arXiv subjects

Zhen-Su She

Publications and source records attributed to Zhen-Su She.

At least 19 recordsLinked to original sources

arXiv2025

Quantifying non-equilibrium pressure-gradient turbulent boundary layers through a symmetry-based framework

This study establishes a symmetry-based framework to quantify non-equilibrium processes in complex pressure gradient (PG) turbulent boundary layers (TBLs), using a Lie-group-informed dilation-symmetry-breaking formalism. We derive a universal multilayer defect scaling law for the evolution of total shear stress (TSS). The law shows that gradually varying adverse pressure gradients (APGs) break the dilation symmetry in the two-layer defect scaling of equilibrium TSS, leading to three-layer TSS structures. For abrupt PG transitions, we identify boundary-layer decoupling into: 1) an equilibrium internal boundary layer, and 2) a history-dependent outer flow, arising from disparate adaptation timescales. The framework introduces a unified velocity scale mapping non-equilibrium TSS to canonical zero-PG scaling. Validation spans different aerodynamic systems, including developing APG on airfoils, APG-to-favorable-PG transition on a Gaussian bump, and favorable PG to rapidly amplifying APG in a converging-diverging channel. The work enables improved prediction of non-equilibrium PG TBL behavior through unified characterization of stress evolution dynamics, providing new physics-based parameterizations that could promote machine learning of complex wall-bounded turbulent flows.

physics.flu-dyn↗

arXiv2023

Quantifying equilibrium pressure-gradient turbulent boundary layers via a symmetry approach

We propose a theory for predicting the mean velocity and Reynolds shear and normal stresses profiles in the wake region of equilibrium adverse pressure-gradient (PG, APG) turbulent boundary layers (TBLs). Firstly, we explore the PG-induced dilation-symmetry-breaking of the total stress $\tau^+$ to construct a modified defect power law for $\tau^+$. Crucially, a PG stress $P_0^+$ is identified, which quantifies the APG-induced total-stress overshoot and is proportional to the Clauser PG parameter $\beta$. The wall-normal location with peak stress is predicted. The total stress profiles with arbitrary $\beta$ are transformed into an invariant profile, which is the ultimate state of the total stress at infinite $\beta$. This transformation is equivalent to the outer scaling of the Reynolds shear stress recently-proposed by Wei & Knopp (JFM, 2023). The Reynolds normal stresses are predicted accordingly based on the similarity of the Reynolds shear and normal stresses in the wake region. Secondly, a defect power law is proposed for the stress and kinetic energy lengths in the wake region. Two critical parameters in the defect power law are identified to depend on $\beta$ and determine the length profiles. With the total stress and stress length models, the streamwise mean-velocity profile is predicted. Especially, an invariant mean velocity profile is derived, which describes the ultimate state of the mean velocity in the wake region at infinite $\beta$. This invariant profile is also equivalent to the outer scaling of Wei & Knopp. The theory also predicts the variation of the Coles' wake parameter $\Pi$ with $\beta$, in close agreement with the empirical relation that correlates hundreds of experimental data. The predictions are validated with five published DNS, LES, and experimental databases on the equilibrium APG TBLs.

physics.flu-dyn↗

arXiv2023

Multi-layer analytic solution for k-ω model equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering CFD, the k-ω model has not been fully understood theoretically because of its high non-linearity and complex model parameter setting. Here, a multi-layer analytic expression is postulated for two lengths (stress and kinetic energy lengths), yielding an analytic solution for the k-ω model equations in pipe flow. Approximate local balance equations are analyzed to determine key parameters in the solution, which are shown to be rather close to the empirically-measured values from numerical solution of the Wilcox k-ω model, hence the analytic construction is fully validated. Furthermore, the predictions of three critical locations in the model's three transition functions are validated, which enables an in-depth understanding of the parameter setting of the model. These results provide clear evidence that the k-ω model sets in it a multi-layer structure, which is similar to but different, in some insignificant details, from the Navier-Stokes turbulence. This finding explains why the k-ω model is so popular, especially in computing the near-wall flow. Finally, the analysis is extended to a newly-refined k-ω model called SED k-ω, showing that the SED k-ω model has improved the multi-layer structure in the outer flow but preserved the setting of the k-ω model in the inner region.

physics.flu-dyn↗

arXiv2023

A symmetry-based theory for the mean velocity profiles of turbulent boundary layers subjected to pressure gradient and historical turbulence effects

The pressure gradient has a significant influence on the mean-flow properties of turbulent boundary layers. Conventional analytical studies on PG turbulent boundary layers are conducted separately for the viscous sub-layer and overlap layer only, with the remaining large portion of the boundary layers less described theoretically. Here a symmetry approach is proposed for modeling whole mean velocity profiles of turbulent boundary layers with both PG and historical turbulence effects. First, a modified defect law is constructed for the total stress profile to capture the Reynolds stress overshoot owing to the PG and historical turbulence effects. Second, the multi-layered power-law formulation of the stress length function in the structural ensemble dynamics theory of the canonical zero-PG turbulent boundary layer (J. Fluid Mechanics, 2017, Vol. 827, pp. 322-35) is extended to describe the PG turbulent boundary layer. Comparing with that of the zero-PG turbulent boundary layers, the stress length of the PG turbulent boundary layer possesses a variable (in magnitude and extension) plateau in the defect layer, which are characterized by three parameters: the buffer layer thickness, the (nominal) K'arm'an constant, and the defect-law exponent. In the case of intense turbulence from upstream flow, a newly-identified "bulk turbulent layer" replaces the conventional buffer layer and overlap layer. With the above formulations, the entire mean velocity profile is predicted analytically, and validated to accurately describe the published direct numerical simulation data on a two-dimensional separation bubble. The study provides a novel method to parameterize PG turbulent boundary layers with high accuracy and sound physics, and paves a way for quantifying complicated boundary-layer flows.

physics.flu-dyn↗

arXiv2019

Boundary layer structure in turbulent Rayleigh-Bénard convection in a slim box

The logarithmic law of mean temperature profile has been observed in different regions in Rayleigh-Bénard turbulence. However, how thermal plumes correlate to the log law of temperature and how the velocity profile changes with pressure gradient are not fully understood. Here, we performed three-dimensional simulations of Rayleigh-Bénard turbulence in a slim-box without the front and back walls with aspect ratio, $L:D:H=1:1/6:1$, in the Rayleigh number $Ra=[1\times10^8, 1\times10^{10}]$ for Prandtl number $Pr=0.7$. The velocity profile is successfully quantified by a two-layer function of a stress length, $\ell_u^+\approx \ell_0^+(z^+)^{3/2}\left[1+\left({z^+}/{z_{sub}^+}\right)^4\right]^{1/4}$, as proposed by She et al. (She 2017), though neither a Prandtl-Blasius-Pohlhausen type nor the log-law is seen in the viscous boundary layer. In contrast, the temperature profile in the plume-ejecting region is logarithmic for all simulated cases, being attributed to the emission of thermal plumes. The coefficient of the temperature log-law, $A$ can be described by composition of the thermal stress length $\ell^*_θ$ and the thicknesses of thermal boundary layer $z^*_{sub}$ and $z^*_{buf}$, i.e. $A\simeq z^*_{sub}/\left(\ell^*_{θ0}{z^*_{buf}}^{3/2}\right)$. The adverse pressure gradient responsible for turning the wind direction contributes to thermal plumes gathering at the ejecting region and thus the log-law of temperature profile. The Nusselt number scaling and local heat flux of the present simulations are consistent with previous results in confined cells. Therefore, the slim-box RBC is a preferable system for investigating in-box kinetic and thermal structures of turbulent convection with the large-scale circulation on a fixed plane.

physics.flu-dyn↗

arXiv2017

Nonlinear transport by vortex tangles in cuprate high-temperature superconductors

A unified model of vortex tangles is proposed to describe unconventional transport in cuprate high-temperature superconductors, which not only captures the fast vortices scenario at low density, but also predicts a novel mechanism of core-core collisions in dense vortex fluid regime. The theory clarifies the nature of vortex fluctuations being the quantum fluctuations of holes and then resolves a discrepancy of two orders of magnitude of Anderson's damping model $\hbar n_v$, with right prediction of the nonlinear field dependence of the resistivity $ρ=ρ_n(B+B_T)/(B_0+B+B_T)$ and the Nernst effect, validated by data of several samples. Consequently, Anderson's vortex tangles concept and phase fluctuation scenario of pseudogap are verified quantitatively.

cond-mat.supr-con↗

arXiv2017

A quantitative description of Nernst effect in high-temperature superconductors

A quantitative vortex-fluid model for flux-flow resistivity $ρ$ and Nernst signal $e_N$ in high-temperature superconductors (HTSC) is proposed. Two kinds of vortices, magnetic and thermal, are considered, and the damping viscosity $η$ is modeled by extending the Bardeen-Stephen model to include the contributions of flux pinning at low temperature and in weak magnetic fields, and vortex-vortex collisions in strong magnetic fields. Remarkably accurate descriptions for both Nernst signal of six samples and flux flow resistivity are achieved over a wide range of temperature $T$ and magnetic field $B$. A discrepancy of three orders of magnitude between data and Anderson's model of Nernst signal is pointed out and revised using experimental values of $η$ from magnetoresistance. Furthermore, a two-step procedure is developed to reliably extract, from the Nernst signal, a set of physical parameters characterizing the vortex dynamics, which yields predictions of local superfluid density $n_s$, the Kosterlitz coefficient $b$ of thermal vortices, and upper critical field and temperature. Application of the model and systematic measurement of relevant physical quantities from Nernst signal in other HTSC samples are discussed.

cond-mat.supr-con↗

arXiv2016

Predictions of canonical wall bounded turbulent flows via a modified $k-ω$ equation

A major challenge in computation of engineering flows is to derive and improve turbulence models built on turbulence physics. Here, we present a physics-based modified $k-ω$ equation for canonical wall bounded turbulent flows (boundary layer, channel and pipe), predicting both mean velocity profile (MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy over a wide range of Reynolds number ($Re$). The result builds on a multi-layer quantification of wall flows, which allows a significant modification of the $k-ω$ equation. Three innovations are introduced: First, an adjustment of the Karman constant to 0.45 is set for the overlap region with a logarithmic MVP. Second, a wake parameter models the turbulent transport near the centerline. Third, an anomalous dissipation factor represents the effect of a meso layer in the overlap region. Then, a highly accurate (above 99\%) prediction of MVPs is obtained in Princeton pipes, improving the original model prediction by up to 10\%. Moreover, the entire SMKP, including the newly observed outer peak, is predicted. With a slight change of the wake parameter, the model also yields accurate predictions for channels and boundary layers.

physics.flu-dyn↗

arXiv2016

Bulk flow scaling for turbulent channel and pipe flows

We report a theory deriving bulk flow scaling for canonical wall-bounded flows. The theory accounts for the symmetries of boundary geometry (flat plate channel versus circular pipe) by a variational calculation for a large-scale energy length, which characterizes its bulk flow scaling by a simple exponent, i.e. $m=4$ for channel and 5 for pipe. The predicted mean velocity shows excellent agreement with several dozen sets of quality empirical data for a wide range of the Reynolds number (Re), with a universal bulk flow constant $κ\approx0.45$. Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.

physics.flu-dyn↗

arXiv2016

Analytic prediction for planar turbulent boundary layers

Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions are the friction velocity $u_τ$: ${ U_e/u_τ}\approx 2.22\ln Re_x+2.86-3.83\ln(\ln Re_x)$; the boundary layer thickness $δ_e$: $x/δ_e \approx 7.27\ln Re_x-5.18-12.52\ln(\ln Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_θ=4.94[{(\ln {{\mathop{\rm Re}\nolimits} _θ } + 1.88)^2} + 1]$, all in good agreement with empirical data.

physics.flu-dyn↗

arXiv2015

Quantifying wall turbulence via a symmetry approach. Part I. A Lie group theory

First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer - TBL) is of great importance from both physics and engineering standpoints. Here (Part I), we present a symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. The new approach begins by identifying a set of order functions (e.g. stress length, shear-induced eddy length), in analogy with the order parameter in Landau's mean-field theory, which aims at capturing symmetry aspects of the fluctuations (e.g. Reynolds stress, dissipation). The order functions are assumed to satisfy a dilation group invariance - representing the effects of the wall on fluctuations - which allows us to postulate three new kinds of invariant solutions of the mean momentum equation (MME), focusing on group invariants of the order functions (rather than those of the mean velocity as done in previous studies). The first - a power law solution - gives functional forms for the viscous sublayer, the buffer layer, the log-layer, and a newly identified central `core' (for channel and pipe, but non-existent for TBL). The second - a defect power law of form $1-r^{m}$ ($r$ being the distance from the center line) - describes the `bulk zone' (the region of balance between production and dissipation). The third - a relation between the group invariants of the stress length function and its first derivative - describes scaling transition between adjacent layers. A combination of these three expressions yields a multi-layer formula covering the entire flow domain, identifying three important parameters: scaling exponent, layer thickness, and transition sharpness. All three kinds of invariant solutions are validated, individually and in combination, by data from direct numerical simulations (DNS).

physics.flu-dyn↗

arXiv2014

Prediction of temperature distribution in turbulent Rayleigh-Benard convection

A quantitative theory is developed for the vertical mean temperature profile (MTP) in turbulent Rayleigh-Benard convection (RBC), which explains the recent experimental and numerical observations of a logarithmic law by Ahlers et al.(Phys. Rev. Lett., 2012). A multi-layer model is formulated and quantified, whose predictions agree with DNS and experimental data for the Rayleigh-number (Ra) over seven decades. In particular, a thermal buffer layer follows a 1/7 scaling like the previously postulated mixing zone (Procaccia et al, Phys. Rev. A,1991), and yields a Ra-dependent log law constant. A new parameterization of Nu(Ra) dependence is proposed, based on the present multi-layer quantification of the bulk MTP.

physics.flu-dyn↗

arXiv2012

A multi-layer model for turbulent kinetic energy in pipe flows

A multi-layer model of an energy length function is developed by employing recent results of the authors. The theory predicts the complete, mean streamwise turbulent kinetic-energy profile (MKP), in good agreement with empirical data for a wide range of Reynolds numbers (Re). In particular, a critical $Re_τ$ is predicted, beyond which a scaling anomaly appears and MKP develops a second peak.

physics.flu-dyn↗

arXiv2012

Logarithmic distribution of mean velocity and turbulent kinetic energy in a pipe flow

A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over a wide range of Re yield 0.45 to be the universal Karman constant. A new spatial invariant characterizing outer dynamics is discovered and validated by reliable experimental data. The theory predicts the mean velocity profile (MVP) with 99% accuracy for high Re experimental data (up to 40 millions), and offers a quantitative explanation for recent observation of logarithmic kinetic energy distribution by Hullmak et al. (Phys. Rev. Lett. 108, 094501).

physics.flu-dyn↗

arXiv2011

Karman constant and accurate mean flow prediction in a turbulent pipe

The Karman constant κ- widely used in atmospheric science and engineering turbulence modelling, and proposed by Prandtl in 1925 and von Karman in 1930 to describe the mean velocity of a turbulent wall-bounded flow - leads to a logarithmic profile in an overlap region near the wall. For over eighty years, its value was believed to be ~0.41. But more recently, many argue that it is not a constant, because of measured variations in different flows and at different Reynolds numbers (Re). Here, a multi-layer analytic theory is shown to lead to a re-interpretation of κas a global constant for both the overlap region and outer flow, and to yield a new method for its measurement. The newly determined value is 0.45 for both channel and pipe. It is shown that this new κ, together with other wall constants, yields a 99% accuracy in the prediction of mean velocity data at all points in high Re (up to 40 million) pipe flow. The theory also describes finite Re effect, and discovers a transition at the friction Re (i.e. Re_τ)=5000. An accurate model for the prediction of turbulent transport in canonical pipe and channel flows is achieved here, and we propose the model to be valid for a wide class of turbulent flows.

physics.flu-dyn↗

arXiv2004

Characterizing large scale base composition structures of genomes

Intermittent density fluctuations of nucleotide molecules (adenine, guanine, cytosine and thymine) along DNA sequences are studied in the framework of a hierarchical structure (HS) model originally proposed for the study of fully developed turbulence [She and Leque, Phys. Rev. Lett. 72}, 336 (1994)]. Large scale (10^3 < \ell < 10^5 bp) base density fluctuation is shown to satisfy the HS similarity. The derived values of a HS parameter $β$ from a large number of genome data (including Bacteria, Archaea, human chromosomes and viruses) characterize different biological properties such as strand symmetry, phylogenetic relations and horizontal gene transfer. It is suggested that the HS analysis offers a useful quantitative description for heterogeneity, sequence complexity and large scale structures of genomes.

q-bio.GN↗

arXiv2004

Hierarchical structure description of spatiotemporal chaos

We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky kinetics, the two-dimensional complex Ginzburg-Landau equation and the modified FitzHugh-Nagumon equation, which all show complex dynamics of spirals and defects. We demonstrate that the spatial-temporal fluctuation fields in the above mentioned systems all display the HS similarity property originally proposed for the study of fully developed turbulence [Z.-S. She and E. Leveque, Phys. Rev. Lett. {\bf 72}, 336 (1994)]. The derived values of a HS parameter $β$ from experimental and numerical data in various physical regimes exhibit consistent trends and characterize the degree of turbulence in the systems near the transition, and the degree of heterogeneity of multiple disorders far from the transition. It is suggested that the HS analysis offers a useful quantitative description for the complex dynamics of two-dimensional spatiotemporal patterns.

nlin.PS↗

arXiv2001

Extended Self-Similarity and Hierarchical Structure in Turbulence

It is shown that the two remarkable properties of turbulence, the Extended Self-Similarity (ESS) [R. Benzi {\it et al.}, Phy. Rev. E {\bf 48}, R29, (1993)] and the She-Leveque Hierarchical Structure (SLHS) [Z.S. She and E. Leveque, Phy. Rev. Lett. {\bf 72}, 336, (1994)] are related to each other. In particular, we have shown that a generalized hierarchical structure together with the most intense structures being shock-like give rise to ESS. Our analysis thus suggests that the ESS measured in turbulent flows is an indication of the shock-like intense structures. Results of analysis of velocity measurements in a pipe-flow turbulence support our conjecture.

nlin.CD↗