We investigate the vorticity dynamics in a turbulent vortex using scattering of acoustic waves. Two ultrasonic beams are adjusted to probe simultaneously two spatial scales in a given volume of the flow, thus allowing a dual channel recording of the dynamics of coherent vorticity structures. Our results show that this allows to measure the average energy transfer time between different spatial length scales, and that such transfer goes faster at smaller scales.
This paper introduces open-source computational fluid dynamics software named open computational fluid dynamic code for scientific computation with graphics processing unit (GPU) system (OpenCFD-SCU), developed by the authors for direct numerical simulation (DNS) of compressible wall-bounded turbulence. This software is based on the finite difference method and is accelerated by the use of a GPU, which provides an acceleration by a factor of more than 200 compared with central processing unit (CPU) software based on the same algorithm and number of message passing interface (MPI) processes, an…
Modelling the sudden depressurisation of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculations. The present study presents a machine learning-assisted computatio…
We present a fluid dynamics video which illustrates the Lagrangian aspects of local heat transfer in turbulent Rayleigh-Benard convection. The data are obtained from a direct numerical simulation.
We derive and test a new heuristic theory for third-order structure functions that resolve the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally in rotating stratified turbulence or magnetohydrodynamical~(MHD) turbulence, for example. The theory has three parameters, namely the upscale/downscale energy transfer rates and the forcing scale, and it includes the classic inertial range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full …
An analysis of the turbulence-radiation interaction in the framework of large eddy simulation (LES) is presented. Direct numerical simulation (DNS) of statistical steady forced homogeneous isotropic turbulence is used to evaluate the relevance of the unclosed terms of the filtered radiative transfer equation (RTE) and to study the influence of parameters like the optical thickness and the turbulence intensity. LES without subgrid-scale models of the filtered RTE has also been investigated. Neglecting the subgrid-scale fluctuations of radiation has proved to be an accurate assumption in various…
The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex …
Preferential concentration of inertial particles by turbulence is a well recognized phenomenon. This study investigates how this phenomenon impacts the mean heat transfer between the fluid phase and the particle phase. Using direct numerical simulations of homogeneous and isotropic turbulent flows coupled with Lagrangian point particle tracking, we explore this phenomenon over wide range of input parameters. Among the nine independent dimensionless numbers defining this problem, we show that particle Stokes number, defined based on large eddy time, and a new identified number called heat mixin…
We perform direct numerical simulations of quasi-static magnetohydrodynamic turbulence, and compute various energy transfers including the ring-to-ring and conical energy transfers, and the energy fluxes of the perpendicular and parallel components of the velocity field. We show that the rings with higher polar angles transfer energy to ones with lower polar angles. For large interaction parameters, the dominant energy transfer takes place near the equator (polar angle $θ\approx \fracπ{2}$). The energy transfers are local both in wavenumbers and angles. The energy flux of the perpendicular com…
The effect of turbulence on the mass and heat transfer between small heavy inertial particles (HIP) and an embedding fluid is studied. Two effects are identified. The first effect is due to the relative velocity between the fluid and the particles, and a model for the relative velocity is presented. The second effect is due to the clustering of particles, where the mass transfer rate is inhibited due to the rapid depletion of the consumed species inside the dense particle clusters. This last effect is relevant for large Damkohler numbers and it may totally control the mass transfer rate for Da…
The back-reaction of dispersed rigid fibers to turbulence is analyzed by means of a state-of-the-art fully-coupled immersed boundary method. The following universal scenario is identified: turbulence at large scales looses a consistent part of its kinetic energy (via a Darcy friction term), which partially re-appears at small scales where a new range of energy-containing scales does emerge. Large-scale mixing is thus depleted in favor of a new mixing mechanism arising at the smallest scales. Anchored fibers cause the same back-reaction to turbulence as moving fibers of large inertia. Our resul…
Recent numerical results show that if a scalar is mixed by periodically forced turbulence, the average mixing rate is directly affected for forcing frequencies small compared to the integral turbulence frequency. We elucidate this by an analytical study using simple turbulence models for spectral transfer. Adding a large amplitude modulation to the forcing of the velocity field enhances the energy transfer and simultaneously diminishes the scalar transfer. Adding a modulation to a random stirring protocol will thus negatively influence the mixing rate. We further derive the asymptotic behaviou…
Rotating turbulence is an example of a three-dimensional system in which an inverse cascade of energy, from the small to the large scales, can be formed. While usually understood as a byproduct of the typical bidimensionalization of rotating flows, the role of the three-dimensional modes is not completely comprehended yet. In order to shed light on this issue, we performed direct numerical simulations of rotating turbulence where the 2D modes falling in the plane perpendicular to rotation are removed from the dynamical evolution. Our results show that while the two-dimensional modes are key to…
We study the transition from fluid at rest to turbulence in a rotating water cylinder. We show that the energy, injected at a given height, is transported by inertial wave packets through the fluid volume. These waves propagate at velocities consistent with those calculated from linearized theory, even when they possess large amplitudes. A clear "front" in the temporal evolution of the energy power spectrum is detected, defining a time scale for energy transport at the linear wave speed in the system. Nonlinear energy transfer between modes is governed by a different time scale that can be muc…
An intrinsic feature of turbulent flows is an enhanced rate of mixing and kinetic energy dissipation due to the rapid generation of small-scale motions from large-scale excitation. The transfer of kinetic energy from large to small scales is commonly attributed to the stretching of vorticity by the strain-rate, but strain self-amplification also plays a role. Previous treatments of this connection are phenomenological or inexact, or cannot distinguish the contribution of vorticity stretching from that of strain self-amplification. In this paper, an exact relationship is derived which quantitat…
The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256^3 to 1024^3, are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity…
A shock-preserving finite volume solver with the generalized Lax-Friedrichs splitting flux for Morphing Continuum Theory (MCT) is presented and verified. The numerical MCT solver is showcased in a supersonic turbulent flow with Mach 2.93 over an $8^{\circ}$ compression ramp. The simulation results validated MCT with experiments as an alternative for modeling compressible turbulence. The required size of the smallest mesh cell for the MCT simulation is shown to be almost an order larger than that in a similar DNS study. The comparison shows MCT is a much more computationally friendly theory tha…
This brief is organized as follows. In Section 2 we introduce the filter-scale energy equations that lead to the subfilter-scale dissipation term P. We discuss the properties of the sources and sinks of kinetic energy, and identify our target features concerning an optimal inter-scale energy transfer (ISET) term. A similar analysis is performed in Section 3 for the kinetic energy associated with the subfilter velocities, and a new ISET term T is introduced. Comparisons between T and P for different flows and for various filters are offered in Section 4 and Section 5. Finally, we present our co…
In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both of the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonan…
The effects of different filtering strategies on the statistical properties of the resolved-to-sub-filter scale (SFS) energy transfer are analyzed in forced homogeneous and isotropic turbulence. We carry out a priori analyses of statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations (DNS) with up to $2048^3$ grid points as a function of the filter cutoff scale. In order to quantify the dependence of extreme events and anomalous scaling on the filter, we compare a sharp Fourier Galerkin projector, a Gaussian filter and a novel class of Ga…
The nonequilibrium dissipation behaviour discovered for decaying fractal square grid-generated turbulence is experimentally investigated using hot-wire anemometry in a wind tunnel. The previous results are consolidated and benchmarked with turbulence generated by regular square-mesh grids, designed to retain certain geometrical parameters of the fractal square grid. This comparison shows that the nonequilibrium behaviour is manifested in both fractal square grid- and regular square-mesh grid-generated turbulence for a downstream region during the turbulence decay up to the first few multiples …
Nonlinear interaction between different scales in turbulence results in both interscale and spatial transport of turbulent energy, and the role of such scale interactions in turbulent heat transfer mechanism is also of practical importance from the engineering viewpoint. In the present study, we investigate a turbulent plane Couette flow with passive-scalar heat transfer at the Prandtl number 0.71, in order to address the similarity/difference between the scale interactions in the velocity and temperature fields. The constant-temperature-difference boundary condition is used so that the mean v…
As a reduced representation of the nonlinear spectral fluxes of ideal invariants in incompressible magnetohydrodynamics, we construct a gradient-diffusion network model that combines phenomenological considerations and geometrical analysis of the exact nonlinear energy transfer function. The reduced-order representation of the conservative spectral transport of energy and cross-helicity is of port-Hamiltonian form, which highlights the flexibility and modularity of this approach. Numerical experiments with Reynolds numbers up to $~10^6$ yield clear power-law signatures of inertial-range energy…
We investigate non-equilibrium turbulence where the non-dimensionalised dissipation coefficient $C_{\varepsilon}$ scales as $C_{\varepsilon} \sim Re_{M}^{m}/Re_{\ell}^{n}$ with $m\approx 1 \approx n$ ($Re_M$ and $Re_{\ell}$ are global/inlet and local Reynolds numbers respectively) by measuring the downstream evolution of the scale-by-scale energy transfer, dissipation, advection, production and transport in the lee of a square-mesh grid and compare with a region of equilibrium turbulence (i.e. where $C_{\varepsilon}\approx \mathrm{constant}$). These are the main terms of the inhomogeneous, ani…
To fully evaluate a turbulent flow, Direct Numerical Simulation (DNS) is the most accurate method by far and requires considerable computational power and time; not optimum for industry standards. Developing an alternative model, providing results with reasonable accuracy would resolve this issue. Reynolds Averaged Navier Stokes (RANS) modeling has proven its worth in addressing this phenomenon. In this study, we investigated the RANS turbulence models from COMSOL for fully developed single-phase flow in a two-dimensional axisymmetric pipe domain with constant heating at the wall and periodic …
A robust energy transfer mechanism is found in nonlinear wave systems, which favours transfers towards modes interacting via non-resonant triads, applicable in meteorology, nonlinear optics and plasma wave turbulence. Transfer efficiency is maximal when the frequency mismatch of the non-resonant triad balances the system's nonlinear frequency: at intermediate levels of oscillation amplitudes an instability is triggered that explores unstable manifolds of periodic orbits, so turbulent cascades are most efficient at intermediate nonlinearity. Numerical simulations confirm analytical predictions.
The inertial-range properties of quasi-stationary hydrodynamic turbulence under solid-body rotation are studied via high-resolution direct numerical simulations. For strong rotation the nonlinear energy cascade exhibits depletion and a pronounced anisotropy with the energy flux proceeding mainly perpendicularly to the rotation axis. This corresponds to a transition towards a quasi-two-dimensional flow similar to a linear Taylor-Proudman state. In contrast to the energy spectrum along the rotation axis which does not scale self-similarly, the perpendicular spectrum displays an inertial range wi…
In this paper we describe the mode-to-mode energy transfers and energy fluxes of MHD turbulence. These energy transfers are very useful for understanding the turbulence dynamics, as well as for applications such as dynamo. We illustrate how the energy fluxes provide valuable insights into the mechanism of growth of the large-scale magnetic energy in dynamo.
The linked fluid dynamics videos depict Rayleigh-Taylor turbulence when driven by a complex acceleration profile involving two stages of acceleration interspersed with a stage of stabilizing deceleration. Rayleigh-Taylor (RT) instability occurs at the interface separating two fluids of different densities, when the lighter fluid is accelerated in to the heavier fluid. The turbulent mixing arising from the development of the miscible RT instability is of key importance in the design of Inertial Confinement Fusion capsules, and to the understanding of astrophysical events, such as Type Ia supern…
We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional MHD-turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from the large scales to kinetic energy at smaller scales, and the transfer of magnetic energy from the large scales to magnetic energy at smaller scales, are local, as is also found in the case of neutral fluids, and in a way that is compatible with Kolmogorov (1941) theory of turbulence. Howe…
In recent years, scale-by-scale energy transport in wall turbulence has been intensively studied, and the complex spatial and interscale transfer of turbulent energy has been investigated. As the enhancement of heat transfer is one of the most important aspects of turbulence from an engineering perspective, it is also important to study how turbulent heat fluxes are transported in space and in scale by nonlinear multi-scale interactions in wall turbulence as well as turbulent energy. In the present study, the spectral transport budgets of turbulent heat fluxes are investigated based on direct …
Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in theoretical and conceptual arguments. Whether the flow follows any or a combination of t…
Using large resolution numerical simulations of GK turbulence, spanning an interval ranging from the end of the fluid scales to the electron gyroradius, we study the energy transfers in the perpendicular direction for a proton-electron plasma in a slab magnetic geometry. In addition, to aid our understanding of the nonlinear cascade, we use an idealized test representation for the energy transfers between two scales, mimicking the dynamics of turbulence in an infinite inertial range. For GK turbulence, a detailed analysis of nonlinear energy transfers that account for the separation of energy …
The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this t…
In this paper we study the enstrophy transers in helical turbulence using direct numerical simulation. We observe that the helicity injection does not have significant effects on the inertial-range energy and helicity spectra ($\sim k^{-5/3}$) and fluxes (constants). We also calculate the separate contributions to enstrophy transfers via velocity to vorticity and vorticity to vorticity channels. There are four different enstrophy fluxes associated with the former channel or vorticity stretching, and one flux associated with the latter channel or vorticity advection. In the inertial range, the …
We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference than the conventional method by an order of magnitude. Moreover, a surprisingly small amount of learning is enough to infer the energy dissipation rate of the Navier-Stokes turbulence because we can, thanks to the small-scale universality of turbulence, transfer a large amount of the knowledge learned from turbulence data at lower Reynolds number.
Developing data-driven subgrid-scale (SGS) models for large eddy simulations (LES) has received substantial attention recently. Despite some success, particularly in a priori (offline) tests, challenges have been identified that include numerical instabilities in a posteriori (online) tests and generalization (i.e., extrapolation) of trained data-driven SGS models, for example to higher Reynolds numbers. Here, using the stochastically forced Burgers turbulence as the test-bed, we show that deep neural networks trained using properly pre-conditioned (augmented) data yield stable and accurate a …
The unit of nonlinear interaction in Navier-Stokes and the Magnetohydrodynamic (MHD) equations is a wavenumber triad ({\bf k,p,q}) satisfying ${\bf k+p+q=0}$. The expression for the combined energy transfer from two of these wavenumbers to the third wavenumber is known. In this paper we introduce the idea of an effective energy transfer between a pair of modes through the mediation of the third mode and then find an expression for it. In fluid turbulence, energy transfer takes place between a pair of velocity modes, whereas in MHD turbulence energy transfer takes places between (1) a pair of v…
In hydrodynamic and magnetohydrodynamic turbulence, expressions for the transfer rates rely on integrals over wavenumber triads $(\textbf{k,p,q})$ satisfying $\textbf{k+p+q=0}$. As an example $S_E^{uu}(\textbf{k|p,q})$ denotes the kinetic energy transfer rate to the mode $\textbf{k}$, from the two other modes in the triad, $\textbf{p}$ and $\textbf{q}$. As noted by Kraichnan (1958), in $S_E^{uu}(\textbf{k|p,q})$, what fraction of the energy transferred to the mode $\textbf{k}$ originated from $\textbf{p}$ and which from $\textbf{q}$ is unknown . Such an expression is thus incongruent with the …
Passive scalars in turbulent channel flows are investigated as canonical problem for heat and mass transfer in turbulent boundary-layer flows. The one-dimensional turbulence model is used to numerically investigate the Schmidt and Reynolds number dependence of the scalar transfer to a wall due to fluctuating wall-normal transport. First, the model is calibrated for low-order velocity statistics. After that, we keep the model parameters fixed and investigate low-order passive scalar statistics for a relevant Schmidt and Reynolds number range. We show that the model consistently predicts the bou…
We investigate experimentally the influence of a background rotation on the energy transfers in decaying grid turbulence. The anisotropic energy flux density, ${\bf F} ({\bf r}) = < δ{\bf u}\,(δ{\bf u})^2 >$, where $δ{\bf u}$ is the vector velocity increment over separation ${\bf r}$, is determined for the first time using Particle Image Velocimetry. We show that rotation induces an anisotropy of the energy flux $\nabla \cdot {\bf F}$, which leads to an anisotropy growth of the energy distribution $E({\bf r}) = < (δ{\bf u})^2 >$, in agreement with the Kármán-Howarth-Monin equation. Surprisingl…
Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of t…
Classically, large-scale forced turbulence is characterized by a transfer of energy from large to small scales via nonlinear interactions. We have investigated the changes in this energy transfer process in broad-band forced turbulence where an additional perturbation of flow at smaller scales is introduced. The modulation of the energy dynamics via the introduction of forcing at smaller scales occurs not only in the forced region but also in a broad range of length-scales outside the forced bands due to non-local triad interactions. Broad-band forcing changes the energy distribution and energ…
The inverse transfer of magnetic helicity is investigated through direct numerical simulations of large-scale-mechanically-driven turbulent flows in the isothermal ideal magnetohydrodynamics (MHD) framework. The mechanical forcing is either purely solenoidal or purely compressive and the turbulent steady-states considered exhibit root mean square (RMS) Mach numbers 0.1 $\lesssim$ M $\lesssim$ 11. A continuous small-scale electromotive forcing injects magnetic helical fluctuations, which lead to the build-up of ever larger magnetic structures. Spectral scaling exponents are observed which, for …
