Beyond Vorticity: An Angular Momentum Perspective on Fluid Flow

While vorticity is the classical tool for analyzing rotational fluid kinematics, it inherently focuses on local, differential spin. This paper introduces a complementary framework based on the angular momentum density field, L = r u, deriving generalized transport equations that explicitly balance macroscopic torque and rotational momentum. This L-perspective offers several distinct theoretical advantages over traditional velocity-vorticity formulations. Specifically, this approach: (i) provides a novel decomposition of the viscous torque into a diffusive component and a local spin-dissipative term; (ii) shows the mechanism by which lift is generated in viscous boundary layers by vorticity acting as a source of angular momentum; it also explains stall (iii) reformulates the hydrodynamic impulse to yield a remarkably clean separation of terms into dilatational, volumetric, and rotational flux components; The L formalism provides the kinematic closure necessary to unify non-circulatory added mass and circulatory lift within a single, dimensionally consistent budget. (iv) enables the direct calculation of the viscous added mass force, accounting for the inertial resistance of boundary layers and separated wakes; (v) simplifies geophysical fluid dynamics by absorbing the planet's rotation—traditionally treated as an artificial virtual vorticity term—directly into the conserved axial angular momentum m, revealing the fundamental physics of global circulation through explicit torque balances; (vi) identifies the rotlet as a fundamental Green's function for the L transport equation in the Stokes regime; and (vii) demonstrates that both oblique shocks and vortex sheets act as singular sources of L that turn the macroscopic flow. abstract