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In this paper, we have found two new nonlinear travelling wave solutions in pipe flows. We investigate possible asymptotic structures at large Reynolds number
when wavenumber is independent of
and identify numerically calculated solutions as finite
realizations of a nonlinear viscous core (NVC) state that collapses towards the pipe centre with increasing
at a rate
. We also identify previous numerically calculated states as finite
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
, though this remains to be confirmed numerically.
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