Yantao Yang

A multiple-resolution strategy for Direct Numerical Simulation of scalar turbulence

In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolution than that of the momentum. The latter usually requires a less refined mesh and integrating both fields on a single grid tailored to the most demanding variable produces an unnecessary computational overhead. A multiple resolution approach is used also in the time integration in order to maintain the stability of the scalars on the finer grid. The method is the more advantageous the less diffusive the scalar is with respect to momentum, therefore it is particularly well suited for large Prandtl or Schmidt number flows. However, even in the case of equal diffusivities the present procedure gives CPU time and memory occupation savings, due to the increased gradients and more intermittent behaviour of the scalars when compared to momentum.

Helical-wave decomposition and applications to channel turbulence with streamwise rotation

Using helical-wave decomposition (HWD), a solenoidal vector field can be decomposed into helical modes with different wavenumbers and polarities. Here, we first review the general formulation of HWD in an arbitrary single-connected domain, along with some new development. We then apply the theory to a viscous incompressible turbulent channel flow with system rotation, including a derivation of helical bases for a channel domain. By these helical bases, we construct the inviscid inertial-wave (IW) solutions in a rotating channel and derive their existing condition. The condition determines the specific wavenumber and polarity of the IW. For a set of channel turbulent flows rotating about a streamwise axis, this channel-domain HWD is used to decompose the flow data obtained by direct numerical simulation. The numerical results indicate that the streamwise rotation induces a polarity-asymmetry and concentrates the fluctuating energy to particular helical modes. At large rotation rates, the energy spectra of opposite polarities exhibit different scaling laws. The nonlinear energy transfer between different helical modes is also discussed. Further investigation reveals that the IWs do exist when the streamwise rotation is strong enough, for which the theoretical predictions and numerical results are in perfect agreement in the core region. The wavenumber and polarity of the IW coincide with that of the most energetic helical modes in the energy spectra. The flow visualizations show that away from the channel walls, the small vortical structures are clustered to form very long columns, which move in the wall-parallel plane and serve as the carrier of the IW. These discoveries also help clarify certain puzzling problems raised in previous studies of streamwise-rotating channel turbulence.

Interactions between inertial particles and shocklets in compressible turbulent flow

Numerical simulations are conducted to investigate the dynamics of inertial particles being passively convected in a compressible homogeneous turbulence. Heavy and light particles exhibit very different types of non-uniform distributions due to their different behaviors near shocklets. Because of the relaxation nature of the Stokes drag, the heavy particles are decelerated mainly at downstream adjacent to the shocklets and form high-number-density clouds. The light particles are strongly decelerated by the added-mass effect and stay in the compression region for a relatively long time period. They cluster into thin filament structures near shocklets.

Statistics and structures of pressure and density in compressible isotropic turbulence

We study statistics and structures of pressure and density in the presence of large-scale shock waves in a forced compressible isotropic turbulence using high-resolution numerical simulation. The spectra for pressure and density exhibit a −2 scaling over an operational definition of the inertial range. Both the numerical simulation and a heuristic PDF model reveal that the PDFs of pressure increment exhibit a −2 power law region for the separation in the operational definition of inertial range, quantitatively similar to the PDF of pressure gradient, which also displays a −2 power law region. Moreover, the statistical relation between density increment and pressure increment has been investigated through a shock-relation model. There is a positive correlation between the vorticity magnitude and pressure, which is different from the case of incompressible turbulence. We argue that this difference is due to large-scale shock waves, another type of intermittent structures in addition to vortex structures in incompressible turbulence.

AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters

Abstract The AFiD code, an open source solver for the incompressible Navier–Stokes equations ( http://www.afid.eu ), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme has been devised to improve the scaling of the Poisson solver, which is the main bottleneck of incompressible solvers. For large meshes the GPU version of the code shows good strong scaling characteristics, and the wall-clock time per step for the GPU version is an order of magnitude smaller than for the CPU version of the code. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh–Benard convection and plane Couette flow are simulated and the results are in excellent agreement with the experimental and computational data that have been published in literature. Program summary Program Title: AFiD-GPU Program Files doi: http://dx.doi.org/10.17632/rwjdg7ry66.1 Licensing provisions: MIT Programming language: Fortran 90, CUDA Fortran, MPI External routines: PGI, CUDA Toolkit, FFTW3, HDF5 Nature of problem: Solving the three-dimensional Navier–Stokes equations coupled with a scalar field in a cubic box bounded between two walls and with periodic boundary conditions in the horizontal directions. Solution method: Second order finite difference method for spatial discretization, third order Runge–Kutta scheme in combination with Crank–Nicolson for the implicit terms for time advancement, two dimensional pencil distributed MPI parallelization, GPU accelerated routines. Additional comments including restrictions and unusual features: The code is available and supported on https://github.com/PhysicsofFluids/AFiD_GPU_opensource .

Flow-induced dissolution of femtoliter surface droplet arrays

The dissolution of liquid nanodroplets is a crucial step in many applied processes, such as separation and dispersion in the food industry, crystal formation of pharmaceutical products, concentrating and analysis in medical diagnosis, and drug delivery in aerosols. In this work, using both experiments and numerical simulations, we quantitatively study the dissolution dynamics of femtoliter surface droplets in a highly ordered array under a uniform flow. Our results show that the dissolution of femtoliter droplets strongly depends on their spatial positions relative to the flow direction, drop-to-drop spacing in the array, and the imposed flow rate. In some particular cases, the droplet at the edge of the array can dissolve about 30% faster than the ones located near the centre. The dissolution rate of the droplet increases by 60% as the inter-droplet spacing is increased from 2.5 μm to 20 μm. Moreover, the droplets close to the front of the flow commence to shrink earlier than those droplets in the center of the array. The average dissolution rate is faster for the faster flow. As a result, the dissolution time (Ti) decreases with the Reynolds number (Re) of the flow as Ti ∝ Re-3/4. The experimental results are in good agreement with the numerical simulations where the advection-diffusion equation for the concentration field is solved and the concentration gradient on the surface of the drop is computed. The findings suggest potential approaches to manipulate nanodroplet sizes in droplet arrays simply by dissolution controlled by an external flow. The obtained droplets with varying curvatures may serve as templates for generating multifocal microlenses in one array.

Vertically bounded double diffusive convection in the finger regime: Comparing no-slip versus free-slip boundary conditions.

Vertically bounded fingering double diffusive convection is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e., the no-slip condition, which is inevitable in the lab-scale experimental researches, and the free-slip condition, which is an approximation for the interfaces in many natural environments, such as the oceans. For both boundary conditions the flow is dominated by fingers and the global responses follow the same scaling laws, with enhanced prefactors for the free-slip cases. Therefore, the laboratory experiments with the no-slip boundaries serve as a good model for the finger layers in the ocean. Moreover, in the free-slip case, although the tangential shear stress is eliminated at the boundaries, the local dissipation rate in the near-wall region may exceed the value found in the no-slip cases, which is caused by the stronger vertical motions of horizontally focused fingers and sheet structures near the free-slip boundaries. This counterintuitive result might be relevant for properly estimating and modeling the mixing and entrainment phenomena at free surfaces and interfaces widespread in oceans and geophysical flows.

Roles of Gag-RNA interactions in HIV-1 virus assembly deciphered by single-molecule localization microscopy

Significance Single-molecule localization microscopy (SMLM) is useful for deciphering dynamic organizations of structures densely labeled by specific proteins in the cellular context with nanoscopic resolution not attainable by conventional imaging tools. Here we employed SMLM to investigate the mechanism by which the HIV-1 viral RNA (vRNA) mediates the assembly of thousands of Gag proteins into a virus particle at the plasma membrane. In contrast to the general notion that vRNA only triggers Gag assembly and is dispensable for subsequent assembly, we found that vRNA is indispensable throughout assembly, scaffolding the formation of assembly intermediates and maintaining their architectures via balancing of external forces acting on the assembly environment. These previously unidentified features may facilitate understanding of HIV-1 and, potentially, other retroviruses. During HIV-1 assembly, the retroviral structural protein Gag forms an immature capsid, containing thousands of Gag molecules, at the plasma membrane (PM). Interactions between Gag nucleocapsid (NC) and viral RNA (vRNA) are thought to drive assembly, but the exact roles of these interactions have remained poorly understood. Since previous studies have shown that Gag dimer- or trimer-forming mutants (GagZiL) lacking an NC domain can form immature capsids independent of RNA binding, it is often hypothesized that vRNA drives Gag assembly by inducing Gag to form low-ordered multimers, but is dispensable for subsequent assembly. In this study, we examined the role of vRNA in HIV-1 assembly by characterizing the distribution and mobility of Gag and Gag NC mutants at the PM using photoactivated localization microscopy (PALM) and single-particle tracking PALM (spt-PALM). We showed that both Gag and GagZiL assembly involve a similar basic assembly unit, as expected. Unexpectedly, the two proteins underwent different subsequent assembly pathways, with Gag cluster density increasing asymptotically, while GagZiL cluster density increased linearly. Additionally, the directed movement of Gag, but not GagZiL, was maintained at a constant speed, suggesting that the two proteins experience different external driving forces. Assembly was abolished when Gag was rendered monomeric by NC deletion. Collectively, these results suggest that, beyond inducing Gag to form low-ordered multimer basic assembly units, vRNA is essential in scaffolding and maintaining the stability of the subsequent assembly process. This finding should advance the current understanding of HIV-1 and, potentially, other retroviruses.

Quantifying Gene Expression in Living Cells with Ratiometric Bimolecular Beacons

Molecular beacons (MBs), a class of oligonucleotide-based probes, have enabled researchers to study various RNA molecules in their native live-cell contexts. However, it is also increasingly recognized that, when delivered into cells, MBs have the tendency to be sequestered into the nucleus where they may generate false positive signals. In an attempt to overcome this issue, MBs have been synthesized with chemically modified oligonucleotide backbones to confer greater biostability. Alternatively, strategies have been developed to minimize nuclear entry. In the latter approach, we have combined functional elements of MBs with functional elements of siRNAs that facilitate nuclear export to create a new RNA imaging platform called ratiometric bimolecular beacons (RBMBs). We showed that RBMBs exhibited long-term cytoplasmic retention, and hence a marginal level of false positive signals in living cells. Subsequent studies demonstrated that RBMBs could sensitively and accurately quantify mRNA transcripts engineered to contain multiple tandem repeats of an MB target sequence at the single-molecule level. In this chapter, we describe the synthesis of RBMBs and their applications for absolute quantification and tracking of single mRNA transcripts in cells.

Inertial waves and mean velocity profiles in a rotating pipe and a circular annulus with axial flow.

In this paper we solve the inviscid inertial wave solutions in a circular pipe or annulus rotating constantly about its axis with moderate angular speed. The solutions are constructed by the so-called helical wave functions. We reveal that the mean velocity profiles must satisfy certain conditions to accommodate the inertial waves at the bulk region away from boundary. These conditions require the axial and azimuthal components of the mean velocity to take the shapes of the zeroth and first order Bessel functions of the first kind, respectively. The theory is then verified by data obtained from direct numerical simulations for both rotating pipe and circular annulus, and excellent agreement is found between theory and numerical results. Large scale vortex clusters are found in the bulk region where the mean velocity profiles match the theoretical predictions. The success of the theory in rotating pipe, circular annulus, and streamwise rotating channel suggests that such inertial waves are quite common in wall bounded flow with background rotation.