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Initial Conditions for the hydro quantities
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The initial Conditions for the hydro dynamical quantities are determined for a disk of gas in equilibrium in the gravitational field of the central star. The gas distribution is azimuthally symmetric therefore all the quantities depend the distance between a gas particle and the star only $`r`$ or on $`(r,\varphi)`$
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where $`\varphi`$ is the colatitude angle. When useful we use cylindrical coordinates $`(R,z)`$ with $`R=r\sin (\varphi)`$ and
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$`z= r\cos(\varphi)`$.
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## Density
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The surface density distribution follows a power law:
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In the classical Minimum Mass Solar Nebula model the surface density distribution is a power law with slope 3/2.
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We generalize this model by considering:
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$`\Sigma(r) = \Sigma_0(r/R0)^{-\alpha}`$
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with $`\Sigma_0`$ the surface density at $r/R0=1$ and $\alpha$ the
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with $`\Sigma_0`$ the surface density at $r/R0=1$ and $`\alpha`$ the
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slope of the power law.
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$`\Sigma_0`$ in code unit is the parameter ```Start``` in the configuration file and
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```$`\alpha`$``` is Slope. They are provided in the ```Density``` block as follows:
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$`\alpha`$ is ```Slope```. They are provided in the ```Density``` block as follows:
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```
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Density
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{
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... | ... | @@ -16,12 +18,28 @@ Density |
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}
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```
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Notice that the user can define a density floor: ```Minimum```
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in c.g.s, i.e. $g/cm^3$ in the case of a 3D simulation and $g/cm^2$ for 2D simulations.
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in c.g.s, i.e. in $`g/cm^3`$ in the case of a 3D simulation and $`g/cm^2`$ for 2D simulations.
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The volume density is obtained by the ``hydrostatical equilibrium`` in the thin disk approximation. In cylindrical coordinates it reads:
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The volume density is obtained by the hydrostatical equilibrium in the thin disk approximation. In cylindrical coordinates it reads:
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$`\rho(R,z) = \rho_0(R) \exp(-R^2/(2H^2)`$
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with $`\rho_0(R) = \Sigma_0 R^{-\alpha-1-\beta}/h_02\pi`$
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with:
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$`\rho_0(R) = \Sigma_0 R^{-\alpha-1-\beta}/h_02\pi`$
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where $`H(R) = h_0R^{1-\beta}`$ is the disc height and $h_0$ is the
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pressure scale height, with typical values around 0.05.
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In the configuration file $`h_0`$ corresponds to ```AspectRatio```
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and $`\beta`$ is the ```FlaringIndex```.
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## Radial Velocity
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The radial transport of gas and therefore the initial radial velocity is obtained from the angular momentum conservation
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and the continuity equations. We consider the thin disk approximation in which gas quantities are vertically averaged and,
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as for the density, we consider the disk azimuthally symmetric.
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## Azimuthal Velocity
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## Polar velocity |
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\ No newline at end of file |