3D Hydrodynamics Research Articles

Single-layer microfluidic device to realize hydrodynamic 3D flow focusing.

The recent rapid growth of microfluidic applications has witnessed the emergence of several particle flow focusing techniques for analysis and/or further processing. The majority of flow focusing techniques employ an external sheath fluid to achieve sample flow focusing independent of the flow rate, in contrast to sheath-free techniques. However, the introduction of a sheath fluid to surround the sample fluid has complicated the device design and fabrication, generally involving multi-layer fabrication and bonding of multiple polydimethylsiloxane (PDMS) layers. Several promising efforts have been made to reduce the complexity of fabrication. However, most of these methods involved the use of inertial/Dean effects, which in turn demanded the use of higher sample flow rates. In this paper, we report a method of flow focusing that uses a sheath fluid to enclose the sample in a single layer of PDMS, and that possesses applicability for a wide range of sample flow rates. This method of flow focusing uses abrupt channel depth variation and a shift of one of the sample-sheath junctions (termed as 'junction-shift') against the direction of the sample flow. This configuration serves to manipulate the sample fluid with respect to the sheath fluid and achieve the desired flow focusing. This design facilitates the attainment of 3D flow focusing in two sequential steps (depth-wise and then along the lateral direction) and in distinct regions, hence enabling the regions to be used in imaging and non-imaging flow cytometric applications, respectively. Simulations were performed to characterize and determine the optimum set of design parameters. Experimental demonstrations of this technique were carried out by focusing fluorescein dye and blood cells in flow.

Coherent network analysis of gravitational waves from three-dimensional core-collapse supernova models

Using predictions from three-dimensional (3D) hydrodynamics simulations of core-collapse supernovae (CCSNe), we present a coherent network analysis to detection, reconstruction, and the source localization of the gravitational-wave (GW) signals. We use the {\tt RIDGE} pipeline for the analysis, in which the network of LIGO Hanford, LIGO Livingston, VIRGO, and KAGRA is considered. By combining with a GW spectrogram analysis, we show that several important hydrodynamics features in the original waveforms persist in the waveforms of the reconstructed signals. The characteristic excess in the spectrograms originates not only from rotating core-collapse, bounce and the subsequent ring down of the proto-neutron star (PNS) as previously identified, but also from the formation of magnetohydrodynamics jets and non-axisymmetric instabilities in the vicinity of the PNS. Regarding the GW signals emitted near at the rotating core bounce, the horizon distance extends up to $\sim$ 18 kpc for the most rapidly rotating 3D model in this work. Following the rotating core bounce, the dominant source of the GW emission shifts to the non-axisymmetric instabilities. The horizon distances extend maximally up to $\sim$ 40 kpc seen from the spin axis. With an increasing number of 3D models trending towards explosion recently, our results suggest that in addition to the best studied GW signals due to rotating core-collapse and bounce, the time is ripe to consider how we can do science from GWs of CCSNe much more seriously than before. Particularly the quasi-periodic signals due to the non-axisymmetric instabilities and the detectability should deserve further investigation to elucidate the inner-working of the rapidly rotating CCSNe.

3D hydrodynamics involving multiple eccentric impellers in unbaffled cylindrical tank

In this paper, the numerical predictions of 3D hydrodynamics and power consumption in a vessel stirred by multiple eccentrically located impellers are presented. The vessel is a flat-bottomed cylindrical one equipped with six-curved bladed impellers. Aqueous solutions of xanthan gum are used, which have a shear thinning behavior with yield stress. The influence of several parameters on the mixing efficiency has been investigated, namely: the stirring rate, fluid rheology, impeller number and impeller clearance from the tank bottom. Our predicted results are compared with other experimental data and a satisfactory agreement is found.

Rogue wave formation under the action of quasi-stationary pressure

The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary “pit”. The fluid motion is supposed to be a vortex one and is described by an exact solution of equations of 2D hydrodynamics for an ideal fluid in Lagrangian coordinates. Liquid particles are moving around circumferences of different radii in the absence of drift flow. Values of amplitude and wave steepness optimal for rogue wave formation are found numerically. The influence of vorticity distribution and pressure drop on parameters of the fluid is investigated.

Gravitational instabilities in a protosolar-like disc – I. Dynamics and chemistry

To date, most simulations of the chemistry in protoplanetary discs have used 1+1D or 2D axisymmetric $\alpha$-disc models to determine chemical compositions within young systems. This assumption is inappropriate for non-axisymmetric, gravitationally unstable discs, which may be a significant stage in early protoplanetary disc evolution. Using 3D radiative hydrodynamics, we have modelled the physical and chemical evolution of a 0.17 M$_{\odot}$ self-gravitating disc over a period of 2000 yr. The 0.8 M$_{\odot}$ central protostar is likely to evolve into a solar-like star, and hence this Class 0 or early Class I young stellar object may be analogous to our early Solar System. Shocks driven by gravitational instabilities enhance the desorption rates, which dominate the changes in gas-phase fractional abundances for most species. We find that at the end of the simulation, a number of species distinctly trace the spiral structure of our relatively low-mass disc, particularly CN. We compare our simulation to that of a more massive disc, and conclude that mass differences between gravitationally unstable discs may not have a strong impact on the chemical composition. We find that over the duration of our simulation, successive shock heating has a permanent effect on the abundances of HNO, CN and NH$_3$, which may have significant implications for both simulations and observations. We also find that HCO$^+$ may be a useful tracer of disc mass. We conclude that gravitational instabilities induced in lower mass discs can significantly, and permanently, affect the chemical evolution, and that observations with high-resolution instruments such as ALMA offer a promising means of characterising gravitational instabilities in protosolar discs.

NEUTRINO-DRIVEN TURBULENT CONVECTION AND STANDING ACCRETION SHOCK INSTABILITY IN THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE

We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a $27$-$M_\odot$ progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), (3) SASI dominated evolution. This confirms previous 3D results of Hanke et al. 2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry out simulations with resolutions differing by up to a factor of $\sim$4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case, since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum $E(\ell)$ develops in the heating layer. Like other 3D studies, we find $E(\ell) \propto \ell^{-1}$ in the "inertial range," while theory and local simulations argue for $E(\ell) \propto \ell^{-5/3}$. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy containing scale, creating a "bottleneck" that prevents an efficient turbulent cascade.

USING REALISTIC MHD SIMULATIONS FOR THE MODELING AND INTERPRETATION OF QUIET-SUN OBSERVATIONS WITH THESOLAR DYNAMICS OBSERVATORYHELIOSEISMIC AND MAGNETIC IMAGER

The solar atmosphere is extremely dynamic, and many important phenomena develop on small scales that are unresolved in observations with the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). For correct calibration and interpretation of the observations, it is very important to investigate the effects of small-scale structures and dynamics on the HMI observables, such as Doppler shift, continuum intensity, spectral line depth, and width. We use 3D radiative hydrodynamics simulations of the upper turbulent convective layer and the atmosphere of the Sun, and a spectro-polarimetric radiative transfer code to study observational characteristics of the Fe I 6173A line observed by HMI in quiet-Sun regions. We use the modeling results to investigate the sensitivity of the line Doppler shift to plasma velocity, and also sensitivities of the line parameters to plasma temperature and density, and determine effective line formation heights for observations of solar regions located at different distances from the disc center. These estimates are important for the interpretation of helioseismology measurements. In addition, we consider various center-to-limb effects, such as convective blue-shift, variations of helioseismic travel-times, and the 'concave' Sun effect, and show that the simulations can qualitatively reproduce the observed phenomena, indicating that these effects are related to a complex interaction of the solar dynamics and radiative transfer.

The Exponential Map Near Conjugate Points In 2D Hydrodynamics

We prove that the weak-Riemannian exponential map of the $$L^2$$ metric on the group of volume-preserving diffeomorphisms of a compact two-dimensional manifold is not injective in any neighbourhood of its conjugate vectors. This can be viewed as a hydrodynamical analogue of the classical result of Morse and Littauer.

One-loop effective actions and 2D hydrodynamics with anomalies

We revisit the study of a 2D quantum field theory in the hydrodynamic regime and develop a formalism based on Euclidean one-loop partition functions that is suitable to analyze transport properties due to gauge and gravitational anomalies. To do so, we generalize the method of a modified Dirac operator developed for zero-temperature anomalies to finite temperature, chemical potentials and rotations.

Scaling and self-similarity in two-dimensional hydrodynamics.

The conditions under which depth-averaged two-dimensional (2D) hydrodynamic equations system as an initial-boundary value problem (IBVP) becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the 2D k-ε turbulence model are also investigated. The self-similarity conditions for the depth-averaged 2D hydrodynamics are found for the flow variables including the time, the longitudinal length, the transverse length, the water depth, the flow velocities in x- and y-directions, the bed shear stresses in x- and y-directions, the bed shear velocity, the Manning's roughness coefficient, the kinematic viscosity of the fluid, the eddy viscosity, the turbulent kinetic energy, the turbulent dissipation, and the production and the source terms in the k-ε model. By the numerical simulations, it is shown that the IBVP of depth-averaged 2D hydrodynamic flow process in a prototype domain can be self-similar with that of a scaled domain. In fact, by changing the scaling parameter and the scaling exponents of the length dimensions, one can obtain several different scaled domains. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal, and economical flexibility in setting up physical hydraulic models in which two-dimensional flow components are important.

Hydrodynamic Nambu brackets derived by geometric constraints

A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an orthogonality condition. As a result, 2D hydrodynamics with vorticity as dynamic variable emerges as a generic model, with conservation laws which can be interpreted as enstrophy and energy functionals. Generalized forms like surface quasi-geostrophy and fractional Poisson equations for the stream-function are also included as results from the derivation. The formalism is extended to a hydrodynamic system coupled to a second degree of freedom, with the Rayleigh–Bénard convection as an example. This system is reformulated in terms of constitutive conservation laws with two additive brackets which represent individual processes: a first representing inviscid 2D hydrodynamics, and a second representing the coupling between hydrodynamics and thermodynamics. The results can be used for the formulation of conservative numerical algorithms that can be employed, for example, for the study of fronts and singularities.

Pathways for Observing Stellar Surfaces Using 3D Hydrodynamical Simulations of Evolved Stars

Evolved stars are among the largest and brightest stars and they are ideal targets for the new generation of sensitive, high resolution instrumentation that provides spectrophotometric, interferometric, astrometric, and imaging observables. The interpretation of the complex stellar surface images requires numerical simulations of stellar convection that take into account multi-dimensional time-dependent radiation hydrodynamics with realistic input physics. We show how the evolved star simulations are obtained using the radiative hydrodynamics code CO5BOLD and how the accurate observables are computed with the post-processing radiative transfer code Optim3D. The synergy between observations and theoretical work is supported by a proper and quantitative analysis using these simulations, and by strong constraints from the observational side.

Hydrodynamic processes and their impacts on the mud deposit in the Southern Yellow Sea

Abstract The sedimentation processes of mud deposits on the continental shelves of the Yellow Sea (YS) are investigated using a combined data analysis and hydrodynamic modeling approach in order to identify the dominant factors that contribute significantly to the formation of these deposits. The data analysis makes extensive use of existing data, especially recently collected deep core data while the hydrodynamic and sediment transport processes are studied using a 3D hydrodynamics model that incorporates the effects of tides, waves and wind. The average deposit rate of the Central Yellow Sea Mud (CS) is estimated to be 3.6 × 107 t a− 1 based on high-resolution Chirp sonar profiles combined with core data. Available sedimentological, mineralogical, geochemical and fluid flow data all indicate that the fine sediments discharged from Huanghe River and Changjiang River as well as the resuspended sediments from the Old Huanghe Delta are the main sources for the mud deposits in the Southern Yellow Sea (SYS). This study confirms that tidal current flow is indeed the main agent for transporting the fine sediment to the mud patch in the central SYS but wave effect is also significant as it is responsible for maintaining suspension concentration and causing sediment resuspension. The wave influence is particularly notable around the Old Huanghe Delta in winter storms as during these storm periods current circulation, mainly caused by the Asian Monsoon, can transport a large quantity of fine sediments from the Old Huanghe Delta to the central SYS. Under the present hydrodynamic conditions, the modeling results showed that approximately 16% (1.33 × 108 t a− 1) of the Huanghe River-derived sediment is transported out of Bohai Strait, of which around 44% (5.72 × 107 t a− 1) will finally be transported to the South Yellow Sea. The corresponding values without accounting for the wave effects are 9.8% and 2.6%, respectively. It is noted that the deposition rate in the CS mud area over the past 12 kyr is virtually constant despite the significant rise in sea-level and associated changes in the tidal current fields and wave distributions in the Yellow Sea. The reason for this is believed to be that the weaker currents and waves during a lower water period is compensated by the shorter distance the suspended sediments have to travel from the paleo-Huanghe River to the CS mud area, thus maintaining a nearly constant deposition rate in the CS mud area.

Performance analysis of a 3D unstructured mesh hydrodynamics code on multi‐core and many‐core architectures

SUMMARYSeveral next generation high performance computing platforms are or will be based on the so‐called many‐core architectures, which represent a significant departure from commodity multi‐core architectures. A key issue in transitioning large‐scale simulation codes from multi‐core to many‐core systems is closing the serial performance gap, that is, overcoming the large difference in single‐core performance between multi‐core and many‐core systems. In this paper, we discuss how this problem was addressed for a 3D unstructured mesh hydrodynamics code, describe how Amdahl's law can be used to estimate performance targets and guide optimization efforts, and present timing studies performed on multi‐core and many‐core platforms. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

DYNAMICS AND ENERGY LOSS IN SUPERBUBBLES

Interstellar bubbles appear to be smaller in observations than expected from calculations. Instabilities at the shell boundaries create three-dimensional ef- fects, and are probably responsible for part of this discrepancy. We investigate instabilities and dynamics in superbubbles by 3D hydrodynamics simulations with time-resolved energy input from massive stars, including the supernova explosions. We find that the superbubble shells are accelerated by supernova explosions, coincident with substantial brightening in soft X-ray emission. In between the explosions, the superbubbles lose energy efficiently, approaching the momentum-conserving snowplow limit. This and enhanced radiative losses due to instabilities reduce the expansion compared to the corresponding radiative bubbles in pressure-driven snowplow models with constant energy input. We note generally good agreement with observations of superbubbles and some open issues. In particular, there are hints that the shell velocities in the X-ray-bright phases is underpredicted.

RKDG2 shallow-water solver on non-uniform grids with local time steps: Application to 1D and 2D hydrodynamics

This paper investigates local time stepping (LTS) with the RKDG2 (second-order Runge–Kutta Discontinuous Galerkin) non-uniform solutions of the inhomogeneous SWEs (shallow water equations) with source terms. A LTS algorithm – recently designed for homogenous hyperbolic PDE(s) – is herein reconsidered and improved in combination with the RKDG2 shallow-flow solver (LTS-RKDG2) including topography and friction source terms as well as wetting and drying. Two LTS-RKDG2 schemes that adapt 3 and 4 levels of LTSs are configured on 1D and/or 2D (quadrilateral) non-uniform meshes that, respectively, adopt 3 and 4 scales of spatial discretization. Selected shallow water benchmark tests are used to verify, assess and compare the LTS-RKDG2 schemes relative to their conventional Global Time Step RKDG2 alternatives (GTS-RKDG2) considering several issues of practical relevance to hydraulic modelling. Results show that the LTS-RKDG2 models could offer (depending on both the mesh setting and the features of the flow) comparable accuracy to the associated GTS-RKDG2 models with a savings in runtime of up to a factor of 2.5 in 1D simulations and 1.6 in 2D simulations.

IMPACTS OF ROTATION ON THREE-DIMENSIONAL HYDRODYNAMICS OF CORE-COLLAPSE SUPERNOVAE

We perform a series of simplified numerical experiments to explore how rotation impacts on the three-dimensional (3D) hydrodynamics of core-collapse supernovae. For the sake of our systematic study, we employ a light-bulb scheme to trigger explosions and a three-flavor neutrino leakage scheme to treat deleptonization effects and neutrino losses from proto-neutron star interior. Using a 15 solar mass progenitor, we compute thirty models in 3D with a wide variety of initial angular momentum and light-bulb neutrino luminosity. We find that the rotation can help onset of neutrino-driven explosions for the models in which the initial angular momentum is matched to that obtained in recent stellar evolutionary calculations (0.3-3 rad/s at the center). For the models with larger initial angular momentum, the shock surface deforms to be more oblate due to larger centrifugal force. This makes not only a gain region more concentrated around the equatorial plane, but also the mass in the gain region bigger. As a result, buoyant bubbles tend to be coherently formed and rise in the equatorial region, which pushes the revived shock ever larger radii until a global explosion is triggered. We find that these are the main reasons that the preferred direction of explosion in 3D rotating models is often perpendicular to the spin axis, which is in sharp contrast to the polar explosions around the axis that was obtained in previous 2D simulations.

Pemodelan Tumpahan Minyak di Teluk Lalong Kabupaten Banggai

Oil distribution cause environmental problems that disrupt marine ecosystems and reduce the aesthetic value of coastal waters in Gulf Lalong Banggai. The aims of this study to build a 2D hydrodynamics model to see the patterns of water mass movement and models of oil spill distribution base on the hydrodynamic models in Gulf of Lalong Banggai Regency (0°57'17,3 latitude and 122 ° 47'52 E) with a potential spill, location, volume, and duration of discharge of oil spills. Based on the results of models oil spill distribution in Gulf Lalong Banggai such us waters prone to oil spills.

Flux corrected remapping using piecewise parabolic reconstruction for 2D cell‐centered ALE methods

SummaryA novel conservative interpolation (remapping) method, in the Arbitrary Lagrangian–Eulerian context for numerical solution of Euler equations on unstructured polygonal grids, is presented. Combination of a piecewise quadratic reconstruction and a flux corrected remapping approach provides a simple, symmetry‐preserving and bounds‐preserving method. The positivity of density and specific internal energy is guaranteed. The complete description of the method and both cyclic remapping and full hydrodynamic 2D numerical examples are given. Copyright © 2014 John Wiley & Sons, Ltd.

Neutrino-driven winds from neutron star merger remnants

We present a detailed, 3D hydrodynamics study of the neutrino-driven winds that emerge from the remnant of a NS merger. Our simulations are performed with the Newtonian, Eulerian code FISH, augmented by a detailed, spectral neutrino leakage scheme that accounts for heating due to neutrino absorption in optically thin conditions. Consistent with the 2D study of Dessart et al. (2009), we find that a strong baryonic wind is blown out along the original binary rotation axis within $100$ ms after the merger. We compute a lower limit on the expelled mass of $3.5 \times 10^{-3} M_{\odot}$, large enough to be relevant for heavy element nucleosynthesis. The physical properties vary significantly between different wind regions. For example, due to stronger neutrino irradiation, the polar regions show substantially larger $Y_e$ than those at lower latitudes. This has its bearings on the nucleosynthesis: the polar ejecta produce interesting r-process contributions from $A\sim 80$ to about 130, while the more neutron-rich, lower-latitude parts produce also elements up to the third r-process peak near $A\sim 195$. We also calculate the properties of electromagnetic transients that are powered by the radioactivity in the wind, in addition to the macronova transient that stems from the dynamic ejecta. The high-latitude (polar) regions produce UV/optical transients reaching luminosities up to $10^{41} {\rm erg \, s^{-1}}$, which peak around 1 day in optical and 0.3 days in bolometric luminosity. The lower-latitude regions, due to their contamination with high-opacity heavy elements, produce dimmer and more red signals, peaking after $\sim 2$ days in optical and infrared. Our numerical experiments indicate that it will be difficult to infer the collapse time-scale of the HMNS to a BH based on the wind electromagnetic transient, at least for collapse time-scales larger than the wind production time-scale.