Hewitt, I. J.; Balmforth, N. J.; Mcelwaine, J. N. Granular and fluid washboards. (English) Zbl 1250.76177 J. Fluid Mech. 692, 446-463 (2012). Summary: 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. Cited in 1 Document MSC: 76T25 Granular flows 76A05 Non-Newtonian fluids 76-05 Experimental work for problems pertaining to fluid mechanics Keywords:fluid-structure interaction; viscoplastic fluids; granular media PDFBibTeX XMLCite \textit{I. J. Hewitt} et al., J. Fluid Mech. 692, 446--463 (2012; Zbl 1250.76177) Full Text: DOI Link References: [1] DOI: 10.1038/427029a · doi:10.1038/427029a [2] DOI: 10.1016/S0378-4371(01)00425-3 · Zbl 0999.74105 · doi:10.1016/S0378-4371(01)00425-3 [3] DOI: 10.1103/PhysRevE.79.061308 · doi:10.1103/PhysRevE.79.061308 [4] Bird, Rev. Chem. Engng 1 pp 1– (1983) · doi:10.1515/revce-1983-0102 [5] DOI: 10.1103/PhysRevLett.99.068003 · doi:10.1103/PhysRevLett.99.068003 [6] DOI: 10.1017/S0022112005006373 · Zbl 1081.76514 · doi:10.1017/S0022112005006373 [7] DOI: 10.1017/S0022112010005057 · Zbl 1225.76016 · doi:10.1017/S0022112010005057 [8] DOI: 10.1007/s10665-008-9226-2 · Zbl 1160.76004 · doi:10.1007/s10665-008-9226-2 [9] DOI: 10.1103/PhysRevE.84.051302 · doi:10.1103/PhysRevE.84.051302 [10] DOI: 10.1002/1099-0526(200007/08)5:6<51::AID-CPLX11>3.0.CO;2-B · doi:10.1002/1099-0526(200007/08)5:6<51::AID-CPLX11>3.0.CO;2-B [11] DOI: 10.1038/scientificamerican0163-128 · doi:10.1038/scientificamerican0163-128 [12] DOI: 10.1103/PhysRevE.65.021303 · doi:10.1103/PhysRevE.65.021303 [13] Gassie, Intl Rail. J. 47 pp 31– (2007) [14] DOI: 10.1007/s003970100178 · doi:10.1007/s003970100178 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.