Volume 561, January 2014
|Number of page(s)||17|
|Published online||06 January 2014|
Here we evaluate Ṗ2 and Ṗ1, the first two coefficients on the right-hand side of Eq. (55). We will show that both coefficients are zero. The first is (A.1)Substituting f2 = β sin θ/2 , this becomes The background flow, while it certainly carries z-momentum, makes no net contribution to the influx.
The integral expression for the second coefficient is lengthier, and we write it as (A.2)where and It is convenient to split up the integral in Eq. (A.2) by region. For the downstream part, which we denote as , we use Eqs. (15) and (16) for f1 and g-1. We find, after algebraic simplification, that (A.3)We now use the identity
to conclude that (A.4)Similarly, the upstream part is (A.5)so that (A.6)For the intermediate piece, to be denoted , we use Eqs. (21) and (22) for f1 and g-1. Although we have established that C = +1 , we will see that is independent of this parameter, so we retain the original notation. After algebraic manipulation, we find (A.7)Using the identity we infer that (A.8)In summary, we have (A.9)
© ESO, 2014
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