arXiv subjects

You-sheng Zhang

Publications and source records attributed to You-sheng Zhang.

4 recordsLinked to original sources

arXiv2026

Generalized Reynolds Analogy for Compressible Wall Turbulence: Unified Velocity--Temperature Relations from Mean to Fluctuating Field

The Reynolds analogy between velocity and temperature fields is a central problem in the statistical theory of compressible wall turbulence. The generalized Reynolds analogy (GRA) established by the author describes the mean velocity--temperature relation accurately, but a self-consistent closure for the fluctuating field has remained elusive. Here, the instantaneous similarity relation that the generalized total enthalpy (minus its wall value) is proportional to the local velocity is shown to close both fields at once. The mean field reproduces the GRA solution, while the fluctuating field yields the closed relation $T'_{rms}/u'_{rms} = f(Re_τ,\Pr)\,\Pr_m^{-1/2}\,|\partial\bar{T}/\partial\bar{u}|$, where the prefactor $f$ is derived from the universal cascade dynamics of turbulence and the Obukhov--Corrsin theory, without adjustable parameters. The relation recovers the refined strong Reynolds analogy (RSRA) of Huang et al.~(2025), the most accurate benchmark to date, recasting it from an empirical relation into a consequence of universality principles and explaining the origin of its fitted prefactor $f=1.09$; and its ratio to boundary-layer and channel direct numerical simulation (DNS) data collapses onto unity across Mach numbers ($2.25$--$14$), Prandtl numbers ($0.025$--$1$) and wall thermal conditions, with an overall accuracy of about $5\%$.

physics.flu-dyn↗

arXiv2017

Competition evolution of Rayleigh-Taylor bubbles

Material mixing induced by a Rayleigh-Taylor instability occurs ubiquitously in either nature or engineering when a light fluid pushes against a heavy fluid, accompanying with the formation and evolution of chaotic bubbles. Its general evolution involves two mechanisms: bubble-merge and bubble-competition. The former obeys a universa1 evolution law and has been well-studied, while the latter depends on many factors and has not been well-recognized. In this paper, we establish a theory for the latter to clarify and quantify the longstanding open question: the dependence of bubbles evolution on the dominant factors of arbitrary density ratio, broadband initial perturbations and various material properties (e.g., viscosity, miscibility, surface tensor). Evolution of the most important characteristic quantities, i.e., the diameter of dominant bubble $D$ and the height of bubble zone $h$, is derived: (i) the $D$ expands self-similarly with steady aspect ratio $β\equiv D/h \thickapprox (1{\rm{ + }}A)/4$, depending only on dimensionless density ratio $A$, and (ii) the $h$ grows quadratically with constant growth coefficient $α\equiv h/(Ag{t^2}) \thickapprox [2ϕ/{\ln}(2{η_{\rm{0}}})]^2$, depending on both dimensionless initial perturbation amplitude ${η_{\rm{0}}}$ and material-property-associated linear growth rate ratio $ϕ\equivΓ_{actual}/Γ_{ideal}\leqslant1$. The theory successfully explains the continued puzzle about the widely varying $α\in (0.02,0.12)$ in experiments and simulations, conducted at all value of $A \in (0,1)$ and widely varying value of ${η_{\rm{0}}} \in [{10^{ - 7}},{10^{ - 2}}]$ with different materials. The good agreement between theory and experiments implies that majority of actual mixing depends on initial perturbations and material properties, to which more attention should be paid in either natural or engineering problems.

physics.flu-dyn↗

arXiv2015

Symmetry and conservation principles of evolution of general Rayleigh-Taylor mixing fronts

A theory determining the evolution of general Rayleigh-Taylor mixing fronts is established to reproduce firstly all of the documented experiments conducted for diverse acceleration histories and all density ratios. The theory is established in terms of the fundamental conservation and symmetry principles, with special consideration given to the symmetry breaking of the density fields occurring in actual flows. The results reveal the sensitivity/insensitivity of the evolution of a mixing front neighbouring light/heavy fluid to the degree of symmetry breaking, and also explain the distinct evolutions in two experiments with the same configurations.

physics.flu-dyn↗

arXiv2013

A general Reynolds analogy theory for the compressible wall-bounded turbulence

A general Reynolds analogy (GRA) theory is proposed for the mean and fluctuating velocity and temperature in compressible wall-bounded turbulent flows. In particular, an exact analogy solution is derived for compressible turbulent pipe and channel flows and an approximate analogy solution is derived for compressible turbulent boundary layers (CTBL), both of which are independent of fluid Prandtl number and wall temperature condition. The analogy solutions are in excellent agreement with direct numerical simulation data, able to reproduce empirical relations, and can be viewed as extensions of existing theories. In contrast to Walz's equation for adiabatic CTBL, the mean temperature-velocity relation derived by GRA can be applied to different wall-bounded flows in non-adiabatic wall condition, which is achieved by extending Walz's adiabatic recovery factor to a heat flux dependent one. The fluctuation temperature-velocity relations derived by GRA are slightly different from the modified strong Reynolds analogy derived phenomenologically by Huang et al. (HSRA), and have a better performance than HSRA. In addition, several key quantities are introduced in GRA, including a general total enthalpy (or temperature) and an adiabatic degree--a well-founded dimensionless parameter for characterizing the wall-temperature effects in non-adiabatic flows. The GRA unveils the universal feature behind the complex nonlinear couplings between the thermal and velocity fields, and makes possible of predicting the mean fields of compressible wall-bounded turbulence with the information of the corresponding incompressible flow.

physics.flu-dyn↗