Uniform shear flow: the state space of near-wall turbulence as Re_τ tends to ∞

There is a growing body of evidence that self-similar coherent structures in the form of Townsend's attached eddies exist. Each of these structures bears a self-sustaining process remarkably similar to that of the near-wall region. To model this universal feature of wall-bounded turbulence, we have designed a shear flow model of near-wall turbulence applicable to various parallel shear flows as Re_τ tends to ∞. As a first step, we consider the minimal unit of near-wall turbulence: the governing equations are rescaled in inner units, while a constant shear stress is imposed as the top boundary condition of the domain located at y⁺≈90. The model is validated against Couette flow, the near-wall region of which is independent of Reynolds number, and there is excellent agreement between velocity statistics & spectra for y⁺<60. Thirteen relative equilibrium solutions are presented, the first discovered for this flow configuration. Through continuation in the spanwise width L_z⁺, the bifurcation behaviour of the equilibria over domain size is examined. The physical properties of the equilibria are also explored through state space projection. Finally, the asymptotic behaviour of the equilibria is studied and three lower-branch solutions are found to scale consistently with VWI theory.