Direct numerical simulation of downshift and inverse cascade for water wave turbulence

By means of direct numerical simulations (DNS) based on the integrodifferential Zakharov equation, we study the long-term evolution of nonlinear random water wave fields. For the first time, formation of powerlike Kolmogorov-type spectra corresponding to weak-turbulent inverse cascade is demonstrated by DNS, and the evolution in time of the resulting spectra is quantitatively investigated. The predictions of the statistical theory for water waves, both qualitative (formation of the direct and inverse cascades, self-similar behavior) and quantitative (the spectra exponents, specific shape of self-similar functions, the rate of time evolution) are found to be in good agreement with the DNS results, except for the initial part of the evolution, where the established statistical theory is not applicable yet and the evolution has a much faster time scale.     

Dynamical thermostatting and statistical ensembles

Dynamical thermostatting constitutes a procedure for computing thermodynamical mean values of classical dynamical systems that is of interest both from the practical and from the conceptual points of view. Here we extend and unify previous partial results, showing that the dynamical thermostatting approach can be implemented in order to simulate a wide family of statistical ensembles of general dynamical systems with a vanishing divergence and admitting an integral of motion. As a particular illustration, the thermostatting procedure is applied to power law-like maximum entropy ensembles.     

Direct numerical simulation of quasi-three-level passive Q-switched laser

The Runge-Kutta method is used to solve numerically the rate equations of quasi-three-level passive Q-switched laser directly without any approximate treatment of these differential equations. The 946 nm self-Q-switched Cr,Nd:YAG laser is chosen for example to describe the details. The time-dependence of intra-cavity photon density is obtained and its detailed real-time changing process is reproduced in numerical solution. The curves of laser output parameters such as average output power, pulse width, repetition rate, pulse energy and peak power changing with different cavity conditions such as pump power, output coupler reflectivity, Cr,Nd:YAG crystal length, Nd³⁺ ion and Cr⁴⁺ ion concentrations are simulated according to direct numerical solution rather than analytical expressions. This direct numerical simulation method can be widely used to describe and optimize the quasi-three-level passive Q-switched laser theoretically.     

Self-similarity degree of deformed statistical ensembles

We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. The related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree q fixed by the condition of invariance under (n+1)-fold action of the related dilatation operator. In slightly deformed phase space, we find the homogeneous function is defined with the linear dependence at n=0, whereas the self-similarity degree equals the gold mean at n=1, and q→n in the limit n→∞. Dilatation of the homogeneous function is shown to decrease the self-similarity degree q at n>0.     

Landauer's principle and non-equilibrium statistical ensembles

Landauer's principle is fundamental for the physics of information. It establishes the least amount of energy that needs to be dissipated in order to erase a bit of information. Using the Beck-Cohen representation of statistical ensemble distributions, we explore an extension of Landauer's principle to systems out of equilibrium.     

Constant pressure ensembles in statistical mechanics

A new statistical procedure is described for obtaining the thermodynamic properties of a molecular system directly as functions of the pressure. This procedure differs in principle from that suggested by Guggenheim [3] in that the members of the representative ensemble are envisaged as being in constant mechanical equilibrium with the exterior. The quantal and classical theories of petit micro-canonical and canonical ensembles of systems at constant pressure are presented, and shown to lead to the established results for perfect and imperfect gases, and for a hypothetical one-dimensional system. The conclusion that the statistical compressibility of a molecular system is essentially positive follows directly from the theory. An alternative procedure which leads to a more satisfactory form of Guggenheim's equation is also described, and its relation to the new approach is shown.     

毫米波回旋速调管放大器的自洽非线性数值模拟

为了实现回旋速调管放大器的快速设计,基于经典的回旋管的稳态单模非线性理论方法,开展了回旋速调管放大器的束波作用效率的理论模拟研究。由于单模理论无法匹配回旋速调管放大器的输入腔、中间腔两端的突变边界条件,所以输入腔与中间腔都只能采用给定场法进行求解。回旋速调管的输出腔的功率输出端通常采用缓变结构,这种腔体可以采用单模自洽理论进行求解。对两腔毫米波回旋速调管放大器进行了理论模拟,并与商业粒子模拟软件的结果进行对比,验证了该数值理论模拟方法的有效性。     

Direct numerical simulation of diluted combustion by evaporating droplets

Diluted combustion has been studied using DNS in a three-dimensional temporally developing reacting shear-layer with the oxidizer stream laden with evaporating droplets. The gaseous phase is described in the Eulerian frame while the discrete droplet phase is treated in the Lagrangian frame, with strong two-way coupling between the two phases through mass, momentum and energy exchange. Grid-resolution-independent results have been obtained in cases without and with droplets. A comprehensive parametric study has been conducted by varying the initial Stokes number (St₀) and mass loading ratio (MLR₀). Detailed field analysis has been conducted to examine the complex nonlinear interactions among droplet dynamics, evaporation, turbulence and combustion, and so on. Effects of evaporating droplets on averaged flow and combustion quantities have also been presented. In particular, the conditional scalar dissipation rate is found to be enhanced by evaporating droplets, which suggests that they can promote micromixing and combustion under certain conditions, in addition to their roles in combustion suppression. The transport equation for the mixture fraction variance has been analyzed, with a focus on the vaporization-related source terms. Such source terms exhibit more complex local variations in the present shear-flow non-premixed flame configuration, compared with the case in the homogeneous decaying turbulence configuration of Réveillon and Vervisch (2000).     

Direct numerical simulation of spray flame/acoustic interactions

Interactions between conical spray flames and sinusoidal velocity modulations due to the propagation of acoustic waves have been studied thanks to direct numerical simulations (DNS). A 2D axi-symmetric configuration has been used to capture the evolution of the pulsating laminar flames. The DNS solver has been coupled with a Lagrangian model to account for the dispersion and evaporation of the liquid fuel in the computational domain. Four main configurations, with a unitary global equivalence ratio, have been studied. Apart from a gaseous reference case, one polydispersed and two monodispersed Bunsen-type injections with various droplets density and inertia have been simulated. DNS results are in good agreement with experimental data. For significant acoustic Stokes numbers, results showed a double effect of the modulations on the flame: a direct disturbance of the flame front and a secondary impact through the local variation of the mixture fraction due to droplets preferential segregation.     

Direct numerical simulation of the turbulent MHD channel flow at low magnetic Reynolds number for electric correlation characteristics

Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.     

Wave scattering by statistical ensembles of inhomogeneities

It is incorrect to solve the problem of wave scattering by clouds of passive reflectors by reducing this problem to one of radiation of a cloud of active radiators.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 1, pp. 125–128, January, 1970.The author thanks F. P. Tarasenko for useful discussions.     

Direct reactions and hauser-feshbach theory II numerical methods and statistical tests

Numerical methods and statistical tests are described which form part of a recent paper dealing with Hauser-Feshbach theory in the presence of direct reactions.     

Direct numerical simulation of scalar transport using unstructured finite-volume schemes

An unstructured finite-volume method for direct and large-eddy simulations of scalar transport in complex geometries is presented and investigated. The numerical technique is based on a three-level fully implicit time advancement scheme and central spatial interpolation operators. The scalar variable at cell faces is obtained by a symmetric central interpolation scheme, which is formally first-order accurate, or by further employing a high-order correction term which leads to formal second-order accuracy irrespective of the underlying grid. In this framework, deferred-correction and slope-limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation. The accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori. A direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method. In spite of the linear character of the scalar transport equation, the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral-properties of interpolation schemes. Although the results show an improved spectral-resolution and greater spatial-accuracy for the high-order operator in the analysis of basic scalar transport problems, the low-order central scheme is found superior for high-fidelity simulations of turbulent scalar transport.     

热对流条件下双颗粒沉降的直接数值模拟

在任意拉格朗日-欧拉(ALE)算法模拟等温惰性颗粒两相流的基础上,增加对能量方程的联立求解,对热对流条件下双颗粒的沉降进行了直接数值模拟.结果表明:双颗粒在等温流体、热流体和冷流体中运动形式是不同的,造成不同的主要因素是热对流引起了颗粒不同的动态尾迹,在热流体中颗粒尾部形成了涡的脱落,在冷流体中颗粒尾部形成了羽流.     

Direct numerical simulation of passive scalar in decaying compressible turbulence

1IntroductionDirectnumericalsimulation(DNS)becomesanimportanttoolinrecentresearchofturbulence[1].DNSofcompressibleturbulenceismoredifficultthanthatoftheincompressibleturbulence.WhentheturbulentMachnumberisgreaterthan0.3theshockletsmayappearinthecompressibleturbulentflowfields.Thereasonandmechanismofshockletsexistencearenotclearyet.TheturbulentMachnumberinDNScannotbeveryhighwiththepresentexistingnumericalmethodsandcomputerresource.Fortheproblemofcompressibleisotropicturbulencewiththeinitia…