Initial Velocity Field Research Articles

The Effect of Domain Length and Initialization Noise on Direct Numerical Simulation of Shear Stratified Turbulence

Direct numerical simulation (DNS) has been employed with success in a variety of oceanographic applications, particularly for investigating the internal dynamics of Kelvin–Helmholtz (KH) billows. However, it is difficult to relate these results directly with observations of ocean turbulence due to the significant scale differences involved (ocean shear layers are typically on the order of tens to hundreds of meters in thickness, compared to DNS studies, with layers on the order of one to tens of centimeters). As efforts continue to inform our understanding of geophysical-scale turbulence by extrapolating DNS results, it is important to understand the impact of model setup and initial conditions on the resulting turbulent quantities. Given that geophysical-scale measurements, whether through microstructures or other techniques, can only provide estimates of averaged TKE quantities (e.g., TKE dissipation or buoyancy flux), it may be necessary to compare mean turbulent quantities derived from DNS (i.e., across one or more complete billow evolutions) with ocean measurements. In this study, we analyze the effect of domain length and initial velocity noise on resulting turbulent quantities. Domain length is important, as dimensions that are not integer multiples of the natural KH billow wavelength may compress or stretch the billows and impact their energetics. The addition of random noise in the initial velocity field is often used to trigger turbulence and suppress secondary instabilities; however, the impact of noise on the resulting turbulent energetics is largely unknown. In this study, we conclude that domain lengths on the order of 1.5 times the natural wavelength or less can affect the resulting turbulent energetics by a factor of two or more. We also conclude that increasing the amplitude of random initial velocity noise decreases the resulting turbulent energetics, but that different realizations of the random noise field may have an even greater impact than amplitude. These results should be considered when designing a DNS experiment.

Protostellar disk accretion in turbulent filaments

Context. Recent observations of protostellar cores suggest that most of the material in the protostellar phase is accreted along streamers. Streamers in this context are defined as velocity coherent funnels of denser material potentially connecting the large-scale environment to the small scales of the forming accretion disk. Aims. Using simulations that simultaneously resolve the driving of turbulence on the filament scale as well as the collapse of the core down to protostellar disk scales, we aim to understand the effect of the turbulent velocity field on the formation of overdensities in the accretion flow. Methods. We performed a three-dimensional numerical study on a core collapse within a turbulent filament using the RAMSES code and analysed the properties of overdensities in the accretion flow. Results. We find that overdensities are formed naturally by the initial turbulent velocity field inherited from the filament and subsequent gravitational collimation. This leads to streams that are not really filamentary but show a sheet-like morphology. Moreover, they have the same radial infall velocities as the low density material. As a main consequence of the turbulent initial condition, the mass accretion onto the disk does not follow the predictions for solid body rotation. Instead, most of the mass is funneled by the overdensities to intermediate disk radii.

Global well-posedness of three-dimensional incompressible Boussinesq system with temperature-dependent viscosity

In this paper, we focus on the global well-posedness of solutions to three-dimensional incompressible Boussinesq equations with temperature-dependent viscosity under the smallness assumption of initial velocity fields u0 in the critical space Ḃ3,10. The key ingredients here lie in the decomposition of the velocity fields and the regularity theory of the Stokes system, which are crucial to get rid of the smallness restricition of the initial temperature θ0. In addition, we mention that the improved decay estimates in time is also necessary.

Evidence for layered anisotropic stratified turbulence in a freely evolving horizontal shear flow

We present evidence for layered anisotropic stratified turbulence (LAST) and mixing produced in a freely evolving uniformly stratified shear layer where the direction of shear is orthogonal to gravity. As originally reported by Basak & Sarkar (J. Fluid. Mech., vol. 568, 2006, pp. 19–54), such a flow develops a rich three-dimensional structure in the form of interlocking columnar vortices formed by horizontal shear instability that remain coherent at large scales due to the stabilising vertical stratification. Here, we modify the initial velocity field by introducing additional small-amplitude vertical perturbations designed to be representative of pre-existing horizontal layers often observed in strongly stratified ocean environments. This reveals a novel finite amplitude, non-normal mode growth mechanism through which the vertical shear between layers may be rapidly amplified by its interaction with the horizontal shear layer prior to the growth of shear instability, leading to a rapid turbulent transition instigated by the subsequent interaction of the layers with the emerging columnar vortices. Through a consideration of relevant flow statistics and associated dimensionless parameters, we demonstrate that turbulence can enter the LAST regime, thereby indicating a generic mechanism leading to the transient development of regions of strongly stratified turbulence in the ocean. We discuss the properties of mixing and the parameterisation of mixing efficiency in terms of the relationship between turbulent length scales in the flow, in particular highlighting links to models based on the classical vertical shear instability paradigm typically associated with more weakly stratified flows that produce isolated turbulent ‘patches’.

Evolution of the Angular Momentum of Molecular Cloud Cores in Magnetized Molecular Filaments

The angular momentum of molecular cloud cores plays a key role in the star formation process. However, the evolution of the angular momentum of molecular cloud cores formed in magnetized molecular filaments is still unclear. In this paper, we perform 3D magnetohydrodynamics simulations to reveal the effect of the magnetic field on the evolution of the angular momentum of molecular cloud cores formed through filament fragmentation. As a result, we find that the angular momentum decreases by 30% and 50% at the mass scale of 1 M ⊙ in the case of weak and strong magnetic field, respectively. By analyzing the torques exerted on fluid elements, we identify the magnetic tension as the dominant process for angular momentum transfer for mass scales ≲3 M ⊙ for the strong magnetic field case. This critical mass scale can be understood semianalytically as the timescale of magnetic braking. We show that the anisotropy of the angular momentum transfer due to the presence of a strong magnetic field changes the resultant angular momentum of the core only by a factor of 2. We also find that the distribution of the angle between the rotation axis and the magnetic field does not show strong alignment even just before the first core formation. Our results also indicate that the variety of the angular momentum of the cores is inherited from the difference in the phase of the initial turbulent velocity field. The variety could contribute to the diversity in size and other properties of protoplanetary disks recently reported by observations.

Global well-posedness of Chemotaxis-Navier–Stokes system with refined rough initial data in [formula omitted

We consider the global solvability of the incompressible Chemotaxis-Navier–Stokes system in Rd,d=2,3. We first investigate the global well-posedness of Chemotaxis-Navier–Stokes equations in R2 by involving a double exponential function of the initial velocity field u0 and the initial chemical concentration c0. By only giving the smallness assumption of initial cell density n0 and the horizontal components of velocity field u0h=(u01,u02) in critical Besov spaces, the global existence and uniqueness of the solution for Chemotaxis-Navier–Stokes equations in R3 is also established. The main contribution of this paper is to supply an improved assumption on initial data and remove the smallness condition on initial chemical concentration c0 in both dimensional two and three.

MAIRNet: weakly supervised anatomy-aware multimodal articulated image registration network.

Multimodal articulated image registration (MAIR) is a challenging problem because the resulting transformation needs to maintain rigidity for bony structures while allowing elastic deformation for surrounding soft tissues. Existing deep learning-based methods ignore the articulated structures and consider it as a pure deformable registration problem, leading to suboptimal results. We propose a novel weakly supervised anatomy-aware multimodal articulated image registration network, referred as MAIRNet, to solve the challenging problem. The architecture of MAIRNet comprises of two branches: a non-learnable polyrigid registration branch to estimate an initial velocity field, and a learnable deformable registration branch to learn an increment. These two branches work together to produce a velocity field that can be integrated to generate the final displacement field. We designed and conducted comprehensive experiments on three datasets to evaluate the performance of the proposed method. Specifically, on the hip dataset, our method achieved, respectively, an average dice of 90.8%, 92.4% and 91.3% for the pelvis, the right femur, and the left femur. On the lumbar spinal dataset, our method obtained, respectively, an average dice of 86.1% and 85.9% for the L4 and the L5 vertebrae. On the thoracic spinal dataset, our method achieved, respectively, an average dice of 76.7%, 79.5%, 82.9%, 85.5% and 85.7% for the five thoracic vertebrae ranging from T6 to T10. In summary, we developed a novel approach for multimodal articulated image registration. Comprehensive experiments conducted on three typical yet challenging datasets demonstrated the efficacy of the present approach. Our method achieved better results than the state-of-the-art approaches.

Deep learning for particle image velocimetry with attentional transformer and cross-correlation embedded

Deep learning-powered methodologies have realized remarkable advancements in the fluid mechanics community, including applications in the particle image velocimetry (PIV) task. However, previous deep learning-based methods still lack robustness and generalization in the real flow scenarios. To solve this problem, we put forward a deep learning architecture called DeepST-CC for PIV estimation, which embeds an attentional transformer and cross-correlation strategy. Specifically, we introduce the Swin Transformer into the optical flow model Recurrent All-pairs Field Transforms (RAFT) to enhance the features of flow images. Then, the global matching between features is efficiently computed by applying a 4D correlation volume. Afterwards, the conventional cross-correlation method derives the initial velocity field from a coarse correlation, which is fed to the GRU-based flow update module. This approach enhances the robustness of the proposed model by incorporating coarse velocity information. Finally, a supervised learning strategy is performed to guide the model training on the synthetic dataset. Extensive experimental are conducted to demonstrate that our proposed approach delivers exceptional performance on the public dataset. In addition, DeepST-CC exhibits good generalization ability towards complex experimental PIV images.

Singularities in finite time of the full compressible Euler equations in [formula omitted

The present article is concerned with the study of blow-up phenomena of the smoooth solutions for the full compressible Euler equations in Rd,d≥1, which have always been a great concern to physicists and mathematicians throughout history. The approach is to construct exact explicit function to study singularities in finite time of the spherically symmetric solutions, provided the initial data satisfy some conditions. Compared with the results obtained by Sideris in 1984 (CMP), in this article, the initial velocity field is not required to have a compact support and the initial density and entropy is not equal to a constant outside the support of the initial velocity field.

Global existence of large solutions for the three‐dimensional incompressible Navier–Stokes–Poisson–Nernst–Planck equations

This work is concerned with the global existence of large solutions to the three‐dimensional dissipative fluid‐dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible Navier–Stokes–Poisson–Nernst–Planck equations. Making full use of the algebraic structure of the system, we obtain the global existence of solutions without smallness assumptions imposed on the third component of the initial velocity field and the summation of initial densities of charged species. More precisely, we prove that there exist two positive constants such that if the initial data satisfies then the incompressible Navier–Stokes–Poisson–Nernst–Planck equations admits a unique global solution.

Dynamic response and vibration modes of multi-layer wound cylindrical shell for hydrogen storage under external blast loading

Multi-layer wound cylindrical shells are the preferred structures for storage vessels working in high pressure and hydrogen atmosphere. However, they are susceptible to external blast loads from accidental hydrogen explosions. In order to study the response of such structures under external blast loading, a numerical model was developed, which combined a thermo-viscoplastic constitutive model and a fluid-structure coupling approach, and was subjected to external blast loads of different TNT equivalency weights. The strain responses and initial velocity fields of the structure were analyzed. A rigid-plastic theoretical model was also developed to calculate the maximum displacement of the inner shell and was compared with the simulation results. Moreover, the axial velocity vibration histories and dominant frequencies at different locations of the steel belts were numerically obtained. In addition, four vibration modes of the steel belts were presented in this paper. Furthermore, strain growth was observed in the high-frequency vibration area, and the possible reasons for the strain growth were analyzed and discussed in detail. The results will be useful for predicting the deformation modes of such multi-layer wound cylindrical shell structures under the risk of external hydrogen explosions.

Compressible Navier‐Stokes equations with ripped density

AbstractWe are concerned with the Cauchy problem for the two‐dimensional compressible Navier‐Stokes equations supplemented with general H1 initial velocity and bounded initial density not necessarily strictly positive: it may be the characteristic function of any set, for instance. In the perfect gas case, we establish global‐in‐time existence and uniqueness, provided the volume (bulk) viscosity coefficient is large enough. For more general pressure laws (like e.g., with ), we still get global existence, but uniqueness remains an open question. As a by‐product of our results, we give a rigorous justification of the convergence to the inhomogeneous incompressible Navier‐Stokes equations when the bulk viscosity tends to infinity. In the three‐dimensional case, similar results are proved for short time without restriction on the viscosity, and for large time if the initial velocity field is small enough.

3D anisotropic Navier–Stokes equations in : stability and large-time behaviour

The study on the large-time behaviour of solutions to the 3D incompressible anisotropic Navier–Stokes (ANS) equations is very recent. Powerful tools designed for the Navier–Stokes equations with full Laplacian dissipation such as the Fourier splitting method no longer apply to the case when there is only horizontal dissipation. For the whole space , as , solutions of the ANS equations converge to the trivial solution and the convergence rate is algebraic. This paper is devoted to the case when the spatial domain Ω is . Our results reveal that the large-time behaviour for is quite different from that for . We show that any small initial velocity field leads to a unique global solution u that remains small in . More importantly, as , the velocity field u converges to a nontrivial steady state. The first two components of the steady state are given by the horizontal average of the first two components of u 0 while the third component vanishes. In addition, this convergence is exponentially fast.

Blow-up for compressible Euler system with space-dependent damping in 1-D

AbstractThis article considers the Cauchy problem for compressible Euler system inR{\bf{R}}with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs toL1(R){L}^{1}\left({\bf{R}})), then the damping is non-effective to the long-time behavior of the solution.

Existence of local suitable weak solutions to the Navier–Stokes equations for initial data in [formula omitted]2loc ([formula omitted

We consider the Navier–Stokes equations in R3 subject to the initial condition with initial velocity field in Lloc2(R3) such that lim supR→+∞R−1‖u0‖L2(B(R))<+∞. Our aim is to show the local existence of a weak solution, global existence of weak solution if C=0 and the partial regularity in the sense of Caffarelli–Kohn–Nirenberg.

Imposing a constraint on the discrete Reynolds–Orr equation demonstrated in shear flows

The Reynolds–Orr equation predicts the unconditional stability limit of a flow. Although this seems to be a desirable aim in engineering applications, the predicted critical Reynolds numbers are one magnitude below the experimental observations. In this paper, an attempt is made to reduce this gap for incompressible shear flows. It is known that the Navier–Stokes equation has no regular solution at the initial time if the initial velocity field does not fulfill the compatibility condition. However, the original solution of the Reynolds–Orr equation, the critical perturbation, does not necessarily fulfill this condition. Therefore, the condition is added to the original problem as a non-linear constraint. This requires the use of a discrete functional, introduced in the paper. Two different formulations are implemented and discussed. The solution is assumed in a waveform. The augmented problem is solved in the cases of planar Poiseuille and the Couette flow. The result shows that adding the constraint increases the critical Reynolds number significantly in the case of a streamwise perturbation but only slightly in the case of a spanwise one. It was demonstrated using numerical simulations that the single waveform assumption was unreasonably strict. The usage of the compatibility condition without assuming the single waveform has a negligible effect on the critical Reynolds number. However, the presented methods can be used for adding other reasonable and complicated constraints to the variational problem.

Computational and experimental analysis of lattices with modulated nonlinearity

There has been growing interest in wave propagation in nonlinear lattices due to their amplitude-dependent dispersion. While previous studies have primarily considered lattices with spatially-uniform stiffness nonlinearity, this work explores lattices with nonlinear stiffness spatially-modulatedin both sign and strength. A multiple scales perturbation analysis reveals exotic dispersion behavior, including the coexistence of hardening and softening within the same branch, the merging of two branches near the band edge, and the suppression of amplitude-dependent dispersion shifting across entire branches. Moreover, this study presents details of the computational and experimental validation of this newly-discovered nonlinear dispersion behavior. For numerical validation, direct simulation of the lattice equations of motion is carried-out. Distinctions are drawn between harmonic excitation of the lattice as compared to prescription of the lattice’s initial displacement and velocity fields. An experimental realization of the lattice is proposed whereby the sign and strength of the nonlinearity is spatially modulated using springs grounded at different angles. Experimentally-feasible lattice parameters are detailed and the experimental set-up is explored computationally using motion simulation and finite element software. [Work supported by the Office of Naval Research.]

Cosmic web & caustic skeleton: non-linear constrained realizations — 2D case studies

The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed non-linear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.

Some exact solutions that describe an ideal fluid flow with a free boundary

The study is aimed at constructing exact solutions that describe unsteady flows of an ideal fluid with a free boundary. Currently existing examples of solutions of this kind have a linear or quadratic initial field of velocities. The object of the present study is flows with a cubic initial velocity field. Several exact solutions are obtained by using a method based on the complex Hopf equation for the complex velocity. One of the main problems in solving the Euler equations in the domain with a free boundary is to study the positions of singular points because these points can reach the free boundary with time, which may lead to solution destruction. In the present case, singularities can be found explicitly. However, as the initial velocity field is defined by a third-power polynomial, one has to study the Riemann surfaces for the function of complex velocity in order to determine the mutual positions of the singularities and flow domain. It is shown that any initial velocity field defined by a cubic polynomial yields one of seven flows described in the paper with time. It is of interest that there are examples of flows that exist for a finite time and break down when the singularities reach the free boundary. Using a certain modification of the Hopf equation, we obtain a two-parameter family of exact solutions that describe fluid flows with a free boundary. Two examples of this family are considered. In one of them, the solution breaks down within a finite time. The second example is of interest because the motion of a singular point in the fluid leads to the formation of a narrow channel with free boundaries.

Global well-posedness for the 3-D Boussinesq system with damping

The present paper is devoted to study the well-posedness issue of solutions of the 3-D Boussinesq system with damping in the whole space. By means of Littlewood-Paley analysis tools we relax the smallness condition and deal with the nonlinear coupling between the horizontal components and the vertical one with the temperature. Finally, we prove that the 3-D Boussinesq system with damping is globally well-posedness when the initial velocity field with the third component being large.