Global climate modeling of the Jupiter troposphere and effect of dry and moist convection on jets

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Volume 687 (July 2024)

A&A, 687 (2024) A274

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Table A.1

Summary of the equations of the thermal plume model described in appendix A.

Vertical mass flux definition	f = αρω	(A.1)
Mass conservation	$\frac{\partial f}{\partial ɀ} = e - d$ ${{\partial f} \over {\partial z}} = e - d$	(A.2)
Tracers transport	$\frac{\partial f ψ}{\partial ɀ} = e ψ_{e} - d ψ$ ${{\partial f\psi } \over {\partial z}} = e{\psi _e} - d\psi$	(A.4)
Vertical momentum conservation	$\frac{\partial f w}{\partial ɀ} = - d w + α ρ Γ$ ${{\partial fw} \over {\partial z}} = - dw + \alpha \rho \Gamma$	(A.7)
Plume acceleration parametrization	Γ = a B − b w²	(A.6)
Entrainment parametrization	$ϵ = β max (\frac{1}{w} \frac{\partial w}{\partial ɀ}; 0) + v$ $= \beta \max \left( {{1 \over w}{{\partial w} \over {\partial z}};0} \right) + v$	(A.3a)
Detrainment parametrization	$δ = β max (- \frac{1}{w} \frac{\partial w}{\partial ɀ}; 0) + v$ $\delta = \beta \max \left( { - {1 \over w}{{\partial w} \over {\partial z}};0} \right) + v$	(A.3b)
Closure relation	$f_{0} = \frac{ω_{max}}{r h \int \frac{e^{2}}{ρ} d ɀ}$ ${f_0} = {{{\omega _{\max }}} \over {rh\int {{{{e^2}} \over \rho }} dz}}$	(A.14)

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