In order to make the equations dimensionless, a characteristic length r 0 , and a characteristic velocity u 0 , need to be defined. These should be chosen such that the dimensionless variables are all of order one. The following dimensionless variables are thus obtained: u ∗ ∗ ≡ ≡ u u 0 , r ∗ ∗ ≡ ≡ r r 0 , t ∗ ∗ ≡ ≡ u 0 r 0 t , p ∗ ∗ ≡ ≡ w u 0 2 , ∇ ∇ ∗ ∗ ≡ ≡ r 0 ∇ ∇ and of the field unit vector : g ^ ^ ≡ ≡ g g ,