  We derive necessary conditions that traveling wave solutions of the
Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow
geometries. Some conditions are exact and must hold for any traveling wave
solution irrespective of the Reynolds number ($Re$). Other conditions are
asymptotic in the limit $Re\to\infty$. The exact conditions are likely to be
useful tools in the study of transitional structures. For the pipe flow
geometry, we give computations up to $Re=100000$ showing the connection of our
asymptotic conditions to critical layers that accompany vortex structures at
high $Re$.
