Intensity and Coherence Characteristics of a Radial Phase-Locked Multi-Gaussian Schell-Model Vortex Beam Array in Atmospheric Turbulence

The theoretical descriptions for a radial phase-locked multi-Gaussian Schell-model vortex (RPLMGSMV) beam array is first given. The normalized intensity and coherence distributions of a RPLMGSMV beam array propagating in free space and atmospheric turbulence are illustrated and analyzed. The results show that a RPLMGSMV beam array with larger total number N or smaller coherence length σ can evolve into a beam with better flatness when the beam array translating into the flat-topped profile at longer distance z and the flatness of the flat-topped intensity distribution can be destroyed by the atmospheric turbulence at longer distance z. The coherence distribution of a RPLMGSMV beam array in atmospheric turbulence at the longer distance will have Gaussian distribution. The research results will be useful in free space optical communication using a RPLMGSMV beam array.

Phase-space structure of cold dark matter haloes inside splashback: multistream flows and self-similar solution

ABSTRACT Using the motion of accreting particles on to haloes in cosmological N-body simulations, we study the radial phase-space structures of cold dark matter (CDM) haloes. In CDM cosmology, formation of virialized haloes generically produces radial caustics, followed by multistream flows of accreted dark matter inside the haloes. In particular, the radius of the outermost caustic called the splashback radius exhibits a sharp drop in the slope of the density profile. Here, we focus on the multistream structure of CDM haloes inside the splashback radius. To analyse this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting on to the haloes, we count their number of apocentre passages, which is then used to reveal the multistream flows of the dark matter particles. The resultant multistream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that $\sim \!30{{\ \rm per\ cent}}$ of the simulated haloes satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterize physical properties of the haloes, including the mass accretion rate and the size of the outermost caustic (i.e. the splashback radius). We discuss in detail the correlation of these fitting parameters and other measures directly extracted from the N-body simulation.

Phase-Lags' Radial Variations Between Velocity, Shear Stress, and Pressure Gradient in Ultrahigh Frequency Pulsating Turbulent Flows

Two-dimensional numerical simulations of wall-bounded turbulent pulsating flow driven by a sinusoidal velocity through a circular smooth tube are carried out. These computations for a Womersley number α ranged from 0.7 to 2069 and a dimensionless frequency ω+ ranged from 1.2×10−5 to 33.5. The aim of this study is to calculate the phase lag inside the unsteady turbulent boundary layer and across the tube. The phase lag of the velocity and shear stress with respect to the pressure gradient is deduced. Also, the instantaneous logarithmic layer and the turbulent parameters are analyzed. It is found that capturing the phase lag near the wall depends on resolving the Stokes layer thickness δst. At ultrahigh frequencies, the centerline velocity was delayed from the pressure gradient and wall shear stress by 45 deg and 90 deg, respectively. Consequently, the velocity and shear stress lagged behind the pressure gradient by 90 deg and 280 deg at the core of the tube, respectively, and by 45 deg at the wall. Thus, the trend of the radial phase lag increases toward the tubes center for ω+>0.06, which contrasts with that at low frequencies. When a reversed flow is caused by increasing the amplitude of the imposed oscillations, the phase lag is not affected noticeably by this increment. The radial phase lag is kept constant outside the oscillatory boundary layer at high frequencies because the radial gradient of the axial velocity has vanished.