For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the Fourier space, which are formed by pairs of particles. These bundles are not present in the Boltzmann, Euler and Navier-Stokes equations, because they are destroyed by the Bogoliubov-Born-Green-Kirkwood-Yvon formalism. However, measurements of the flow can detect certain bulk effects shared across these bundles, such as the power scaling of the kinetic energy. We estimate the scaling effects produced by two types of potentials: the Thomas-Fermi interatomic potential (as well as its variations, such as the Ziegler-Biersack-Littmark potential), and the electrostatic potential. In the near-viscous inertial range, our estimates yield the inverse five-thirds power decay of the kinetic energy for both the Thomas-Fermi and electrostatic potentials. The electrostatic potential is also predicted to produce the inverse cubic power scaling of the kinetic energy at large inertial scales. Standard laboratory experiments confirm the scaling estimates for both the Thomas-Fermi and electrostatic potentials at near-viscous scales. Surprisingly, the observed kinetic energy spectrum in the Earth atmosphere at large scales behaves as if induced by the electrostatic potential. Given that the Earth atmosphere is not electrostatically neutral, we cautiously suggest a hypothesis that the atmospheric kinetic energy spectra in the inertial range are indeed driven by the large scale flow via the electrostatic potential coupling.
We present convincing evidence of a direct connection between the pressure drop, viscous dissipation, and the turbulent energy spectrum. We use this finding to explain Nikuradse's experimental results of pressure drop for turbulent flows in rough pipes, in terms of a modified Kolmogorov length scale that varies with the surface roughness. Furthermore, we use Laufer's measurements of turbulent energy spectra in pipe flow to calculate -- to a good approximation -- the turbulent component of the pressure drop directly from an averaged turbulent energy spectrum. We also show that the incompressibi…
Direct numerical simulations (DNS) of turbulent channel flows up to $Re_τ \approx 1000$ are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber-frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber-frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping…
The role of turbulent effects for dynamos in the Sun and stars continues to be debated. Mean-field (MF) theory provides a broadly used framework to connect these effects to fundamental magnetohydrodynamics. While inaccessible observationally, turbulent effects can be directly studied using global convective dynamo (GCD) simulations. We measure the turbulent effects in terms of turbulent transport coefficients, based on the MF framework, from an exemplary GCD simulation using the test-field method. These coefficients are then used as an input into an MF model. We find a good agreement between t…
Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory
J. Nikuradse在20世纪30年代进行了粗糙管道中湍流摩擦的经典实验。70年后，他们继续挑战理论。在这里，我们使用Kolmogórov的现象学理论来模拟Nikuradse的实验，该理论被广泛认为只适用于高度理想化的流动。我们的研究结果包括了Blasius和Strickler的经验标度，并且在其他方面与实验有着细微的定性一致性;它们表明，现象学理论可能与其他实际感兴趣的流动有关;它们揭示了实验和理论湍流这两个里程碑之间存在着密切的联系。
We investigate the statistics of phase fluctuations of an acoustic wave propagating through a turbulent flow in line of sight (LOS) configuration. Experiments are performed on a closed von Karman swirling flow whose boundaries are maintained at a constant temperature. In particular, we analyze the root mean square (RMS) and the power spectrum density (PSD) of phase fluctuations. A model is developed and analytical predictions obtained for these quantities using geometrical acoustics are shown to be in agreement with experimental observations.
The modeling of surface pressure wave number spectra beneath a turbulent boundary layer is reviewed and reconsidered in terms of the vorticity in the flow. Using a solution based on the vorticity equation and Squires theorem, which was originally given by Chase(1991), it is shown that the complete solution for surface pressure spectrum can be specified using the non-linear turbulence-turbulence interaction terms as sources. It is then shown that the surface pressure can be directly related to the vorticity in the flow. The results are checked against a Direct Numerical Simulation of a channel …
We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. In spite of the strong anisotropy of the forcing, we find that turbulence recovers almost complete isotropy at small scales. Nonetheless, the signature of the forcing remains in the mean flow (averaged over time and over the homogeneous direction) and this allows to introduce a friction factor, whose dependence on the Reynolds number is investigated. We further find that the flow is characterized by large temporal fluc…
Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived ana…
The ubiquitous turbulence in astrophysical plasmas is important for both magnetic reconnection and reconnection acceleration. We study the particle acceleration during fast 3D turbulent reconnection with reconnection-driven turbulence. Particles bounce back and forth between the reconnection-driven inflows due to the mirror reflection and convergence of strong magnetic fields. Via successive head-on collisions, the kinetic energy of the inflows is converted into the accelerated particles. Turbulence not only regulates the inflow speed but also introduces various inflow obliquities with respect…
We consider the effects of thermal noise on the Batchelor-Kraichnan theory of high Schmidt-number mixing in the viscous-dissipation range of turbulent flows. Using fluctuating hydrodynamics for a binary fluid mixture at low Mach numbers, we justify linearization around the deterministic Navier-Stokes solution in the dissipation range. For the latter solution we adopt the standard Kraichnan model and derive asymptotic high-Schmidt limiting equations for the concentration field, in which the thermal velocity fluctuations are exactly represented by a Gaussian random velocity which is white in tim…
