arXiv subjects

Z. Yin

Publications and source records attributed to Z. Yin.

23 records · Page 2Linked to original sources

arXiv2005

Resolving Small-scale Structures in Two-dimensional Boussinesq Convection by Spectral Methods with High Resolutions

Two-dimensional Boussinesq convection is studied numerically with very fine spatial resolutions up to 4096^2. Our numerical study starts with a smooth asymmetric initial condition, which is chosen to make the flow field well confined in the computational domain until the blow-up time (T_c). Our study shows that the vorticity will blow up at a finite time with |ω|_{max} \~{(T_c-t)}^{-1.61} and |\nabla θ|_{max} ~ {(T_c - t)}^{-3.58}.

physics.flu-dyn↗

arXiv2004

A new parallel strategy for two-dimensional incompressible flow simulations using pseudo-spectral methods

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluids, 33, 509 (2004)] and parallelized Fast Fourier Transform scheme. The performances of the resulting MPI Fortran90 codes with the new procedure on SGI 3800 are reported. For fixed resolution of the same problem, the peak speed of the new scheme can be twice as fast as the old parallel methods. The parallelized codes are used to solve some challenging numerical problems governed by the Navier-Stokes equations and the Boussinesq equations. Two interesting physical problems, namely, the double-valued $ω$-$ψ$ structure in two-dimensional decaying turbulence and the collapse of the bubble cap in the Boussinesq simulation, are solved by using the proposed parallel algorithms.

physics.comp-ph↗

arXiv2004

On final states of 2D decaying turbulence

Numerical and analytical studies of "final states" of two-dimensional (2D) decaying turbulence are reported. The first part of this work is trying to give a definition for final states of 2D decaying turbulence. Although the functional relation of $ω-ψ$ is frequently used as the characterization of those "final states," it is just a sufficient but not necessary condition so it is not proper to be used as the definition. It is found the way through the value of the effective area S covered by the scatter $ω-ψ$ plot, which is initially suggested by Read, is more general, and more suitable for the definition. Based on this concept, we gave out a definition that can cover all existing results in late states of decaying 2D flows, including some weird double-valued $ω-ψ$ scatter plots that can not be explained before. The rest part of the paper is trying to further investigate 2D decaying turbulence with the assistance of our new definition. Some new numerical results, which lead to "bar" final states and further verify the predictive ability of statistical mechanics [2], are reported. It is realized that some simulations with narrow-band energy spectral initial conditions, which can be called "turbulence" doubtfully, lead to some final states that can not be very well explained by the statistical theory (in the meanwhile, they are still in the scope of our new definition of the "final state"). For those simulations with initial conditions of broadband energy spectra that lead to the famous dipole, we give out a mathematical re-interpreting for the so-called sin-hyperbolic ("sinh") $ω-ψ$ scatter plot in final states. We suggest the term "sinh" here should be replaced by "sinh-like." The corresponding physical meaning of this re-interpreting will also be discussed.

physics.flu-dyn↗

arXiv2002

Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points"

Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy predictions for the decayed, late-time state. Both formulations define an entropy through a somewhat ad hoc discretization of vorticity to the "particles" of which statistical mechanical methods are employed to define an entropy, before passing to a mean-field limit. In one case, the particles are delta-function parallel "line" vortices ("points" in two dimensions), and in the other, they are finite-area, mutually-exclusive convected "patches" of vorticity which in the limit of zero area become "points." We use time-dependent, spectral-method direct numerical simulation of the Navier-Stokes equations to see if initial conditions which should relax to different late-time states under the two formulations actually do so.

physics.flu-dyn↗

arXiv1996

Supersymmetric Cycles in Exceptional Holonomy Manifolds and Calabi-Yau 4-Folds

We derive in the SCFT and low energy effective action frameworks the necessary and sufficient conditions for supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau 4-folds. We show that the Cayley cycles in $Spin(7)$ holonomy eight-manifolds and the associative and coassociative cycles in $G_2$ holonomy seven-manifolds preserve half of the space-time supersymmetry. We find that while the holomorphic and special Lagrangian cycles in Calabi-Yau 4-folds preserve half of the space-time supersymmetry, the Cayley submanifolds are novel as they preserve only one quarter of it. We present some simple examples. Finally, we discuss the implications of these supersymmetric cycles on mirror symmetry in higher dimensions.

hep-th↗