A REVISION OF A PREVIOUS DISCUSSION ON THE CORRECTNESS OF CURLE’S AND THE FFOWCS WILLIAMS AND HAWKINGS EQUATIONS

It is well known that noise generated by fluid flow around propellers and hulls of maritime platforms significantly contributes to their acoustic signature. The level of this noise is often determined by means of Curle’s and the Ffowcs Williams and Hawkings (FW-H) equations, according to which the noise level depends on the total force acting upon the rigid boundary and the velocity of the boundary. The author and his previous co-author claimed that these equations are incorrect and suggested another equation where the noise level was determined by the acoustic pressure and its normal derivative, i.e. the potential component of velocity, on the boundary. The purpose of this paper is to reconsider the arguments which the author and his co-author presented during the discussion on the correctness of these equations. It is shown that the FW-H equation in the integral form and the equation derived previously by the present author can be obtained from the FW-H equation in the differential form utilising different ways of evaluating integrals of the source terms. It is demonstrated that the equation derived by the author does not contradict the FW-H and Curle’s equations and is another form of these equations expressed via a different set of variables. It is concluded that viscous stresses as well as the rotational component of velocity do not contribute to the acoustic radiation from a rigid boundary in fluid flow.