In this paper, we have found two new nonlinear travelling wave solutions in pipe flows. We investigate possible asymptotic structures at large Reynolds number R when wavenumber is independent of R and identify numerically calculated solutions as finite R realizations of a nonlinear viscous core (NVC) state that collapses towards the pipe centre with increasing R at a rate R-1/4. We also identify previous numerically calculated states as finite R realizations of a vortex wave interacting (VWI) state with an asymptotic structure similar to the ones in channel flows studied earlier by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178-205). In addition, asymptotics suggests the possibility of a VWI state that collapses towards the pipe centre like R-1/6, though this remains to be confirmed numerically.
- nonlinear instability
- transition to turbulence