In a recent work, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential - for example, the interatomic potential at short ranges, and the electrostatic potential at long ranges. Here, we examine the proposed mechanics of turbulence formation in a simple model of two particles, which interact solely via a potential. Following the kinetic theory approach, we derive a hierarchy of the velocity moment transport equations, and then truncate it via a novel closure based on the high Reynolds number condition. While standard closures of the velocity moment hierarchy of the Boltzmann equation lead to the compressible Euler and Navier-Stokes systems of equations, our closure leads to a transport equation for the velocity alone, which is driven by the potential forcing. Starting from a large scale laminar shear flow, we numerically simulate the solutions of our velocity transport equation for the electrostatic, gravity, Thomas-Fermi and Lennard-Jones potentials, as well as the Vlasov-type large scale mean field potential. In all studied scenarios, the time-averaged Fourier spectra of the kinetic energy clearly exhibit Kolmogorov's "five-thirds" power decay rate.
The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence. Here, the transition to condensate formation is investigated as a function of the magnitude of the force and for different types of forcing. Random forces with constant mean energy input lead to a supercritical transition, while forcing through a small-scale linear instability results in a subcritical transition with bistability and hysteresis. That is, the transition to condensate formation in two-dimensional turbulence is nonuniversal. For the supercritical cas…
Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the active turbulence phase calls for a statistical description. Borrowing techniques from turbulence theory, we here establish a quantitative description of correlation functions and spectra of a minimal continuum model for active turbulence. Further exploring the parameter space, we also report on a surprising type of turbulence-driven pattern formation far b…
The present work is aimed at examining the ability of different models in predicting soot formation in Delft flame III, which is a non-premixed pilot stabilized natural gas flame. The turbulence-chemistry interactions are modeled using a laminar steady flamelet model (SLFM). One step and two step models are used to describe the formation, growth, and oxidation of soot particles. One Step is an empirical model which solves the soot mass fraction equation. The two-step models are semi empirical models, where the soot formation is modelled by solving the governing transport equations for the soot…
Integrable turbulence and formation of rogue waves
在聚焦非线性薛定谔（NLS）方程的框架下，数值研究了凝聚体调制不稳定性（MI）的非线性阶段。正如预期的那样，MI的发展导致了“可积湍流”的形成[V.E. Zakharov，Turbulence in可积系统，Stud. in Appl.Math.122，no.3，219-234，（2009）]。我们研究了它的主要特征的时间演化平均跨越实现的初始数据-凝聚解决方案播种的小随机噪声与固定的统计特性。测量的量为：（1）波作用谱和空间关联函数;（2）波振幅及其动量的概率密度函数;（3）动能和势能。
Structure formation in turbulence is effectively an instability of "plasma" formed by fluctuations serving as particles. These "particles" are quantumlike; namely, their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding "kinetic equation" describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we extend it to compressible Navier--Stokes turbulence, where the fluctuation Hamiltonian is a five-dimensional ma…
In a viscoelastic flow over a microfluidic canopy of polymeric pillars, we report the spontaneous emergence of waves in the form of propagating regions of low flow velocity compared to the surrounding flow. The occurrence of the wave is chaotic and shows characteristics of elastic turbulence. We systematically study the coupling between the low velocity wave and the microfluidic canopy by combining flow velocimetry experiments and high speed tracking of the pillars. The waves form an angle $β$ with the primary flow direction that depends on the geometry of the pillar array. If the canopy is co…
Bacterial cellulose is an important class of biomaterials which can be grown in well-controlled laboratory and industrial conditions. The cellulose structure is affected by several biological, chemical and environmental factors, including hydrodynamic flows in bacterial suspensions. In this work, we explore the possibility of using well controlled turbulent flow to control the bacterial cellulose production. Turbulent flows leading to random motion of fluid elements may affect the structure of the extracellular polymeric matrix produced by bacteria. Here we show that two-dimensional turbulence…
The rate of collision and the relative velocities of the colliding particles in turbulent flows is a crucial part of several natural phenomena, e.g., rain formation in warm clouds and planetesimal formation in a protoplanetary disks. The particles are often modeled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of in the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three dimensional turbulent fl…
We investigate the effects of condensation and liquid water loading on the stably stratified surface layer, with an eye towards understanding the influence of turbulent mixing on fog formation. Direct numerical simulations (DNS) of dry and moist open channel flows are conducted, where in both a constant cooling rate is applied at the ground to mimic longwave radiative cooling. Depending on the cooling rate, it can lead to either turbulent (weakly stable) or laminar (very stable) flows. Compared to the completely dry case, the condensation of liquid water in the moist case enables slightly high…
Computational advances and challenges in simulations of turbulence and star formation
Research School of Astronomy and Astrophysics, Australian National University（澳大利亚国立大学天体物理与天文研究学院）；Astronomy Department, The University of Texas at Austin（德克萨斯大学奥斯汀分校天文系）
This thesis presents a newly developed theory for the formation and maintenance of eddy-driven jets in planetary turbulence. The novelty is that jet formation and maintenance is studied as a dynamics of the statistics of the flow rather than a dynamics of individual realizations. This is pursued using Stochastic Structural Stability Theory (S3T), which studies the closed dynamics of the first two cumulants of the full statistical state dynamics of the flow after neglecting or parameterizing third and higher-order cumulants. Using this statistical closure, large-scale structure formation is stu…
Turbulence and Star Formation Suppression in Elliptical Galaxies: The Role of Active Galactic Nucleus Jet Wind Interaction
Astrophysics Division, Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台天体物理分部）；ShanghaiTech University（上海科技大学）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Astronomy and Astrophysics and Department of Physics, Fudan University（复旦大学天文与空间科学中心及物理系）；Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), Fudan University（复旦大学核物理与离子束应用教育部重点实验室）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Re…
Turbulence in the interstellar medium (ISM) is crucial in the process of star formation. Shocks produced by supernova explosions, jets, radiation from massive stars, or galactic spiral-arm dynamics are amongst the most common drivers of turbulence in the ISM. However, it is not fully understood how shocks drive turbulence, in particular whether shock driving is a more solenoidal(rotational, divergence-free) or a more compressive (potential, curl-free) mode of driving turbulence. The mode of turbulence driving has profound consequences for star formation, with compressive driving producing thre…
