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Polar dB diagram of the scattered field at \(r=1.5R_{in}\) for \(M_\infty = 0.1, 0.3\) , with \(\Delta r=1dB\). Effect of \(\sigma _{PG}\): comparison between Prandl-Glauert’s operator isolation method in Eqs. (8) and (9), and the metric tensors formulation in Eq. (16).