  A new theory of coherent structure in wall turbulence is presented.
  The theory is the first to predict packets of hairpin vortices and other
structure in turbulence, and their dynamics, based on an analysis of the
Navier-Stokes equations, under an assumption of a turbulent mean profile. The
assumption of the turbulent mean acts as a restriction on the class of possible
structures. It is shown that the coherent structure is a manifestation of
essentially low-dimensional flow dynamics, arising from a critical layer
mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech,
658, 2010), complex coherent structure is recreated from minimal superpositions
of response modes predicted by the analysis, which take the form of
radially-varying travelling waves. By way of example, simple combinations of
these modes are offered that predicts hairpins and modulated hairpin packets.
  The phase interaction also predicts important skewness and correlation
results known in the literature.
  It is also shown that the very large scale motions act to organise
hairpin-like structures such that they co-locate with areas of low streamwise
momentum, by a mechanism of locally varying the shear profile.
  The relationship between Taylor's hypothesis and coherence is discussed and
both are shown to be the consequence of the localisation of the response modes
around the critical layer.
  A pleasing link is made to the classical laminar inviscid theory, whereby the
essential mechanism underlying the hairpin vortex is captured by two obliquely
interacting Kelvin-Stuart (cat's eye) vortices. Evidence for the theory is
presented based on comparison to observations of structure reported in the
experimental, transitional flow and turbulent flow numerical simulation
literature.
