The linear (rapid) source in the incompressible pressure Poisson equation supplies a Reynolds-number-independent offset to inner-scaled wall-pressure variance while the nonlinear (slow) source supplies the logarithmic coefficient with frictional Reynolds number.
A note on Poisson’s equation for pressure in a turbulent flow
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On the Poisson-Source Basis of Logarithmic Wall-Pressure-Variance Growth
The linear (rapid) source in the incompressible pressure Poisson equation supplies a Reynolds-number-independent offset to inner-scaled wall-pressure variance while the nonlinear (slow) source supplies the logarithmic coefficient with frictional Reynolds number.