Closed bilayer membranes (vesicles) display a plethora of non-spherical shapes under equilibrium conditions, unlike drops and bubbles which are kept spherical by surface tension. Even more complex behaviour arises under applied flow. Intriguingly, a vesicle can adopt asymmetric shapes even under symmetric forcing such as uniaxial extensional flow. Narasimhan, Spann & Shaqfeh (J. Fluid Mech., vol. 750, 2014, pp. 144–190) explain the mechanism of this peculiar instability and trace its origin to the tension which develops in the area-incompressible membrane in response to the applied stress. The authors also show that this mechanism is relevant to the pearling of tubular vesicles. This study raises many questions, e.g. whether other soft particles with load-dependent tension such as capsules can undergo similar shape transformations.

The generation of discrete acoustic tones in the compressible flow around an aerofoil is addressed in this work by means of nonlinear numerical simulations and global stability analyses. The nonlinear simulations confirm the appearance of discrete tones in the acoustic spectrum and, for the chosen flow case, the global stability analyses of the mean-flow dynamics reveal that the linearized operator is stable. However, the flow response to incoming disturbances exhibits important transient growth effects that culminate in the onset of aeroacoustic feedback loops, involving instability processes on the suction- and pressure-surface boundary layers together with their cross-interaction by acoustic radiation at the trailing edge. The features of the aeroacoustic feedback loops and the appearance of discrete tones are then related to the features of the least-stable modes in the global spectrum: the spatial structure of the direct modes displays the coupled dynamics of hydrodynamic instabilities on the suction surface and in the near wake. Finally, different families of global modes will be identified and the dynamics that they represent will be discussed.

A novel type of surface roughness is deployed in a zero-pressure-gradient boundary layer with the goal of delaying the onset of laminar-to-turbulent transition for drag reduction purposes. This proof-of-concept experiment relies on forcing phase-triggered Tollmien–Schlichting (TS) waves across a range of initial amplitudes to produce amplified boundary-layer disturbances in a controlled and repeatable manner. Building on earlier work demonstrating attenuation of forced disturbances and delay of transition with spanwise arrays of discrete roughness and miniature vortex generators (MVGs), the present work seeks a roughness shape which might find success in a wider range of flows. Toward that end, streamwise-elongated humps are regularly spaced in the spanwise direction to form a wavy wall. By direct modulation of the mean flow, growth rates of the forced disturbances are increased or decreased, depending on the roughness configuration. Boundary-layer velocity measurements with hot-wire probes have been performed in a parametric study of the effects of roughness-field geometry and forcing amplitude on TS-wave growth and transition. The roughness field proves detrimental to passive flow control efforts in some configurations, while a reduction in the TS-wave amplitudes compared with the smooth-wall reference case is observed at other conditions. Substantial delays in the onset of transition are demonstrated when TS waves are forced with large amplitudes.

In this paper large-eddy simulations (LES) of forced stratified turbulence using two common subgrid scale (SGS) models, the Kraichnan and Smagorinsky models, are studied. As found in previous studies using regular and hyper-viscosity, vorticity contours show elongated horizontal motions, which are layered in the vertical direction, along with intermittent Kelvin–Helmholtz (KH) instabilities. Increased stratification causes the layer thickness to collapse towards the dissipation scale, ultimately suppressing these instabilities. The vertical energy spectra are relatively flat out to a local maximum, which varies with the buoyancy frequency $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}N$. The horizontal energy spectra depend on the grid spacing $\varDelta $; if the resolution is fine enough, the horizontal spectrum shows an approximately $-5/3$ slope along with a bump at the buoyancy wavenumber $k_b = N/u_{rms}$, where $u_{rms}$ is the root-mean-square (r.m.s.) velocity. Our results show that there is a critical value of the grid spacing $\varDelta $, below which dynamics of stratified turbulence are well-captured in LES. This critical $\varDelta $ depends on the buoyancy scale $L_b$ and varies with different SGS models: the Kraichnan model requires $\varDelta < 0.47 L_b$, while the Smagorinsky model requires $\varDelta < 0.17 L_b$. In other words, the Smagorinsky model is significantly more costly than the Kraichnan approach, as it requires three times the resolution to adequately capture stratified turbulence.

We provide empirical evidence that the eddy diffusivity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}D_{{t}\alpha }$ and the turbulent Schmidt number ${\mathit{Sc}}_{{t}\alpha }$ of species $\alpha $ ($\alpha =\mathrm{A}, \mathrm{B}$ or $\mathrm{R}$) change with a second-order chemical reaction ($\mathrm{A} + \mathrm{B} \rightarrow \mathrm{R}$). In this study, concentrations of the reactive species and axial velocity are simultaneously measured in a planar liquid jet. Reactant A is premixed into the jet flow and reactant B is premixed into the ambient flow. An optical fibre probe based on light absorption spectrometry is combined with I-type hot-film anemometry to simultaneously measure concentration and velocity in the reactive flow. The eddy diffusivities and the turbulent Schmidt numbers are estimated from the simultaneous measurement results. The results show that the chemical reaction increases ${\mathit{Sc}}_{t\mathrm{A}}$; ${\mathit{Sc}}_{t\mathrm{B}}$ is negative in the region where the mean concentration of reactant B decreases in the downstream direction, and is positive in the non-reactive flow in the entire region on the jet centreline. It is also shown that ${\mathit{Sc}}_{t\mathrm{R}}$ is positive in the upstream region whereas it is negative in the downstream region. The production terms of axial turbulent mass fluxes of reactant B and product R can produce axial turbulent mass fluxes opposite to the axial gradients of the mean concentrations. The changes in the production terms due to the chemical reaction result in the negative turbulent Schmidt number of these species. These results imply that the gradient diffusion model using a global constant turbulent Schmidt number poorly predicts turbulent mass fluxes in reactive flows.

Prosthetic heart valves have been widely used to replace diseased or defective native heart valves. Flow through bileaflet mechanical heart valves (BMHVs) have previously demonstrated complex phenomena in the vicinity of the valve owing to the presence of two rigid leaflets. This study aims to accurately capture the complex flow dynamics for pulsatile flow through a 23 mm St Jude Medical (SJM) Regent™ BMHV. The lattice-Boltzmann method (LBM) is used to simulate pulsatile flow through the valve with the inclusion of reverse leakage flow at very high spatiotemporal resolution that can capture fine details in the pulsatile BMHV flow field. For higher-Reynolds-number flows, this high spatiotemporal resolution captures features that have not been observed in previous coarse resolution studies. In addition, the simulations are able to capture with detail the features of leaflet closing and the asymmetric b-datum leakage jet during mid-diastole. Novel flow physics are visualized and discussed along with quantification of turbulent features of this flow, which is made possible by this parallelized numerical method.

We investigate the propagation of a premixed flame subject to thermal expansion through a narrow channel against a Poiseuille flow of large amplitude. This is the first study to consider the effect of a large-amplitude flow, characterised by a Péclet number of order one, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Pe}=O(1)$, on a variable-density premixed flame in the asymptotic limit of a narrow channel. It is also the first study on Taylor dispersion in the context of combustion. The relationship between the propagation speed and Péclet number is investigated, with the effect of large flame-front thickness $\epsilon $ and activation energy $\beta $ studied asymptotically in an appropriate distinguished limit. The premixed flame for $\epsilon \to \infty $, with $\mathit{Pe}=O(1)$, is found to be governed by the equation for a planar premixed flame with an effective diffusion coefficient. In this case the premixed flame can be considered to be in the Taylor regime of enhanced dispersion due to a parallel flow. The infinite activation energy limit $\beta \to \infty $ is taken to provide an analytical description of the propagation speed. Corresponding results are obtained for a premixed flame in the constant-density approximation. The asymptotic results are compared to numerical results obtained for selected values of $\epsilon $ and $\beta $ and for moderately large values of the Péclet number. Physical reasons for the differences in propagation speed between constant- and variable-density flames are discussed. Finally, the asymptotic results are shown to agree with those of previous studies performed in the limit $\mathit{Pe}\to 0$.

Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. The model is combined with Lagrangian time histories of the velocity gradient tensor extracted from direct numerical simulations (DNS) of turbulence to obtain simulated droplet evolutions. These are used to characterize the size, shape and orientation statistics of small droplets in turbulence. A critical capillary number is identified associated with unbounded growth of one or two of the droplet’s semi-axes. Exploiting analogies with dynamics of polymers in turbulence, the critical capillary number can be predicted based on the large deviation theory for the largest finite-time Lyapunov exponent quantifying the chaotic separation of particle trajectories. Also, for subcritical capillary numbers near the critical value, the theory enables predictions of the slope of the power-law tails of droplet size distributions in turbulence. For cases when the viscosities of droplet and outer fluid differ in a way that enables vorticity to decorrelate the shape from the straining directions, the large deviation formalism based on the stretching properties of the velocity gradient tensor loses validity and its predictions fail. Even considering the limitations of the assumed ellipsoidal droplet shape, the results highlight the complex coupling between droplet deformation, orientation and the local fluid velocity gradient tensor to be expected when small viscous drops interact with turbulent flows. The results also underscore the usefulness of large deviation theory to model these highly complex couplings and fluctuations in turbulence that result from time integrated effects of fluid deformations.

This paper uses measurements of surface heat transfer to study roughness-induced turbulent wedges in a hypersonic boundary layer on a blunt cylinder. A family of wedges was produced by changing the height of an isolated roughness element, providing conditions in the following range: fully effective tripping, for the largest element, with a turbulent wedge forming immediately downstream of the element; a long wake, in length several hundred times the boundary layer thickness, leading ultimately to transition; and retention of laminar flow, for the smallest element. With appropriate element size, a fully intermittent wedge formed, comprising a clear train of turbulent spots.

We investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

We consider the mechanics of coupled underwater-acoustic and surface-gravity waves generated by surface pressure disturbances in a slightly compressible fluid. We show that pressure changes on the ocean surface, localised in space and time, can induce appreciable underwater compression waves which are precursors of the surface gravity waves. Although the physical properties of acoustic-gravity waves have already been discussed in the literature, such dynamics was not investigated in previous studies. We derive new results for the underwater compression wave field and discuss the dynamics of its generation and propagation. This work could lead to the design of innovative alert systems for coastal flooding management.

The onset and the nature of dynamic instabilities experienced by the wake of a marine propeller set in oblique flow are investigated by means of detached eddy simulations. In particular, the destabilization process is inspected by a systematic comparison of the wake morphology of a propeller operating in pure axisymmetric flow and in drift with angle of 20°, under different loading conditions. The wake behaviour in oblique flow shows a markedly different character with respect to the axisymmetric condition: in the latter, the destabilization is triggered by an increasing interaction of the main vorticity confined in the tip vortex; whereas, in the former, the role of the secondary vorticity (oriented in the streamwise direction) as well as the hub vortex seems to be crucial. The features of the wake have been investigated by the $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\lambda _{2}$ criterion (Jeong & Hussain, J. Fluid Mech., vol. 285, 1995, pp. 69–94) and typical flow variables (pressure, velocity and vorticity), for both the averaged and instantaneous flow fields. Moreover, in order to further inspect the evolution of the vortical structures, as well as their interaction and destabilization, the spectra of the kinetic energy have been considered. This investigation aims to broaden the knowledge from previous works on the subject of rotor wake instabilities, focusing on the differences between an ideal (axisymmetric) and actual operating conditions occurring in typical engineering applications.

A new approach to the construction of exact solutions of unsteady equations for plane flows of an ideal incompressible fluid with a free boundary is proposed. It is demonstrated that the problem is significantly simplified and reduces to solving the Hopf equation if the acceleration on the free surface is equal to zero. Some examples of exact solutions are given.

We present experimental results focused on the hydraulic properties of free-surface flows of viscoplastic fluids. The objective is to investigate the possibility of predicting macroscopic flow properties on the base of conventional rheometrical characterization of the fluids. The experiments are performed in an inclined conveyor-belt channel allowing us to generate gravity-driven surges which remain stationary in the laboratory frame. Two different types of materials are studied: Kaolin slurries and Carbopol microgels. Global height–velocity relationships and local velocity profiles are measured in the uniform zone for different experimental conditions (slope angle, rheological parameters). These data are then compared to theoretical predictions based on the Herschel–Bulkley constitutive law and independent measurements of the rheological parameters. Great care has been devoted to the determination of experimental uncertainties, including those associated with the rheometrical characterization. For Kaolin, the experimental results show excellent agreement with theoretical predictions. With Carbopol, on the contrary, a systematic discrepancy between measured and theoretical flow heights is observed. The velocity profiles do nevertheless remain consistent with a Herschel–Bulkley rheology, and we show that all experimental data can be explained by increasing the rheological parameters (yield stress and consistency) by 10–20 % compared to the values measured in the rheometer. Potential interpretations for this discrepancy are discussed.

We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger’s group (Burkardt, Gunzburger & Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337–355) and transition matrix models introduced in fluid dynamics in Eckhardt’s group (Schneider, Eckhardt & Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam–Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron–Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.

The current work analyses the onset characteristics of Rayleigh–Bénard convection in confined two-dimensional two-layer systems. Owing to the interfacial interactions and the possibilities of convection onset in the individual layers, the two-layer systems typically exhibit diverse excitation modes. While the attributes of these modes range from the non-oscillatory mechanical/thermal couplings to the oscillatory standing/travelling waves, their regimes of occurrence are determined by the numerous system parameters and property ratios. In this regard, the current work aims at characterising their respective influence via methodical linear and fully nonlinear analyses, carried out on fluid systems that have been selected using the concept of balanced contrasts. Consequently, the occurrence of oscillatory modes is found to be associated with certain favourable fluid combinations and interfacial heights. The further branching of oscillatory modes into standing and travelling waves seems to additionally rely on the aspect ratio of the confined cavity. Specifically, the modulated travelling waves have been observed to occur (amidst standing wave modes) at discrete aspect ratios for which the onset of oscillatory convection happens at unequal fluid heights. This behaviour corresponds to the typical $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}m$:$n$ resonance where the critical wavenumbers of convection onset in the layers are dissimilar. Based on all of these observations, an attempt has been made in the present work to identify the oscillatory excitation modes with a reduced number of non-dimensional parameters.

Kinetic energy and reactive scalar spectra in turbulent premixed flames are studied from compressible three-dimensional direct numerical simulations (DNS) of a temporally evolving rectangular slot-jet premixed flame, a statistically one-dimensional configuration. The flames correspond to a lean premixed hydrogen–air mixture at an equivalence ratio of 0.7, preheated to 700 K and at 1 atm, and three DNS are considered with a fixed jet Reynolds number of 10 000 and a jet Damköhler number varying between 0.13 and 0.54. For the study of spectra, motivated by the need to account for density change, which can be locally strong in premixed flames, a new density-weighted definition for two-point velocity/scalar correlations is proposed. The density-weighted two-point correlation tensor retains the essential properties of its constant-density (incompressible) counterpart and recovers the density-weighted Reynolds stress tensor in the limit of zero separation. The density weighting also allows the derivation of balance equations for velocity and scalar spectrum functions in the wavenumber space that illuminate physics unique to combusting flows. Pressure–dilatation correlation is a source of kinetic energy at high wavenumbers and, analogously, reaction rate–scalar fluctuation correlation is a high-wavenumber source of scalar energy. These results are verified by the spectra constructed from the DNS data. The kinetic energy spectra show a distinct inertial range with a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}-5/3$ scaling followed by a ‘diffusive–reactive’ range at higher wavenumbers. The exponential drop-off in this range shows a distinct inflection in the vicinity of the wavenumber corresponding to a laminar flame thickness, $\delta _L$, and this is attributed to the contribution from the pressure–dilatation term in the energy balance in wavenumber space. Likewise, a clear spike in spectra of major reactant species (hydrogen) arising from the reaction-rate term is observed at wavenumbers close to $\delta _L$. It appears that in the inertial range classical scaling laws for the spectra involving the Kolmogorov scale are applicable, but in the high-wavenumber range where chemical reactions have a strong signature the laminar flame thickness produces a better collapse. It is suggested that a full scaling should perhaps involve the Kolmogorov scale, laminar flame thickness, Damköhler number and Karlovitz number.

The diffusion of a plume of dye in uniformly sheared turbulent flow in a water tunnel was investigated using simultaneous stereoscopic particle image velocimetry (SPIV) and planar laser-induced fluorescence (PLIF). Maps of the mean concentration and the turbulent concentration fluxes in planes normal to the plume axis were constructed, from which all components of the second-order turbulent diffusivity tensor were determined for the first time. Good agreement between the corresponding apparent and true diffusivities was observed. The turbulent diffusivity tensor was found to have strong off-diagonal components, whereas the streamwise component appeared to be counter-gradient. The different terms in the advection–diffusion equation were estimated from the measurements and their relative significance was discussed. All observed phenomena were explained by physical arguments and the results were compared to previous ones.

We present a theoretical investigation of the effects of low-frequency vibrations on the motion of two-dimensional droplets on heterogeneous substrates in the presence of gravity and substrate heterogeneities, both chemical and topographical. A combined analytical and numerical approach is undertaken, extending the work of Savva & Kalliadasis (J. Fluid Mech., vol. 725, 2013, pp. 462–491) on inclined heterogeneous substrates to include the effects of substrate vibrations. Via a matching procedure and under the quasi-static assumption, we obtain evolution equations for the moving fronts. These equations are then invoked in a wide variety of case studies. It is demonstrated that vertically vibrated horizontal ratcheted substrates can induce unidirectional motion. For inclined substrates, we focus on a number of qualitative aspects of the peculiar vibration-induced climbing of droplets reported in experiments by Brunet, Eggers & Deegan (Phys. Rev. Lett., vol. 99, 2007, art. 144501). We examine the effects of weak inertia on the dynamics, deduce analytical criteria for the uphill motion in the limit of weak gravitational and vibrational effects, and demonstrate that substrate heterogeneities may be utilised to enhance droplet transport.

A conducting drop suspended in a viscous dielectric and subjected to a uniform DC electric field deforms to a steady-state shape when the electric stress and the viscous stress balance. Beyond a critical electric capillary number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ca}$, which is the ratio of the electric to the capillary stress, a drop undergoes breakup. Although the steady-state deformation is independent of the viscosity ratio $\lambda $ of the drop and the medium phase, the breakup itself is dependent upon $\lambda $ and $\mathit{Ca}$. We perform a detailed experimental and numerical analysis of the axisymmetric shape prior to breakup (ASPB), which explains that there are three different kinds of ASPB modes: the formation of lobes, pointed ends and non-pointed ends. The axisymmetric shapes undergo transformation into the non-axisymmetric shape at breakup (NASB) before disintegrating. It is found that the lobes, pointed ends and non-pointed ends observed in ASPB give way to NASB modes of charged lobes disintegration, regular jets (which can undergo a whipping instability) and open jets, respectively. A detailed experimental and numerical analysis of the ASPB modes is conducted that explains the origin of the experimentally observed NASB modes. Several interesting features are reported for each of the three axisymmetric and non-axisymmetric modes when a drop undergoes breakup.