Granular and fluid washboards

• Published in: Journal of fluid mechanics Vol. 692; pp. 446 - 463
• Main Authors: Hewitt, I. J., Balmforth, N. J., McElwaine, J. N.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.02.2012
• Subjects: Computational fluid dynamics; Cross-disciplinary physics: materials science; rheology; Deformation; Exact sciences and technology; Fluid flow; Fluid mechanics; Fluid-structure interaction; Fluids; Fundamental areas of phenomenology (including applications); Granular solids; Instability; Material form; Oscillations; Physical properties; Physics; Rheology; Solid mechanics; Stability; Structural and continuum mechanics; Substrates; Thresholds; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Viscosity; viscoplastic fluids; fluid-structure interaction; granular media; Fluid structure interaction; Viscoelastic material; Experimental study; Test facility; Granular material; Inclined plate
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2011.523

We investigate the dynamics of an object towed over the surface of an initially flat, deformable layer. Using a combination of simple laboratory experiments and a theoretical model, we demonstrate that an inclined plate, pivoted so as to move up and down, may be towed steadily over a substrate at low speed, but become unstable to vertical oscillations above a threshold speed. That threshold depends upon the weight of the plate and the physical properties of the substrate, but arises whether the substrate is a viscous fluid, a viscoplastic fluid, or a granular medium. For the latter two materials, the unstable oscillations imprint a permanent rippled pattern on the layer, suggesting that the phenomenon of the ‘washboard road’ can arise from the passage of a single vehicle (i.e. the absolute instability of a flat bed). We argue that the mechanism behind the instability originates from the mound of material that is pushed forward ahead of the object: the extent of the mound determines the resultant force, whereas its growth is controlled by the object’s height relative to the undisturbed surface, allowing for an unstable coupling between the vertical motion and the substrate deformation.