Studying Lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database

Abstract

A recently developed public turbulence database system (http://turbulence.pha.jhu.edu) provides new ways to access large datasets generated from high-performance computer simulations of turbulent flows to perform numerical experiments. The database archives 1024⁴ (spatial and time) data points obtained from a pseudo-spectral direct numerical simulation (DNS) of forced isotropic turbulence. The flow's Taylor-scale Reynolds number is Re _λ=443, and the simulation output spans about one large-scale eddy turnover time. Besides the stored velocity and pressure fields, built-in first- and second-order space differentiation, as well as spatial and temporal interpolations are implemented on the database. The resulting 27 terabytes of data are public and can be accessed remotely through an interface based on a modern Web-services model. Users may write and execute analysis programs on their host computers, while the programs make subroutine-like calls (getFunctions) requesting desired variables (velocity and pressure, and their gradients) over the network. The architecture of the database and the initial built-in functionalities are described in a previous paper of Journal of Turbulence (Y. Li, E. Perlman, M. Wan, Y. Yang, R. Burns, C. Meneveau, R. Burns, S. Chen, A. Szalay, and G. Eyink, A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbul. 9 (2008), p. N31). In the present paper, further developments of the database system are described; mainly the newly developed getPosition function. Given an initial position, integration time-step, as well as an initial and end time, the getPosition function tracks arrays of fluid particles and returns particle locations at the end of the trajectory integration time. The getPosition function is tested by comparing with trajectories computed outside of the database. It is then applied to study the Lagrangian velocity structure functions as well as the tensor-based Lagrangian time correlation functions. The roles of pressure Hessian and viscous terms in the evolution of the symmetric and antisymmetric parts of the velocity gradient tensor are explored by comparing the time correlations with and without these terms. Besides the getPosition function, several other updates to the database are described such as a function to access the forcing term in the DNS, a new more efficient interpolation algorithm based on partial sums, and a new Matlab interface.

Keywords:

• forced isotropic turbulence
• Lagrangian time correlation
• particle tracking
• turbulence database
• web services

Acknowledgements

The authors acknowledge the valuable assistance from other members of the database team (Jan VandeBerg, Rich Ercolani, Sue Werner, and Victor Paul). This research is supported by a National Science Foundation CDI-II grant no. CMMI-0941530. E. Frederick acknowledges international travel support from the Eindhoven University of Technology.