The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in solids is explored. It allows an extension of the Navier-Stokes equations making the simple shear flows unstable. Following von Mises [4], the existence of maximal allowed shear stress or "yield stress" in fluid is assumed. After the actual stresses have reached this value, a new physical mechanism will be activated attempting to reduce them. This mechanism results in a pressure-like force, which has to be added to the Navier-Stokes equations. The yield stress itself is a material constant, which does not depend on the Reynolds number of particular flow. It will be shown how to estimate its value from experimental data. To demonstrate how the character of flow changes if the additional force is taken into account, an unsteady flow in a 2D nozzle is presented. The momentum source was introduced in the Navier-Stokes equations through the user-defined function's interface offered by Fluent [6]. The initial data and the results of simulation are summarized in appendix.
We present a novel reaction analogy (RA) based forcing method for generating stationary scalar fields in incompressible turbulence. The new method can produce more general scalar PDFs (e.g. double-delta) than current methods, while ensuring that scalar fields remain bounded. Such features are useful for generating initial fields in non-premixed combustion or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formula…
Generalized Reynolds Analogy for Compressible Wall Turbulence: Unified Velocity--Temperature Relations from Mean to Fluctuating Field
Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；Center for Applied Physics and Technology, HEDPS, College of Engineering, Peking University（北京大学工程与应用能源学院应用物理与技术中心）；National Key Laboratory of Computational Physics（计算物理学国家重点实验室）
The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with h…
This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein. J. Fluid Mech 488, pp. 315-333, 2003) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers ($Ma$). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low frequency/small sprea…
Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992)] we introduce a modified version of helical shell models for turbulence with non-local triadic interactions. By using both an analytical argument and numerical simulation, we show that there exists a class of models, with a specific helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions. We further support th…
We explore the laminar to turbulence transition of round jets at low Reynolds number (Re < 1000) using a novel experimental setup and linear stability theory (LST). The setup has a large domain and a low disturbance environment which increases the critical Re to approximately 500, permitting the appearance of a hitherto unknown puff-like instability (PFI). The instability is identified in the self-similar region of the jet through clean flow visualizations (FV) and further corroborated by particle image velocimetry (PIV) measurements. For 400< Re <700, the flow exhibits PFI embedded in a puff-…
Turbulence in superfluid helium~II is a tangle of quantized vortex lines which interact via the classical Biot-Savart law. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonlocal contributions, we find that in Vinen tangles the motion of vortex lines depends mainly on the local curvature, wherea…
The term "solid-state turbulence" may sound like an oxymoron, but in fact it is not. In this article we demonstrate that solid-state turbulence may emerge owing to a defining property of the solid state: the ability of a solid to retain its shape. We consider shear flow of layers of solids with different stiffness and show that the stiffer ones may spontaneously decompose into a set of blocks. This breakdown of isometry is a key to plasticity of solids and is fundamental for the occurrence of solid-state turbulence. To visualise the piecewise isometric transformations of the blocky structure i…
At the very heart of turbulent fluid flows are many interacting vortices that produce a chaotic and seemingly unpredictable velocity field. Gaining new insight into the complex motion of vortices and how they can lead to topological changes of flows is of fundamental importance in our strive to understand turbulence. Our aim is form an understanding of vortex interactions by investigating the dynamics of point vortex dipoles interacting with a hierarchy of vortex structures using the idealized point vortex model. Motivated by its close analogy to the dynamics of quantum vortices in Bose-Einste…
Passive scalar transport in turbulent channel flow subject to spanwise system rotation is studied by direct numerical simulations. The Reynolds number $Re = U_b h/ν$ is fixed at $20\,000$ and the rotation number $Ro = 2 Ωh/U_b$ is varied from 0 to 1.2, where $U_b$ is the bulk mean velocity, $h$ the half channel gap width and $Ω$ the rotation rate. The scalar value is constant but different at the two walls, leading to steady scalar transport across the channel. The rotation causes an unstable channel side with relatively strong turbulence and turbulent scalar transport, and a stable channel si…
Noise measurements of heated axisymmetric jets at fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The `spectral quietening' effect has been observed both experimentally and computationally using Large Eddy Simulations (LES). It was explained by Afsar {\it et al}. (M. Z. Afsar and M. E. Goldstein $\&$ A. M. Fagan AIAAJ., Vol. 49, p. 2522, 2011) through the cancellation introduced by enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give…
In the present paper, recent experimental results on large scale coherent steady states observed in experimental von K{á}rm{á}n flows are revisited from a statistical mechanics perspective. The latter is rooted on two levels of description. We first argue that the coherent steady states may be described as the equilibrium states of well-chosen lattice models, that can be used to define global properties of von K{á}rm{á}n flows, such as their temperatures. The equilibrium description is then enlarged, in order to reinterpret a series of results about the stability of those steady states, their …
Generalized Navier-Stokes (GNS) equations describing three-dimensional (3D) active fluids with flow-dependent spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by realising chiral Beltrami-type chaotic flows. To rationalise these findings, we study here the triad truncations of polynomial and Gaussian GNS models focusing on modes lying in the energy injection range. Identifying a previously unknown cubic invariant, we show that the asymptotic triad dynamics reduces to that of a forced rigid body coupled to a particle m…
Hydrodynamics of Dense Active Fluids: Turbulence-Like States and the Role of Advected Activity
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Department of Mechanical Engineering, Indian Institute of Technology Kanpur（坎普尔印度理工学院机械工程系）
This paper is concerned with the numerical investigation of Quantum Turbulence (QT) described by the Gross-Pitaevskii (GP) equation. Numerical simulations are performed using a parallel (MPI-OpenMP) code based on a pseudo-spectral spatial discretization and second order splitting for the time integration. We start by revisiting (in the framework of high-performance/high-accuracy computations) well-known GP-QT settings, based on the analogy with classical vortical flows: Taylor-Green (TG) vortices and Arnold-Beltrami-Childress (ABC) flow. Two new settings are suggested to build the initial cond…
Queen Mary University of London（伦敦大学女王玛丽学院）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Santa Fe Institute（圣塔菲研究所）；Complexity Science Hub Vienna（维也纳复杂科学中心）；Dipartimento di Fisica e Astronomia Ettore Majorana, Via S. Sofia 64, Catania 95123, Italy（埃托雷·马约拉纳物理与天文学系）
