A note on the Kraichnan—Phillips theorem

The Kraichnan-Phillips theorem asserts that, for incompressible, homogeneous, turbulent flow over a plane, rigid wall, the wall-pressure wavenumber-frequency spectrum P ( k , ω) → 0 as the planar wavenumber k → 0 provided the frequency ω ≠ 0. A proof of this theorem is given by use of a general formula that expresses the normal force on an arbitrary rigid body in terms of volume and surface integrals involving the vorticity. Implications for the theory of flow-induced surface vibrations are briefly discussed.