Turbulence development of a vertical natural convection boundary layer

The present study considers the development of a turbulent natural convection boundary layer (NCBL) adjacent to a vertical isothermal wall with periodic boundary conditions. Results obtained from direct numerical simulations show evidence that the turbulent flow has two distinct stages depending on Grashof (or Reynolds) number. By investigating the turbulent statistics and energy spectra, it is shown that the near-wall region at relatively low Grashof number remains laminar while the outer boundary layer is fully turbulent (classical turbulent regime); whereas at higher Grashof number, the near wall is shown to become turbulent, indicating onset of an ultimate regime (Kraichnan 1962; Grossmann & Lohse 2011). It is found that the near-wall turbulence in the classical turbulent regime is predominantly sustained by the pressure transport from the outer shear layer; while in the ultimate turbulent regime the near-wall turbulence is generated and sustained locally via shear production. The transition from the classical to the ultimate turbulent regime is also clearly discerned using scaling and momentum balance arguments and by the appearance of near-wall streaks with constant spanwise spacing.