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Lattice models of advection-diffusion.
1University of Chicago, Chicago, Illinois.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
This study explores tracer concentration distributions under diffusion and advection. The freely decaying case exhibits fat tails, while the forced case shows Gaussian cores and exponential tails, highlighting fluctuation impacts.
Area of Science:
- Physics
- Fluid Dynamics
- Statistical Mechanics
Background:
- Passive tracer concentration is influenced by diffusion and advection.
- Understanding probability distributions is key in fluid dynamics.
- Theoretical models often simplify complex flow dynamics.
Purpose of the Study:
- To synthesize theoretical results on passive tracer concentration probability distributions.
- To contrast freely decaying and equilibrium advection-diffusion cases.
- To introduce and validate a lattice model for advection-diffusion.
Main Methods:
- Theoretical analysis of advection-diffusion processes.
- Development of a computationally efficient lattice model.
- Numerical simulations to test theoretical predictions and explore model limits.
Main Results:
- Freely decaying tracer concentration shows fat tails with slower-than-exponential decay.
- Additively forced cases exhibit Gaussian cores and exponential tails.
- Temporal fluctuations in diffusion and dissipation significantly shape tail distributions.
Conclusions:
- The lattice model effectively probes advection-diffusion theories.
- The model is adaptable for rough flows and chemically reacting tracers.
- Fluctuations play a critical role in determining tracer concentration statistics.