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(0.91.0) Make hydrostatic pressure anomaly optional in `Nonhydrostati…
…cModel` (#3574) * Add kwarg for hydrostatic pressure anomaly, make nothing by default * Modify regression tests to separate hydrostatic pressure * Update docs on pressure decomposition plus nonhydrostatic model docs * Bugfix plus discontinue support for "trying" to set boundary conditions on pressure * Fix regression tests * Bump minor version * Use nonhydrostatic pressure for aux data * Add some validation of the pressure fields * Bugfix * Make sure buoyancy gets added when hydrostatic pressure is omitted * fix typos/phrasing * remove PressureField(s) * Fix AB2 test, which was wrong because update_state computes tendencies now * Relax requirement that w==0 in jld2 output writer test * Try again to get a good comparison * Dont test halo filling for hydrostatic pressure cause who cares --------- Co-authored-by: Navid C. Constantinou <[email protected]>
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docs/src/numerical_implementation/pressure_decomposition.md
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,62 +1,51 @@ | ||
| # [Pressure decomposition](@id pressure_decomposition) | ||
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| In the numerical implementation of the momentum equations, the kinematic pressure ``p`` | ||
| is split into "hydrostatic" and "non-hydrostatic" parts via | ||
| In the numerical implementation of the momentum equations in the `NonhydrostaticModel`, the kinematic pressure ``p`` | ||
| is split into "background" and "dynamic" parts via | ||
| ```math | ||
| \begin{equation} | ||
| \label{eq:pressure} | ||
| p(\boldsymbol{x}, t) = p_{\text{total hydrostatic}}(\boldsymbol{x}, t) + p_{\rm{non}}(\boldsymbol{x}, t) \, . | ||
| p(\boldsymbol{x}, t) = p_{\text{background}}(\boldsymbol{x}, t) + p'(\boldsymbol{x}, t) \, . | ||
| \end{equation} | ||
| ``` | ||
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| The hydrostatic pressure component in \eqref{eq:pressure} is defined so that the vertical | ||
| component of its gradient balances gravity: | ||
| The background pressure component in \eqref{eq:pressure} is defined so that the vertical | ||
| component of its gradient balances the background density field: | ||
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| ```math | ||
| \begin{align} | ||
| \partial_z p_{\text{total hydrostatic}} & = - g \left ( 1 + \frac{\rho_*}{\rho_0} + \frac{\rho'}{\rho_0} \right ) \, , | ||
| \partial_z p_{\text{total hydrostatic}} & = - g \left ( 1 + \frac{\rho_*}{\rho_0} \right ) \, , | ||
| \end{align} | ||
| ``` | ||
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| Above, we use the notation introduced in the [Boussinesq approximation](@ref boussinesq_approximation) | ||
| section. | ||
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| We can further split the hydrostatic pressure component into | ||
| Optionally, we may further decompose the dynamic pressure perturbation ``p'`` into | ||
| a "hydrostatic anomaly" and "nonhydrostatic" part: | ||
| ```math | ||
| \begin{align} | ||
| p_{\text{total hydrostatic}}(\boldsymbol{x}, t) = p_{*}(z) + p_{\rm{hyd}}(\boldsymbol{x}, t) \, , | ||
| p'(\boldsymbol{x}, t) = p_{\rm{hyd}}(\boldsymbol(x), t) + p_{\rm{non}}(\boldsymbol{x}, t) \, , | ||
| \end{align} | ||
| ``` | ||
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| i.e., a component that only varies in ``z`` (``p_*``) and a "hydrostatic anomaly" (``p_{\rm{hyd}}``) defined | ||
| so that | ||
| where | ||
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| ```math | ||
| \begin{align} | ||
| \partial_z p_{*} & = - g \left ( 1 + \frac{\rho_*}{\rho_0} \right ) \, ,\\ | ||
| \partial_z p_{\rm{hyd}} & = \underbrace{- g \frac{\rho'}{\rho_0}}_{= b} \, . | ||
| \partial_z p_{\rm{hyd}} \equiv \underbrace{- g \frac{\rho'}{\rho_0}}_{= b} \, . | ||
| \end{align} | ||
| ``` | ||
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| Doing so, the gradient of the kinematic pressure becomes: | ||
| With this pressure decomposition, the kinematic pressure gradient that appears in the momentum equations | ||
| (after we've employed the the [Boussinesq approximation](@ref boussinesq_approximation)) becomes | ||
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| ```math | ||
| \begin{align} | ||
| \boldsymbol{\nabla} p & = \boldsymbol{\nabla} p_{\rm{non}} + \boldsymbol{\nabla}_h p_{\rm{hyd}} + ( \partial_z p_{*} + \partial_z p_{\rm{hyd}} ) \boldsymbol{\hat z}\, , | ||
| \boldsymbol{\nabla} p &= - g \frac{\rho}{\rho_0} \hat {\boldsymbol{z}} + \boldsymbol{\nabla} p' | ||
| &= - g \frac{\rho}{\rho_0} \hat {\boldsymbol{z}} + \boldsymbol{\nabla} p_{\rm{non}} + \boldsymbol{\nabla}_h p_{\rm{hyd}} \, . | ||
| \end{align} | ||
| ``` | ||
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| where ``\boldsymbol{\nabla}_h \equiv \boldsymbol{\hat x} \partial_x + \boldsymbol{\hat y} \partial_y`` | ||
| is the horizontal gradient. | ||
| where ``\boldsymbol{\nabla}_h \equiv \boldsymbol{\hat x} \partial_x + \boldsymbol{\hat y} \partial_y``. | ||
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| Under this pressure decomposition, the kinematic pressure gradient that appears in the momentum equations | ||
| (after we've employed the the [Boussinesq approximation](@ref boussinesq_approximation)) combines with | ||
| the gravity force to give: | ||
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| ```math | ||
| \begin{align} | ||
| \boldsymbol{\nabla} p + g \frac{\rho}{\rho_0} \hat {\boldsymbol{z}} = \boldsymbol{\nabla} p_{\rm{non}} + \boldsymbol{\nabla}_h p_{\rm{hyd}} \, . | ||
| \end{align} | ||
| ``` | ||
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| Mathematically, the non-hydrostatic pressure ``p_{\rm{non}}`` enforces the incompressibility constraint. |
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@JuliaRegistrator register
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Registration pull request created: JuliaRegistries/General/106235
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Heh true. I was gonna bundle this with the RK3 default update, but we can bump minor version again instead