How to decide the Reflection parameter alpha value? (flow)  Coast/Estuary  Delft3D
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How to decide the Reflection parameter alpha value? (flow)
EE
Esther Espinoza, modified 2 Years ago.
How to decide the Reflection parameter alpha value? (flow)
Padawan Posts: 25 Join Date: 4/6/17 Recent Posts 00
Hi, I'm modelling water level for an estuary area (1 month) and I would like to know if you can explain me a little bit about the reflection parameter alpha that it's needed in the bounday section of the flow module. I've read the manual, but I'm not sure how to decide it's value or how big is the influence of that parameter on the results of the water level simulation.
Thank you
Thank you
Bert Jagers, modified 2 Years ago.
RE: How to decide the Reflection parameter alpha value? (flow)
Jedi Knight Posts: 201 Join Date: 12/22/10 Recent Posts 20
Hi Esther,
For an estuary I would expect to implement an alpha value on the downstream (sea) water level boundary.
The alpha value suggested in the manual equation (9.76) for a water level boundary equals Td * sqrt(H/g) where Td is the time it takes for a free surface wave to travel from the left boundary to the right boundary of the model area, H is the water depth, and g is the gravitational acceleration (about 9.8).
Here the words "left" and "right" boundary refer to the typical upstream and downstream boundaries, but shorter characteristic distances that may reflect free surface waves may be appropriate instead. A free surface wave travels with U +/ sqrt(g*H) which is for small average velocity U well approximated by sqrt(g*H). The time Td then equals L / sqrt(g*H) where L is the aforementioned characteristic length. If we insert this approximation for Td in (9.76) the expression for alpha at the water level boundary becomes: L / g, that is the characteristic length divided by about 10.
For an estuary with characteristic length scale of 20 km we would thus preferably use an alpha value of 20000/10 = 2000 to avoid boundary reflections inside the domain. The larger the estuary, the large the alpha value. Now, the question arises: can we increase alpha without complications? Unfortunately, no.
By increasing alpha, the boundary starts also to dampen any variations that itself tries to send in. I believe that values up to about 1000 are usually safe, but I recommend to compare the the imposed boundary forcing signal with the observed signal at the boundary and check whether it corresponds satisfactorily for the alpha value that you would like to use. Note that it will not match perfectly if the observation point is inside the grid whereas the forcing is imposed in a virtual grid cell just outside the grid.
Hope this helps,
Bert
For an estuary I would expect to implement an alpha value on the downstream (sea) water level boundary.
The alpha value suggested in the manual equation (9.76) for a water level boundary equals Td * sqrt(H/g) where Td is the time it takes for a free surface wave to travel from the left boundary to the right boundary of the model area, H is the water depth, and g is the gravitational acceleration (about 9.8).
Here the words "left" and "right" boundary refer to the typical upstream and downstream boundaries, but shorter characteristic distances that may reflect free surface waves may be appropriate instead. A free surface wave travels with U +/ sqrt(g*H) which is for small average velocity U well approximated by sqrt(g*H). The time Td then equals L / sqrt(g*H) where L is the aforementioned characteristic length. If we insert this approximation for Td in (9.76) the expression for alpha at the water level boundary becomes: L / g, that is the characteristic length divided by about 10.
For an estuary with characteristic length scale of 20 km we would thus preferably use an alpha value of 20000/10 = 2000 to avoid boundary reflections inside the domain. The larger the estuary, the large the alpha value. Now, the question arises: can we increase alpha without complications? Unfortunately, no.
By increasing alpha, the boundary starts also to dampen any variations that itself tries to send in. I believe that values up to about 1000 are usually safe, but I recommend to compare the the imposed boundary forcing signal with the observed signal at the boundary and check whether it corresponds satisfactorily for the alpha value that you would like to use. Note that it will not match perfectly if the observation point is inside the grid whereas the forcing is imposed in a virtual grid cell just outside the grid.
Hope this helps,
Bert
EE
Esther Espinoza, modified 2 Years ago.
RE: How to decide the Reflection parameter alpha value? (flow)
Padawan Posts: 25 Join Date: 4/6/17 Recent Posts 00
Thank you so much Bert, it was really helpful!