is driving behind another that is generating turbulence.

With flooding the number of trees and vegetation washed into the river during a downpour need to be considered etc. The problem on the wiki page suggests a very short river section but what about the blocked bridge arch two miles further downstream.

For a >50% prediction, the weather tomorrow is going to be the same as it is today.

Many of the planets in our solar system have settled into their 'spot' due to harmonics with adjacent planets.

I would say they can, up to a point. The strength of any model is to respect its bounds of accuracy.

Funnily at one time that was the most accurate prediction and more reliable that the Met Office. I'm pretty sure that is no longer the case.

Well, they use both because at the end of the day data is the only thing that matters, and they use the wind tunnels to validate the computer models. It would be interesting to see the breakdown of the budgets, but I bet they do much more modelling in software than in hardware, these days.

Yes well that is the biggest flaw. There are variations over all sorts of timescales. The root cause of some is known, others are a complete mystery. But it's easy to sell a lie on flawed short term data.

Maybe I am using the wrong term. Doing multiple runs with slightly different start parameters is how they can derive probabilities, and these are *very* useful to people like farmers.

I reckon it is *very much* better.

Where's the evidence that the Met Office, WMO, ForecastWatch et al have all been lying?