Yu-Lu Liu | Searcharxiv

arXiv2024

Evolution of unpolarized transverse momentum dependent parton distributions of twist-3

We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal {O}(\alpha_s)$. Unlike the existing calculations in the literature, which are based on the background field method, we derive the evolution equations directly through diagram expansion. Additionally, instead of using the $\delta$ regulator, we employ the exponential regulator to regularize the rapidity divergences. We find that the evolutions of the four twist-3 TMD PDFs are governed by eight homogeneous equations. Our evolution kernels agree with one set of results in the literature, but differ from another by a sign. Considering the advantages of the exponential regulator in high-order perturbative calculations, our results are crucial for computing the twist-3 TMD PDFs at $\mathcal {O}(\alpha_s^2)$.

hep-ph↗

arXiv2011

Experimental Investigation of Longitudinal Space-Time Correlations of the Velocity Field in Turbulent Rayleigh-Bénard Convection

We report an experimental investigation of the longitudinal space-time cross-correlation function of the velocity field, $C(r,τ)$, in a cylindrical turbulent Rayleigh-Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while the Taylor's frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows [He & Zhang, \emph{Phys. Rev. E} \textbf{73}, 055303(R) (2006)] is valid for the present velocity field for all over the cell, i.e., the isocorrelation contours of the measured $C(r,τ)$ have a shape of elliptical curves and hence $C(r,τ)$ can be related to $C(r_E,0)$ via $r_E^2=(r-βτ)^2+γ^2τ^2$ with $β$ and $γ$ being two characteristic velocities. We further show that the fitted $β$ is proportional to the mean velocity of the flow, but the values of $γ$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell's central region. It is found that $β$ and $γ$ are approximately the same near the sidewall, while $β\simeq0$ at cell center.

physics.flu-dyn↗