In:
Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 946 ( 2022-09-10)
Abstract:
We demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh–Plateau (RP) instability on a liquid cylinder by subjecting it to a radial oscillatory body force. Viscosity is found to play a crucial role in this stabilisation. Linear stability predictions are obtained via Floquet analysis demonstrating that RP unstable modes can be stabilised using radial forcing. We also solve the linearised, viscous initial-value problem for free-surface deformation obtaining an equation governing the amplitude of a three-dimensional Fourier mode. This equation generalizes the Mathieu equation governing Faraday waves on a cylinder derived earlier in Patankar et al. ( J. Fluid Mech. , vol. 857, 2018, pp. 80–110), is non-local in time and represents the cylindrical analogue of its Cartesian counterpart (Beyer & Friedrich, Phys. Rev. E, vol. 51, issue 2, 1995, p. 1162). The memory term in this equation is physically interpreted and it is shown that, for highly viscous fluids, its contribution can be sizeable. Predictions from the numerical solution to this equation demonstrate the predicted RP mode stabilisation and are in excellent agreement with simulations of the incompressible Navier–Stokes equations (up to the simulation time of several hundred forcing cycles).
Type of Medium:
Online Resource
ISSN:
0022-1120
,
1469-7645
DOI:
10.1017/jfm.2022.533
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2022
detail.hit.zdb_id:
1472346-3
detail.hit.zdb_id:
218334-1
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