arXiv subjects

Lohit Kayal

Publications and source records attributed to Lohit Kayal.

4 recordsLinked to original sources

arXiv2024

Focusing of concentric free-surface waves

Gravito-capillary waves at free-surfaces are ubiquitous in several natural and industrial processes involving quiescent liquid pools bounded by cylindrical walls. These waves emanate from the relaxation of initial interface distortions, which often take the form of a cavity (depression) centred on the symmetry axis of the container. These surface waves reflect from the container walls leading to a radially inward propagating wave-train converging (focussing) onto the symmetry axis. Under the inviscid approximation and for sufficiently shallow cavities, the relaxation is well-described by the linearised potential-flow equations. Naturally, adding viscosity to such a system introduces viscous dissipation that enervates energy and dampens the oscillations at the symmetry axis. However, for viscous liquids and deeper cavities, these equations are qualitatively inaccurate. In this study, we elucidate a modal approach to study the initial-value problem for concentric gravito-capillary waves generated on a free-surface for inviscid as well as viscous liquids. For a sufficiently deep cavity, the inward focusing of waves results in large interfacial oscillations at the axis, necessitating a second-order nonlinear theory. We demonstrate that this theory effectively models the interfacial behavior and highlights the crucial role of nonlinearity near the symmetry axis. Contrary to expectations, the addition of slight viscosity further intensifies the oscillations at the symmetry axis. This finding underscores the limitations of the potential flow model and suggests avenues for more accurate modelling of such complex free-surface flows.

physics.flu-dyn↗

arXiv2023

Standing waves and jets on a sessile, incompressible bubble

We show numerically that large amplitude, \textit{shape deformations}, imposed on a spherical-cap, incompressible, sessile gas bubble pinned on a rigid wall can produce a sharp, wall-directed jet. For such a bubble filled with a permanent gas, the temporal spectrum for surface-tension driven, linearised perturbations has been studied recently in \citet{ding2022oscillations} in the potential flow limit. We reformulate this as an initial-value problem. Linear theory is validated by distorting the shape of the pinned, spherical cap employing eigenmodes obtained theoretically, as the initial perturbation for our numerical simulations. It is seen that linearised predictions show good agreement with nonlinear simulations at small distortion amplitude producing standing waves. Beyond the linear regime, we observe the formation of a dimple followed by a slender, wall-directed jet analogous to similar jets observed in other geometries from collapsing wave troughs\cite{farsoiya2017axisymmetric,kayal2022dimples}. This jet can eject with an instantaneous velocity exceeding nearly twenty times that predicted by linear theory. By projecting the shape of the bubble surface around the time instant of jet ejection, into the linearised eigenspectrum we show that the jet ejection coincides with the nonlinear spreading of energy into a large number of eigenmodes. We demonstrate that the velocity-field associated with the dimple plays a crucial role in evolving it into a jet and without which, the jet does not form. Our inferences also complement well-known results of \citet{naude1961mechanism} and \citet{plesset1971collapse} demonstrating that wall-directed jets can be generated from \textit{volume preserving}, shape deformation of a pinned bubble.

physics.flu-dyn↗

arXiv2023

Jet from a very large, surface-gravity wave

We demonstrate that gravity acting alone at large length scales, can produce a jet from a large amplitude, axisymmetric surface deformation imposed on a quiescent, deep pool of liquid. Mechanistically, the jet owes it origin to the focussing of a concentric, surface wave towards the axis of symmetry, quite analogous to such focussing of capillary waves and resultant jet formation, observed during bubble collapse at small scales. A weakly non linear theory based on the method of multiple scales and the potential flow limit, is presented for a modal (single mode) initial condition representing the solution to the primary Cauchy Poisson problem. A pair of novel, coupled, amplitude equations are derived governing the modulation of the primary mode. For moderate values of the perturbation parameter epsilon (a measure of the initial perturbation amplitude), our second order theory captures the overshoot (incipient jet) at the axis of symmetry quite well, demonstrating good agreement with numerical simulation of the incompressible, Euler's equation with gravity (Popinet 2014) and no surface tension. Expectedly, our theory becomes inaccurate as epsilon approaches unity. In this strongly nonlinear regime, slender jets form with surface accelerations exceeding gravity by three orders of magnitude. In this inertial regime, the jets observed in our simulations show excellent agreement with the inertial, self-similar, analytical solution by Longuet-Higgins (1983). The physical mechanism of axisymmetric jet formation is explained based on mass conservation arguments. We demonstrate that the underlying wave focussing mechanism, may be understood in terms of radially inward motion of nodal points of a linearised, axisymmetric, standing wave.

physics.flu-dyn↗

arXiv2022

Dimple, jets and self-similarity in nonlinear capillary waves

Numerical studies of dimple and jet formation from a collapsing cavity often model the initial cavity shape as a truncated sphere, mimicking a bursting bubble. In this study, we present a minimal model containing only nonlinear inertial and capillary forces, which produces dimples and jets from a collapsing, capillary wave trough. The trough develops from an initial perturbation, chosen to be an eigen-mode to the linearised problem.We explain the physical mechanism of dimple formation and demonstrate that, for moderate steepness, the sharp dimple seen in simulations is well captured by the weakly nonlinear theory developed here. For steepness >> 1 the regime is strongly nonlinear spreading surface energy into many modes and the precursor dimple now develops into a sharply rising jet. Here, simulations reveal a novel localised window (in space and time) where the jet evolves self-similarly following inviscid Keller & Miksis (1983) scales. We develop an analogy of this regime to a self-similar solution of the first kind, for linearised, capillary waves. Our first principles study demonstrates that at sufficiently small scales, dimples and jets form due to radial focussing of capillary waves requiring (nonlinear) inertial and capillary contributions, sans viscous or gravitational interventions.

physics.flu-dyn↗