Two deep learning (DL) models addressing the super-resolution (SR) reconstruction of turbulent flows from low-resolution coarse flow field data are developed. One is the static convolutional neural network (SCNN), and the other is the novel multiple temporal paths convolutional neural network (MTPC). The SCNN model takes instantaneous snapshots as an input, while the MTPC model takes a time series of velocity fields as an input, and it includes spatial and temporal information simultaneously. Three temporal paths are designed in the MTPC to fully capture features in different time ranges. A weight path is added to generate pixel-level weight maps of each temporal path. These models were first applied to forced isotropic turbulence. The corresponding high-resolution flow fields were reconstructed with high accuracy. The MTPC seems to be able to reproduce many important features as well, such as kinetic energy spectra and the joint probability density function of the second and third invariants of the velocity gradient tensor. As a further evaluation, the SR reconstruction of anisotropic channel flow with the DL models was performed. The SCNN and MTPC remarkably improve the spatial resolution in various wall regions and potentially grasp all the anisotropic turbulent properties. It is also shown that the MTPC supplements more under-resolved details than the SCNN. The success is attributed to the fact that the MTPC can extract extra temporal information from consecutive fluid fields. The present work may contribute to the development of the subgrid-scale model in computational fluid dynamics and enrich the application of SR technology in fluid mechanics.

The near-wall structures and statistics of fluctuating pressure (p′) in compressible turbulent channel flows (CTCF) with isothermal walls have been investigated by direct numerical simulations. Two typical cases for high bulk Mach number Ma = 3.83 and low one Ma = 1.56 are considered. A novel type of near-wall pressure structures named “alternating positive and negative structures (APNS)” is found in the high-Ma case based on the comprehensive analysis of spectra and dynamic mode decomposition of p′. These APNS of p′ are identified to have the streamwise and spanwise length scales of (λx/h, λz/h) ≈ (0.9, 1.5), where h is the channel half-height, and prefer to inhabit the low-speed wall streaks. It is also verified via a pressure splitting method that the APNS of p′ are dominated by the compressibility effects. Based on the linear stability analysis, the APNS of p′ can be intimately related to a linear stability eigenmode of the high-Ma CTCF and are sustained by the transient growth mechanism as the disturbances of the APNS length scales. Furthermore, these APNS of p′ offer an extra mechanism to generate the near-wall p′ for the high-Ma case. Moreover, it is found that the APNS of p′ have a dominating effect on the pressure-dilatation correlation and the production of Reynolds shear stress. The present study may provide a reliable way to achieve a better understanding and modeling of compressibility effects in the wall-bounded turbulence of high Ma.

Introduction.In recent years much work, both theoretical and experimental, has been done in the exploration of magnetogasdynamic or plasmadynamic phenomena, their engineering applications and their astrophysical implications. A good deal of this work, however, has included the approximation that the electric current always flows in the direction of the electric field vector. In reality, charged particles in a magnetic field do not move in straight lines, but rather tend to drift in a direction perpendicular to both the electric and magnetic fields, giving rise to the so-called Hall current or Hall effect. Because of the Hall effect, Ohm's law is modified in such a way that the electrical conductivity becomes a tensor quantity. The usual approximation of scalar conductivity is valid only when the collision frequency of the particles is so large that the particles have negligible time to drift across the magnetic field lines between collisions, i.e. when the cyclotron frequency of the particles is much less than their collision frequency. For cases where this condition is not met, the Hall effect must be taken into consideration. This paper extends our earlier results [1] to account for this phenomenon. We consider a dense plasma with a plasma frequency much greater than the cyclotron frequency of the particles present which, in turn, is much larger than the inverse of the characteristic flow time (i.e. the ratio of the free stream velocity to the characteristic length of the obstacle). In addition, the cyclotron frequency for the electrons is assumed to be of the same order of magnitude as the collision frequency between electrons and ions. We begin Sec. 2 by stating the equations pertinent to this problem. After linearization

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Steady, linearized, aligned-fields flow of a collisionless plasma past slender bodies is investigated. An approach similar to that of Chew, Goldberger, and Low is used to derive a consistent set of hydrodynamiclike equations for treating collisionless magnetogasdynamic flows in the presence of a strong magnetic field. The nature of the behavior predicted by this system of equations, in contrast to the original Chew-Goldberger-Low system, is similar to that predicted by the continuum equations of Sears and Resler. For certain specialized upstream conditions these two systems are identical. The close mathematical relationship that exists between them provides a convenient interpretation of collisionless plasmadynamic phenomena in terms of continuum variables.