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Improve implementation of imposed U(y) in SingleLayerQG #365

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navidcy opened this issue Jul 29, 2024 · 2 comments
Open

Improve implementation of imposed U(y) in SingleLayerQG #365

navidcy opened this issue Jul 29, 2024 · 2 comments

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@navidcy
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navidcy commented Jul 29, 2024

#360 implemented the ability of U(y) in SingleLayerQG module.

  • If imposed zonal flow is constant ($U_0$) then term $- i k_x U_0$ is included in the L operator & the $U_0 \partial_x \eta$ term in N.
  • If imposed zonal flow varies with y ($U(y)$) then all extra advection terms are added in N.

A potential improvement is that we should take any prescribed imposed zonal flow $U(y)$ and decompose it into its y-mean and deviation from that, e.g.,

$$ U(y) = U_0 + u(y)$$

with $\int u(y) \mathrm{d} y = 0 $. Then we add the $U_0$ via L (as 1 above) and the rest via N (as 2 above).

cc @mncrowe

@mncrowe
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mncrowe commented Jul 29, 2024

I did consider it as an option as you can just define $U_0$ as the zero Fourier mode of $U$. I started implementing it but in the end used the current approach as it was simpler to write down the Nonlinear term this way.

If we're going to do this, it might be worth implementing @glwagner's suggestion of including support for U as a function of $y$ and $t$ at the same time.

@navidcy
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navidcy commented Jul 29, 2024

If we're going to do this, it might be worth implementing @glwagner's suggestion of including support for U as a function of y and t at the same time.

Good point.

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