Temporal decorrelations in compressible isotropic turbulence

Abstract

Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components, while the classic random sweeping model is proposed for solenoidal components. The swept-wave model shows that the temporal decorrelations in dilatational fluctuations are dominated by two physical processes: random sweeping and wave propagation. These models are supported by the direct numerical simulation of compressible isotropic turbulence, in the sense that all curves of normalized time correlations for different wave numbers collapse into a single one using the normalized time separations. The swept-wave model is further extended to account for a constant mean velocity. [7,8]. The space-time correlation models are used to predict the scalings of wave number or frequency energy spectra in turbulent flows [9][10][11][12]. The decorrelation processes are also relevant to the non-Gaussian statistics [13] and intermittency [14]. Their further applications can be found in turbulence generated noise [15]. The recently increasing studies on compressible isotropic turbulence raise such a question on the effects of compressibility on decorrelation processes [16][17][18]. In this Rapid Communication, we will study the decorrelation processes in compressible isotropic turbulence and propose a model for space-time correlations of dilatational components.A compressible turbulence is associated with two characteristic velocities: fluid velocity and sound speed, whereas an incompressible one is only associated with fluid velocity. Therefore, the decorrelation processes in compressible turbulence are very different from the incompressible one. A space-time correlation is the essential quantity to measure the decorrelation processes in turbulent flows. Three typical models exist for space-time correlations in turbulence theory. The first one is, as stated above, the random sweeping model for incompressible turbulence [1]. We will show that it cannot characterize the dilatational components in compressible turbulence. The second one is the Taylor frozen flow model [19]. It has been shown that this model is not a good approximation for dilatational components [20]. The third one is the linear wave propagation model [20]. This model has been used for dilatational components when compressible turbulence has a dominating mean velocity. However, it does not decrease with increasing temporal separation, which violates the nature of correlation functions.In this Rapid Communication, we will develop a space-time correlation model for compressible isotropic turbulence. This * hgw@lnm.imech.ac.cn is achieved by the Helmholtz decomposition: a velocity field can be split into the solenoidal and dilatational components. A swept-wave model will be developed for the dilatational components, while the solenoidal components are expected to follow the random sweeping model. The swept-wave model will be numerically validated and further us...

Space-Time Correlations and Dynamic Coupling in Turbulent Flows

“…This model predicts the main characteristics of space-time correlations of dilatation modes, namely, that the well-correlated regions oscillate in a preferential direction. Li et al (2013) generalized the linear-wave propagation model by including random sweeping effects. They argued that dilatation modes are swept by energy-containing eddies as they propagate at the speed of sound relative to the moving fluid.…”

Scaling of energy spectra in weakly compressible turbulence

“…where G dd (k, t) is the response function and R dd ( p, t) the space-time correlation for dilatational components, respectively. The recently developed swept-wave model [17] proposes the space-time correlations for dilatational modes as…”

“…However, if the decorrelation timescales are taken as the sweeping time of energy-contained eddies, it yields an incorrect prediction of scaling −3/2 [16]. For compressible turbulence, dilatational components display the different decorrelation timescales from solenoidal ones [2,17]. In this paper, we will find the decorrelation timescales from the space-time correlation models and use them to derive the scalings of compressible energy spectra.…”

Thermodynamic Performance and Optimal Analysis of A Multi-Level Quantum Dot Thermal Amplifier

“…[18][19][20] Other three-terminal thermoelectric devices which are driven by phonons, magnons, photons, also have been analyzed. [21][22][23][24][25][26][27][28][29] On the basis of the previous works, we propose a multi-level quantum dot thermal amplifier. The main focus in this paper is to analyze the thermodynamic performance characteristics and the optimal performance of a multi-level quantum dot thermal amplifier.…”