viscoussublayer

The viscous sublayer, or near-wall region, is the portion of a turbulent boundary layer immediately adjacent to a solid boundary where viscous forces dominate over turbulent fluctuations. In this layer the flow velocity increases roughly linearly with distance from the wall, and the shear stress is largely governed by molecular viscosity rather than Reynolds stresses. The characteristic relation is μ du/dy ≈ τw, where τw is the wall shear stress and μ is the dynamic viscosity.

The sublayer has a characteristic thickness determined by the balance of viscosity and the near-wall shear, commonly described in wall units. In dimensionless terms, y+ = uτ y / ν, with uτ = sqrt(τw/ρ) the friction velocity and ν the kinematic viscosity. The viscous sublayer typically extends to y+ ≈ 5, corresponding to a physical distance on the order of a fraction of a millimeter in air flows, depending on flow conditions. Beyond this region lies the buffer layer and the logarithmic (log-law) region, where turbulent stresses become more significant.

In practice, resolving the viscous sublayer is important for accurate prediction of wall-bounded flows. Direct numerical simulation and high-resolution turbulence models aim to capture this region; models that use wall functions approximate the near-wall behavior to avoid resolving the sublayer directly. Roughness, pressure gradients, and flow transitions can modify the thickness and structure of the sublayer, influencing skin-friction predictions and near-wall heat transfer. The viscous sublayer provides a fundamental reference frame for understanding near-wall dynamics in turbulent boundary layers.