Yuan-Nan Young

A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

The turbulent Rayleigh–Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitude hb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensiti...

On the miscible Rayleigh{Taylor instability: two and three dimensions

We investigate the miscible Rayleigh{Taylor (RT) instability in both two and three dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We rst consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: we identify three distinct evolutionary phases in this development, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed dierences between two- and three-dimensional RT instability; the analysis also leads us to concentrate on the RT models which (i) work equally well for both laminar and turbulent flows, and (ii) do not depend on turbulent scaling within the mixing layer between fluids. These candidate RT models are based on point sources within bubbles (or plumes) and their interaction with each other (or the background flow). With this motivation, we examine the evolution of single plumes, and relate our numerical results (for single plumes) to a simple analytical model for plume evolution.

On the C/O Enrichment of Nova Ejecta

Using the results of recent work in shear instabilities in stratified fluids, we show that the resonant interaction between large-scale flows in the accreted H/He envelope of white dwarf stars and interfacial gravity waves can mix the stars envelope with the white dwarfs surface material, leading to the enhancement of the envelopes C/O abundance to levels required by extant models for nova outbursts.

Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit. The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure. The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender threads formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant.

Dynamics of the Primary Cilium in Shear Flow

In this work, the equilibrium shape and dynamics of a primary cilium under flow are investigated by using both theoretical modeling and experiment. The cilium is modeled as an elastic beam that may undergo large deflection due to the hydrodynamic load. Equilibrium results show that the anchoring effects of the basal body on the cilium axoneme behave as a nonlinear rotational spring. Details of the rotational spring are elucidated by coupling the elastic beam with an elastic shell. We further study the dynamics of cilium under shear flow with the cilium base angle determined from the nonlinear rotational spring, and obtain good agreement in cilium bending and relaxing dynamics when comparing between modeling and experimental results. These results potentially shed light on the physics underlying the mechanosensitive ion channel transport through the ciliary membrane.

Stratified Kolmogorov flow

In this study we investigate the Kolmogorov flow (a shear flow with a sinusoidal velocity profile) in a weakly stratified, two-dimensional fluid. We derive amplitude equations for this system in the neighbourhood of the initial bifurcation to instability for both low and high Peclet numbers (strong and weak thermal diffusion, respectively). We solve amplitude equations numerically and find that, for low Peclet number, the stratification halts the cascade of energy from small to large scales at an intermediate wavenumber. For high Peclet number, we discover diffusively spreading, thermal boundary layers in which the stratification temporarily impedes, but does not saturate, the growth of the instability; the instability eventually mixes the temperature inside the boundary layers, so releasing itself from the stabilizing stratification there, and thereby grows more quickly. We solve the governing fluid equations numerically to compare with the asymptotic results, and to extend the exploration well beyond onset. We find that the arrest of the inverse cascade by stratification is a robust feature of the system, occurring at higher Reynolds, Richards and Peclet numbers – the flow patterns are invariably smaller than the domain size. At higher Peclet number, though the system creates slender regions in which the temperature gradient is concentrated within a more homogeneous background, there are no signs of the horizontally mixed layers separated by diffusive interfaces familiar from doubly diffusive systems.

Flash code: studying astrophysical thermonuclear flashes

The Center for Astrophysical Thermonuclear Flashes is constructing a new generation of codes designed to study runaway thermonuclear burning on the surface or in the interior of evolved compact stars. The center has completed the first version of Flash, Flash-1, which addresses various astrophysics problems. Flash-1 represents a major advance toward a fully flexible code for solving general astrophysical fluid dynamics problems. Flash-1 is modular and adaptive and operates in parallel computing environments. It was designed to let users configure initial and boundary conditions, change algorithms, and add new physical effects with minimal effort. It uses the Paramesh library to manage a block-structured adaptive grid, placing resolution elements only where needed most. It also uses the message passing interface (MPI) library to achieve portability and scalability on a variety of different message passing parallel computers.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed et al., J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier–Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the St...

A hybrid immersed boundary and immersed interface method for electrohydrodynamic simulations

In this paper, we develop a hybrid immersed boundary (IB) and immersed interface method (IIM) to simulate the dynamics of a drop under an electric field in Navier-Stokes flows. Within the leaky dielectric framework with piecewise constant electric properties in each fluid, the electric stress can be treated as an interfacial force on the drop interface. Thus, both the electric and capillary forces can be formulated in a unified immersed boundary framework. The electric potential satisfies a Laplace equation which is solved numerically by an augmented immersed interface method which incorporates the jump conditions naturally along the normal direction. The incompressible Navier-Stokes equations for the fluids are solved using a projection method on a staggered MAC grid and the potential is solved at the cell center. The interface is tracked in a Lagrangian manner with mesh control by adding an artificial tangential velocity to transport the Lagrangian markers to ensure that the spacing between markers is uniform throughout the computations. A series of numerical tests for the present scheme have been conducted to illustrate the accuracy and applicability of the method. We first compute the potential and its gradient (electric field) to perform the accuracy check for the present augmented IIM. We then check the convergence of the interfacial electric force and the fluid variables. We further run a series of simulations with different permittivity and conductivity ratios and compare with the results obtained by the small deformation theory and other numerical results in literature. In addition, we also study the electric effect for a drop under shear flow.

Stratified Kolmogorov flow. Part 2

Forced stratified flows are shown to suffer two types of linear long-wave instability: a ‘viscous’ instability which is related to the classical instability of Kolmogorov flow, and a ‘conductive instability’, with the form of a large-scale, negative thermal diffusion. The nonlinear dynamics of both instabilities is explored with weakly nonlinear theory and numerical computations. The introduction of stratification suppresses the viscous instability, but also makes it subcritical. The second instability arises with stronger stratification and creates a prominent staircase in the buoyancy field; the steps of the staircase evolve over long timescales by approaching one another, colliding and merging (coarsening the staircase).