Hydrodynamic Basset Force & Memory Kernel

The Basset-Boussinesq-Oseen (BBO) equation describes a particle in an unsteady viscous flow. The Basset history force is a convolution integral: F_B = -6πaμ√(ν/π) ∫₀ᵗ (du/dτ)(t-τ)^{-1/2} dτ, encoding the particle's entire velocity history via a t^{-1/2} memory kernel. This non-Markovian term creates anomalous memory-enhanced drag distinct from Stokes drag.