  Most coastal flows are turbulent and cannot be accurately described by
shallow water equations. This paper presents a novel theory for characterizing
accelerated coastal flows, offering improved representation of turbulent flows.
The theory builds on second-order approximation long-wave theory, utilizing a
dual-velocity vector approach (comprising a mean velocity and a
turbulence-induced distortion velocity) in the primary flow directions. The
resulting second-order long-wave model consists of five equations, which is one
fewer than the number derived from averaged models that incorporate turbulence
as reported in the literature, yet it retains equivalent physical and
hydrodynamic characteristics. The eigenstructure of the model is presented.
This modeling approach shows promise for addressing a variety of engineering
problems.
