# Wolfram Language™

## Visualize Hurricane Data

The simple model for a vortex is given by the combination of body rotation within a core and decreasing angular velocity outside.

show complete Wolfram Language input
In:= `w = 6; rcore = 3; a = 1; g = 9.82; rho = 1; Subscript[rho, 0] = 1;`
In:= `wind[r_, z_] := If[r <= rcore, w r, (w a^2)/r];`

The formula for finding pressure gives the following formula in terms of radius and elevation.

In:= ```pressure[r_, z_] := If[r < rcore, 1/2 rho w^2 r^2 - rho g z + Subscript[rho, 0], -((rho w^2 rcore^4)/(2 r^2)) - rho g z + rho w^2 rcore^2 + Subscript[rho, 0]];```

Plot the wind speeds, which are fastest outside the center of the system.

In:= ```SliceContourPlot3D[ wind[Sqrt[x^2 + y^2], z], {x^2 + y^2 == 3 z, x^2 + y^2 == 6 z, x^2 + y^2 == 1 z}, {x, -5, 5}, {y, -5, 5}, {z, 1, 5}, Contours -> 20, RegionFunction -> Function[{x, y, z}, x < 0 || y > 0], PlotTheme -> "NoAxes", PlotLegends -> Automatic, PlotLabel -> "Wind Strength", ImageSize -> 400]```
Out= Plot the wind directions as a vector field.

In:= ```SliceVectorPlot3D[{(wind[Sqrt[x^2 + y^2], z] y)/ Norm[{x, y}], (-wind[Sqrt[x^2 + y^2], z] x)/Norm[{x, y}], 0}, {x^2 + y^2 == z, x^2 + y^2 == 3 z, x^2 + y^2 == 6 z}, {x, -5, 5}, {y, -5, 5}, {z, 1, 5}, ImageSize -> 400, PlotLegends -> None, VectorStyle -> "Arrow3D", VectorScale -> {Medium, 0.5, Automatic}, VectorPoints -> 8, RegionFunction -> Function[{x, y, z}, x < 0 || y > 0], PlotTheme -> "NoAxes", PlotLabel -> "Wind Direction"]```
Out= Plot the pressure as a 3D density. Note the low relative pressure in the center of the system.

In:= ```DensityPlot3D[ pressure[Sqrt[x^2 + y^2], z], {x, -5, 5}, {y, -5, 5}, {z, 1, 5}, ImageSize -> 400, PlotLegends -> Automatic, PlotTheme -> "NoAxes", RegionFunction -> Function[{x, y, z}, (x^2 + y^2 <= 6 z) && (x < 0 || y > 0)], PlotLabel -> "Air Pressure", OpacityFunction -> Function[f, f/5 + 0.1]]```
Out= 