  We study the evolution of velocity fluctuations due to an isolated
spatio-temporal impulse using the linearized Navier-Stokes equations. The
impulse is introduced as an external body force in incompressible channel flow
at $Re_\tau=10000$. Velocity fluctuations are defined about the turbulent mean
velocity profile. A turbulent eddy viscosity is added to the equations to fix
the mean velocity as an exact solution, which also serves to model the
dissipative effects of the background turbulence on large-scale fluctuations.
An impulsive body force produces flowfields that evolve into coherent
structures containing long streamwise velocity streaks that are flanked by
quasi-streamwise vortices; some of these impulses produce hairpin vortices. As
these vortex-streak structures evolve, they grow in size to be nominally
self-similar geometrically with an aspect ratio (streamwise to wall-normal) of
approximately $10$, while their kinetic energy density decays monotonically.
The topology of the vortex-streak structures is not sensitive to the location
of the impulse, but is dependent on the direction of the impulsive body force.
All of these vortex-streak structures are attached to the wall, and their
Reynolds stresses collapse when scaled by distance from the wall, consistent
with Townsend's attached eddy hypothesis.
