arXiv subjects

Ratul Dasgupta

Publications and source records attributed to Ratul Dasgupta.

At least 19 recordsLinked to original sources

arXiv2026

A windy sea surface with Stokes waves

Predicting the transition of wind-forced, gravito-capillary surface waves from smooth to corrugated states remains a longstanding problem in nonlinear surface wave mechanics. Solving driven-dissipative, nonlinear potential flow equations we map these waves ($4-13$ cm) onto a Reynolds number -- wave energy phase-space. We identify a transition band separating smooth from corrugated wave states - the wave steepness exhibits a non-monotonic dependence on Reynolds number within this. Subharmonic (in)stability analysis reveals that the fastest-growing mode intensifies corrugations on alternate faces of the carrier wave. Our results offer insights into parasitic capillary wave formation on steep carrier waves and are of interest to ocean remote-sensing.

physics.flu-dyn↗

arXiv2026

Interfacial waves from pressure forcing: revisiting classical theories from an IVP perspective

A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem formulation within the linearised, inviscid, potential flow framework. The steady-state interface exhibits short capillary waves ahead of the forcing and long gravity waves behind it, arising from an asymmetric cancellation of Fourier components in the far field. The time-dependent part of the solution, decaying algebraically with time, plays a crucial role in this mechanism. This contrasts with classical steady approaches, which require additional conditions to select a unique solution. We extend this approach to a two-fluid interface and validate the predictions against nonlinear simulations.

physics.flu-dyn↗

arXiv2025

Free oscillations of a standing surface wave and its mechanical analogue

We present an analogy between natural oscillations of the standing wave type on a pool of liquid with an interface and a mechanical oscillator model. It is shown that the equations of motion governing both systems have qualitatively similar solutions - trivial as well as time-periodic with finite amplitude. The time-periodic solutions can be linearly unstable in both cases depending on the oscillation amplitude, thereby leading to interesting dynamics. Linear stability results of both systems are discussed in detail; a novel Mathieu-like equation is derived for the stability of the standing wave to a super-harmonic perturbation. This is obtained through a much simpler approach that yields linear stability results while also reinforcing the analogy. Analytical predictions are compared against numerical solutions to the full nonlinear governing equations for both systems. A good match is obtained in most cases with theory; mismatches are further analysed and the limitations of this analogy are also pointed out.

physics.flu-dyn↗

arXiv2025

Waves in a shear flow: transition between the KH, Holmboe and Miles instability

We investigate shear driven wave generation at the interface between two immiscible fluids, using an exponential velocity profile with a sharp density interface representing stable stratification. At low Froude and high Bond numbers, conditions relevant to geophysical and astrophysical flows, we identify a novel transition in the fastest growing mode: from Kelvin Helmholtz (KH) instability at high density ratio (delta = 0.9), to Holmboe (H) instability as delta approaches 0.5, and ultimately to the Miles (1957) critical layer instability as delta approaches 0.001, representative of the air water system. Remarkably, the Miles mode, characterized by a sharp jump in inviscid Reynolds stress (tau) at the critical layer, persists up to delta = 0.01, i.e., ten times the air water value. As delta increases, the vertical variation of tau undergoes a qualitative change, from a sharp jump at the critical layer for delta much less than 1 to a smooth transition through it for delta greater than or equal to 0.5. A theoretical explanation is provided. In the moderate to high density ratio regime, comparison with a piecewise-linear (PL) velocity profile confirms the presence of both H and KH instabilities in the exponential profile. Nonlinear simulations of the incompressible Euler equations with gravity and surface tension show excellent agreement with linear theory for delta = 0.01 up to five wave periods. At delta = 0.1, waves saturate into finite-amplitude structures with capillary ripples, while at delta = 0.5, the waves develop sheared cusps and emit spume, resembling asymmetric Holmboe waves observed experimentally. At delta = 0.9, the waves rapidly evolve into classic KH spirals. Comparisons with the PL profile highlight the role of background curvature and the critical layer. This work presents, for the first time, all three canonical instabilities within a single background state.

physics.flu-dyn↗

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↗

arXiv2023

Surface and internal gravity waves on a viscous liquid layer: initial-value problems

We study a class of initial value problems (IVPs) involving perturbations on a density stratified, quiescent, viscous liquid layer with a free-surface. The geometry is a two-dimensional, rectangular configuration taking into account surface-tension and gravity. Linearised predictions are obtained by solving the IVP analytically for free-surface and vortical initial perturbations. The viscous spectrum comprises a discrete spectrum of propagating surface and internal modes and damped vorticity modes. Continuous spectra may also exist depending on whether the domain is bounded or unbounded. It is shown that independent of stratification, the vorticity modes in the spectrum play an important role. For an unstratified pool of a highly viscous liquid, the vorticity modes are found to make a large contribution to the temporal evolution of the transient vorticity layer, at the free-surface. It is demonstrated that the temporal evolution of localised vortical perturbations sufficiently deep inside the pool, cannot be captured by surface modes (capillarity-gravity modes) and require contributions from the vorticity modes. The free-surface signature of a deep, localised, vortical perturbation is however found to be negligible. On a stratified pool of viscous liquid, such vortical initial perturbations are shown to have significant projections on vorticity as well as internal gravity modes. In the infinite depth limit of an unstratified pool, the contribution from the continuous spectrum vorticity modes is analysed vis-a-vis that from their finite depth, discrete spectrum counterparts. Several analytical predictions are compared against direct numerical simulations (DNS) obtaining excellent agreement. Our results extend classical ones due to Lamb (1932), Yih (1960), Prosperetti (1976), Prosperetti and Cortelezzi (1982) and receive support from nonlinear simulations.

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↗

arXiv2022

Dynamic stabilisation of Rayleigh-Plateau modes on a liquid cylinder

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 generalises the Mathieu equation governing Faraday waves on a cylinder derived earlier in Patankar et al. (2018), is non-local in time and represents the cylindrical analogue of its Cartesian counterpart (Beyer & Friedrich 1995). 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 demonstrates RP mode stabilisation upto several hundred forcing cycles and is in excellent agreement with numerical simulations of the incompressible, Navier-Stokes equations.

physics.flu-dyn↗

arXiv2019

Geometry-controlled Failure Mechanisms of Amorphous Solids on the Nanoscale

Amorphous solids, confined on the nano-scale, exhibit a wealth of novel phenomena yet to be explored. In particular, the response of such solids to a mechanical load is not well understood and, as has been demonstrated experimentally, it differs strongly from bulk samples made of the same materials. Failure patterns and mechanisms are strongly affected by the geometry of the confinement and the interplay between interfacial effects in the sample and the time scale, imposed by an external mechanical field. Here, we present the mechanism of cavity formation in a confined model glass, subjected to expansion with a constant strain rate. This system is studied for varying geometric aspect ratio and sample size. Our results show that for a given temperature and straining condition, the sample shows cavitation when the aspect ratio reaches a critical value and below this aspect ratio the sample breaks by forming a neck. The critical aspect ratio is associated with a critical curvature of the neck that depends on strain rate and temperature. If this critical curvature is exceeded, the free energy of the system is minimized by the formation of a cavity. Our study reveals a novel mechanism of cavity formation on the nanoscale. This is probably a generic mechanism for material's failure in small confined systems under mechanical load.

cond-mat.stat-mech↗

arXiv2013

Atomistic Simulations of Magnetic Amorphous Solids: Magnetostriction, Barkhausen noise and novel singularities

We present results of atomistic simulations of a new model of a magnetic amorphous solid subjected to external mechanical strains and magnetic fields. The model employed offers new perspectives on important effects like Barkhausen noise and magnetostriction. It is shown that the plastic response in such systems exhibit singularities characterized by unexpected exponents requiring careful theoretical reasoning. The spatial structure of the plastic events requires a new coarse grained elasto-magnetic theory which is provided here.

cond-mat.soft↗

arXiv2013

Shear localization in 3-Dimensional Amorphous Solids

In this paper we extend the recent theory of shear-localization in 2-dimensional amorphous solids to 3-D. In 2-D the fundamental instability of shear-localization is related to the appearance of a line of displacement quadrupoles, that makes an angle of 45 degrees with the principal stress axis. In 3-D the fundamental plastic instability is also explained by the formation of a lattice of anisotropic elastic inclusions. In the case of pure external shear stress, we demonstrate that this is a 2-dimensional triangular lattice of similar elementary events. It is shown that this lattice is arranged on a plane, that, similarly to the 2-D case, makes an angle of 45 degrees with respect to the principal stress axis. This solution is energetically favorable only if the external strain exceeds a yield-strain value, which is determined by the strain parameters of the elementary events and the Poisson ratio. The predictions of the theory are compared to numerical simulations and very good agreement is observed.

cond-mat.soft↗

arXiv2013

Micro-alloying and the Toughness of Glasses: Modeling with Pinned Particles

The usefulness of glasses, and particularly of metallic glasses, in technological applications is often limited by their toughness, which is defined as the area under the stress vs. strain curve before plastic yielding. Recently toughness was found to increase significantly by the addition of small concentrations of foreign atoms that act as pinning centers. We model this phenomenon at zero temperature and quasi-static straining with randomly positioned particles that participate in the elastic deformation but are pinned in the non-affine return to mechanical equilibrium. We find a very strong effect on toughness via the increase of both the shear modulus and the yield stress as a function of the density of pinned particles. Understanding the results calls for analyzing separately the elastic, or "Born term" and the contributions of the "excess modes" that result from glassy disorder. Finally we present a scaling theory that collapses the data on one universal curve as a function of rescaled variables.

cond-mat.mtrl-sci↗

arXiv2012

The Yield-Strain in Shear Banding Amorphous Solids

In recent research it was found that the fundamental shear-localizing instability of amorphous solids under external strain, which eventually results in a shear band and failure, consists of a highly correlated array of Eshelby quadrupoles all having the same orientation and some density $ρ$. In this paper we calculate analytically the energy $E(ρ,γ)$ associated with such highly correlated structures as a function of the density $ρ$ and the external strain $γ$. We show that for strains smaller than a characteristic strain $γ_Y$ the total strain energy initially increases as the quadrupole density increases, but that for strains larger than $γ_Y$ the energy monotonically decreases with quadrupole density. We identify $γ_Y$ as the yield strain. Its value, derived from values of the qudrupole strength based on the atomistic model, agrees with that from the computed stress-strain curves and broadly with experimental results.

cond-mat.soft↗

arXiv2012

Microscopic Mechanism of Shear Bands in Amorphous Solids

The fundamental instability responsible for the shear localization which results in shear bands in amorphous solids remains unknown despite enormous amount of research, both experimental and theoretical. As this is the main mechanism for the failure of metallic glasses, understanding the instability is invaluable in finding how to stabilize such materials against the tendency to shear localize. In this Letter we explain the mechanism for shear localization under shear, which is the appearance of highly correlated lines of Eshelby-like quadrupolar singularities which organize the non-affine plastic flow of the amorphous solid into a shear band. We prove analytically that such highly correlated solutions in which $\C N$ quadrupoles are aligned with equal orientations are minimum energy states when the strain is high enough. The line lies at 45 degrees to the compressive stress.

cond-mat.soft↗

arXiv2012

Derivation of the Johnson-Samwer $T^{(2/3)}$ Temperature Dependence of the Yield Strain in Metallic Glasses

Metallic Glasses are prone to fail mechanically via a shear-banding instability. In a remarkable paper Johnson and Samwer demonstrated that this failure enjoys a high degree of universality in the sense that a large group of metallic glasses appears to possess a yield-strain that decreases with temperature following a $-T^{2/3}$ law up to logarithmic corrections. In this Letter we offer a theoretical derivation of this law. We show that our formula fits very well simulational data on typical amorphous solids.

cond-mat.soft↗

arXiv2011

Universality of the Plastic Instability in Strained Amorphous Solids

By comparing the response to external strains in metallic glasses and in Lenard-Jones glasses we find a quantitative universality of the fundamental plastic instabilities in the athermal, quasistatic limit. Microscopically these two types of glasses are as different as one can imagine, the latter being determined by binary interactions, whereas the former by multiple interactions due to the effect of the electron gas that cannot be disregarded. In spite of this enormous difference the plastic instability is the same saddle-node bifurcation. As a result the statistics of stress and energy drops in the elasto-plastic steady state are universal, sharing the same system-size exponents.

cond-mat.soft↗