On the control volume arbitrariness in the Navier-Stokes equation

We present a continuum theory to demonstrate the implications of considering general tractions developed on arbitrary control volumes where the surface enclosing it lacks smoothness. We then tailor these tractions to recover the Navier-Stokes-alpha beta equation and its thermodynamics. Consistent with the surface balances postulated to propose this theory, we provide an alternative approach to derive the natural boundary conditions.

Automated summary

The continuum theory presented in this study demonstrates the implications of considering general tractions developed on control volumes with surfaces lacking smoothness. These tractions are tailored to recover the Navier-Stokes-alpha beta equation and its thermodynamics. By postulating surface balances, an alternative approach to deriving natural boundary conditions is provided.