An inner-scaled, shear stress-driven flow is considered as a model of independent
near-wall turbulence as Reτ → ∞. In this limit, the model is applicable to the nearwall region and the lower part of the logarithmic layer of various parallel shear flows,
including turbulent Couette flow, Poiseuille flow and Hagen-Poiseuille flow. The model
is validated against damped Couette flow and there is excellent agreement between the
velocity statistics and spectra for y
+ < 40. A near-wall flow domain of similar size to
the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen
invariant solutions are computed, the first discovered for this flow configuration. Through
continuation in the spanwise width L
+
z
, the bifurcation behaviour of the solutions over
the domain size is investigated. The physical properties of the solutions are explored
through phase portraits, including the energy input and dissipation plane, and streak,
roll and wave energy space. Finally, a Reynolds number is defined in outer units and the
high-Re asymptotic behaviour of the equilibria is studied. Three lower branch solutions
are found to scale consistently with vortex-wave interaction (VWI) theory, with wave
forcing localising around the critical layer.