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docs/src/examples.md

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@@ -118,8 +118,8 @@ Follows the momentum equations with vertical diffusion and Coriolis force:
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These are discretized using the following:
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```math
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\begin{align}
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\frac{\partial u}{\partial t} &\approx D_{f2c}\left(\nu G_{c2f}(u)\right) + f(v - v_g) - A(w, u) \\
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\frac{\partial v}{\partial t} &\approx D_{f2c}\left(\nu G_{c2f}(v)\right) - f(u - u_g) - A(w, v)
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\frac{\partial u}{\partial t} &\approx D_\left(\nu G(u)\right) + f(v - v_g) - A(w, u) \\
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\frac{\partial v}{\partial t} &\approx D_\left(\nu G(v)\right) - f(u - u_g) - A(w, v)
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\end{align}
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```
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Because this is a 1D vertical problem, we utilize the staggered vertical grid with:
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- `G_{c2f}` is the [gradient operator from cell centers to faces](https://clima.github.io/ClimaCore.jl/stable/operators/#ClimaCore.Operators.GradientC2F), called `gradc2f` in the example code.
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- `D_{f2c}` is the [divergence operator from faces to centers](https://clima.github.io/ClimaCore.jl/stable/operators/#ClimaCore.Operators.DivergenceF2C), called `divf2c` in the example code.
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- `A` is the [advection operator](https://clima.github.io/ClimaCore.jl/stable/operators/#ClimaCore.Operators.AdvectionC2C), called `A` in the example code.
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- ``D`` is the [face-to-center divergence](https://clima.github.io/ClimaCore.jl/dev/operators/#ClimaCore.Operators.DivergenceF2C) operator, called `divf2c` in the example code
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- ``G`` is the [center-to-face gradient](https://clima.github.io/ClimaCore.jl/dev/operators/#ClimaCore.Operators.GradientC2F) operator, called `gradc2f` in the example code
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- ``A`` is the [center-to-center vertical advection](https://clima.github.io/ClimaCore.jl/stable/operators/#ClimaCore.Operators.AdvectionC2C) operator, called `A` in the example code.
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#### Problem flow and set-up
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##### Reconstructions
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**$I^f$** is the [center-to-face reconstruction operator](https://clima.github.io/ClimaCore.jl/stable/operators/#ClimaCore.Operators.InterpolateC2F), called `If` in the example code.
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**$I^f$** is the [center-to-face reconstruction](https://clima.github.io/ClimaCore.jl/stable/operators/#ClimaCore.Operators.InterpolateC2F) operator, called `If` in the example code.
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Currently this is implemented as the arithmetic mean.
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##### Differentiation operators

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