Physical Nature and Spatial Localization of Hydrodynamic Added Mass (Part II): Eliminating Matrix Artifacts and Conservation Inconsistencies

A preceding study demonstrated that the Kirchhoff added mass matrix – a cornerstone of marine hydrodynamics for over 160 years – is inconsistent with fundamental conservation laws. The present work examines the consequences of that finding by re–investigating what added mass physically represents and where it is spatially located. The analysis establishes two principal results. First, added mass is an inherently localized, scalar quantity whose magnitude is determined entirely by the wetted boundary geometry through a measurable displacement path 𝐿 eff , not by an abstract tensor entry. Second, the apparent “cross–coupling coefficients” (𝐴𝑖 𝑗 , 𝑖 ≠ 𝑗) linking translational and rotational degrees of freedom are not genuine physical interactions; they are projection artifacts that arise when an inherently scalar boundary reaction is decomposed into an orthogonal coordinate basis. No cross–coupling exists in the underly- ing physics – it exists only in the matrix.