Narwhals in pipes

Recent years have seen significant progress in understanding flows of polymeric fluids in parallel shear flows. The identification of a novel linear instability by Shankar and colleagues [1] has led to the discovery of the three-dimensional 'narwhal' coherent states as the building blocks of purely elastic turbulence in channel flows [2]. However, whether similar dynamics emerge in other parallel shear geometries remains an open question.

Here, we report the discovery of stable, coherent nonlinear elastically sustained travelling-wave structures in viscoelastic pipe flow at vanishing Reynolds number (nearly zero inertia). In sufficiently long pipes, they localise into stable axisymmetric spatially localised wave packets along the flow direction. Remarkably, narwhal states in pipe flow are strictly two-dimensional, preserving full rotational symmetry about the pipe axis.

Fully three-dimensional simulations confirm that these two-dimensional states remain robust under 3D perturbations, indicating their relevance to realistic turbulent flows. Our results demonstrate the first persistent self-sustained elastic wave in a straight pipe. This finding highlights how flow geometry can fundamentally alter viscoelastic flow transitions, offering new insight into the mechanisms that sustain purely elastic turbulence.

[1] M. Khalid et al, J. Fluid Mech., 915, A43 (2021)

[2] M. Lellep, M. Linkmann, A. Morozov, PNAS, 121, e2318851121 (2024)