NUMERICAL SIMULATION OF
LAGRANGIAN TURBULENT QUANTITIES
IN TWO AND THREE DIMENSIONS
RICHARD L. PESKIN
Daparmmenf of Mechanical, Industrial und Aerospace Enyineeririg.
Geophysical Fluid Dynamics Prqrrunr. Ritrgcrs l'niwrsir c
New Rrunswfck. New Jerwy 08903. LI.X.4.
1. INTRODUCTION
The diffusive character of fluid dynamic turbulence is one of the least
understood, yet most practically important features of such flows. Whether
one is concerned with transport of pollutants under actual atmospheric
circumstances, or with the fundamental problem of energy cascade in
idealized turbulent flows, an understanding of turbulent diffusion is essential; yet such an understanding has remained elusive primarily because turbulent diffusion of single tracer points is controlled by that portion of the
energy spectrum, namely, the larger wave numbers, where theoretical
analysis is difficult. Furthermore, while diffusion is most naturally described
in the Lagrangian system, data acquisition is most practically accomplished
using the Eulerian description of the flow. Thus one is f a d with the difficult
choice of attempting to perform experiments to measure Lagrangian quantities directly, a formidable task, or alternatively using Eulerian measurements
and relying on the, as yet, unavailable understanding of the relation between
Eulerian and Lagrangian quantities.
Ideally, one would like to be able to perform Lagrangian experiments and
simultaneously obtain Eulerian information. While practical problems restrict this possibility in actual physical situations, numerical simulation used
as an experimental tool opens up interesting perspectives in this field of
study. In principle, both Euleriiln and Lagrangian information can be obtained with relative ease from a numerical simulation of turbulent flow, and
one can obtain information to establish Eulerian-Lagrangian relations,
which are useful in translating Eulerian data into Lagrangian diffusion information. Of course, idealization to this extent is not yet possible in computer
simulation. Precise simulation of threcdimensional turbulent flow which
141
LAGRANGIAN TURBULENT QUANTITIES
IN TWO AND THREE DIMENSIONS
RICHARD L. PESKIN
Daparmmenf of Mechanical, Industrial und Aerospace Enyineeririg.
Geophysical Fluid Dynamics Prqrrunr. Ritrgcrs l'niwrsir c
New Rrunswfck. New Jerwy 08903. LI.X.4.
1. INTRODUCTION
The diffusive character of fluid dynamic turbulence is one of the least
understood, yet most practically important features of such flows. Whether
one is concerned with transport of pollutants under actual atmospheric
circumstances, or with the fundamental problem of energy cascade in
idealized turbulent flows, an understanding of turbulent diffusion is essential; yet such an understanding has remained elusive primarily because turbulent diffusion of single tracer points is controlled by that portion of the
energy spectrum, namely, the larger wave numbers, where theoretical
analysis is difficult. Furthermore, while diffusion is most naturally described
in the Lagrangian system, data acquisition is most practically accomplished
using the Eulerian description of the flow. Thus one is f a d with the difficult
choice of attempting to perform experiments to measure Lagrangian quantities directly, a formidable task, or alternatively using Eulerian measurements
and relying on the, as yet, unavailable understanding of the relation between
Eulerian and Lagrangian quantities.
Ideally, one would like to be able to perform Lagrangian experiments and
simultaneously obtain Eulerian information. While practical problems restrict this possibility in actual physical situations, numerical simulation used
as an experimental tool opens up interesting perspectives in this field of
study. In principle, both Euleriiln and Lagrangian information can be obtained with relative ease from a numerical simulation of turbulent flow, and
one can obtain information to establish Eulerian-Lagrangian relations,
which are useful in translating Eulerian data into Lagrangian diffusion information. Of course, idealization to this extent is not yet possible in computer
simulation. Precise simulation of threcdimensional turbulent flow which
141