TY - JOUR

T1 - Interfacial capillary waves in the presence of electric fields

AU - Grandison, Scott

AU - Papageorgiou, Demetrios T.

AU - Vanden-Broeck, Jean-Marc

PY - 2007

Y1 - 2007

N2 - Large amplitude capillary waves on an inviscid, incompressible fluid layer of density ?1 bounded by a second inviscid, incompressible
fluid of density ?2 are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed
configuration. Periodic travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field
is studied. The solutions extend the results of Papageorgiou and Vanden-Broeck [D.T. Papageorgiou, J.-M. Vanden-Broeck, Largeamplitude
capillary waves in electrified fluid sheets, J. Fluid Mech. 508 (2004) 71–88; D.T. Papageorgiou, J.-M. Vanden-Broeck,
Antisymmetric capillary waves in electrified fluid sheets, Eur. J. Appl. Math. 16 (2004) 609–623] where the case of ?2 = 0 was
treated. Fully nonlinear solutions are computed using boundary integral equation methods. It is shown that there are both symmetric
and antisymmetric waves and their characteristics are explored and compared. When there is a jump in the undisturbed horizontal
velocities, the flow is susceptible to Kelvin–Helmholtz instability. It is shown analytically in the linear regime, that even in the
absence of surface tension, the flow is stabilized by sufficiently large electric fields. In such situations two wave speeds are possible
for given electric fields and we construct these branches numerically when the amplitudes are not infinitesimal, both in the absence
and presence of surface tension.

AB - Large amplitude capillary waves on an inviscid, incompressible fluid layer of density ?1 bounded by a second inviscid, incompressible
fluid of density ?2 are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed
configuration. Periodic travelling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field
is studied. The solutions extend the results of Papageorgiou and Vanden-Broeck [D.T. Papageorgiou, J.-M. Vanden-Broeck, Largeamplitude
capillary waves in electrified fluid sheets, J. Fluid Mech. 508 (2004) 71–88; D.T. Papageorgiou, J.-M. Vanden-Broeck,
Antisymmetric capillary waves in electrified fluid sheets, Eur. J. Appl. Math. 16 (2004) 609–623] where the case of ?2 = 0 was
treated. Fully nonlinear solutions are computed using boundary integral equation methods. It is shown that there are both symmetric
and antisymmetric waves and their characteristics are explored and compared. When there is a jump in the undisturbed horizontal
velocities, the flow is susceptible to Kelvin–Helmholtz instability. It is shown analytically in the linear regime, that even in the
absence of surface tension, the flow is stabilized by sufficiently large electric fields. In such situations two wave speeds are possible
for given electric fields and we construct these branches numerically when the amplitudes are not infinitesimal, both in the absence
and presence of surface tension.

U2 - 10.1016/j.euromechflu.2006.06.005

DO - 10.1016/j.euromechflu.2006.06.005

M3 - Article

VL - 26

SP - 404

EP - 421

JO - European Journal of Mechanics - B/Fluids

JF - European Journal of Mechanics - B/Fluids

SN - 0997-7546

IS - 3

ER -