The relationship between the surface pressure spectrum and transverse velocity spectrum in a Rapid-distortion theory model of trailing edge noise

Accurate jet-surface interaction noise prediction remains an important aspect of the aircraft design process. This is particularly true for the next generation aircraft configurations, one of which could see the exhaust system tightly integrated to the airframe. Use of Rapid- distortion theory of turbulence (RDT) to determine the radiated sound represents one such approach to model the sound generation/propagation process. Recent work on the application of RDT to the canonical problem of a jet flow interacting with a flat plate trailing edge gave accurate predictions across the frequency and acoustic Mach number range. In this paper we ascertain whether an RDT based model that uses the unsteady surface pressure spectrum as the source term can also be utilized to determine accurate edge noise predictions. Surface pressure based models have been widely used in the Amiet formulation of trailing edge noise. The upstream boundary condition in the RDT formulation enters via a streamwise convected quantity, ω ̃c(τ − y1/U(yT ), yT ), that is an arbitrary function of its arguments. But since the pressure fluctuation possesses an upstream asymptote that decays algebraically faster than curl of the out-of-plane vorticity fluctuation in the local hydrodynamic relation given by Eq. 3.9 in Goldstein, Leib & Afsar (J. Fluid Mech., vol. 824, pp. 477-512, 2017), this latter relation cannot be used to determine the surface pressure near the trailing edge. In this paper we show to obtain this relation using an inversion of Fourier transforms similar to that used in our earlier paper Goldstein, Afsar & Leib (J. Fluid Mech., vol. 736, pp. 532-569, 2013). The relation we obtain shows how the surface pressure spectrum can therefore be related to the velocity fluctuation correlation function