Computation of acoustic scattered fields and derived radiation force and torque for axisymmetric objects at arbitrary orientations

This study presents a theoretical framework for calculating acoustic scattering fields, as well as radiation force and torque resulting from the interaction between an incident wave and an axisymmetric object positioned at arbitrary orientations. Grounded in the partial-wave expansion method, it formulates scattering products using beam-shape and scalar scattering coefficients. The incorporation of geometric features into the scalar scattering coefficients is achieved through the conformal transformation approach. Notably, its applicability is restricted to scenarios where the object is positioned at its standard orientation, a limitation circumvented by employing rotational transformations to extend the model to non-standard orientations. A rotational transformation tunes the original frame (observation coordinate system) into a reference frame (computation coordinate system), for any deviated orientation and facilitating solution of scattering products. While the non-intuitive nature of rotational transformations disrupts the inheritability of the partial-wave expressions for the scattering products, an alternative approach is provided based on rotation addition theorem. This method directly incorporates object orientations into the beam-shape and scalar scattering coefficients, bypassing rotational transformations and preserving the partial-wave format. Comparative analysis with full three-dimensional numerical simulations shows theoretical methods are computationally more efficient while ensuring substantial consistency.