Fluid-particle separation in a random flow described by the telegraph model.

Area of Science:

• Fluid Dynamics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Understanding particle dispersion in turbulent flows is crucial for various scientific and engineering applications.
• Previous models often relied on simplified noise assumptions, limiting their applicability to real-world scenarios.

Purpose of the Study:

• To investigate the statistical properties of relative separation between two fluid particles in a random flow.
• To model Lagrangian strain using a telegraph noise process for a more realistic representation.
• To derive analytical solutions for interparticle distance statistics under finite-correlated noise.

Main Methods:

• Utilized a telegraph noise model for Lagrangian strain, a stationary random Markov process.
• Derived closed equations for interparticle distance in the presence of finite-correlated noise.
• Performed analytical calculations for one-dimensional (1D) and two-dimensional (2D) incompressible isotropic cases.

Main Results:

• In 1D, analytically determined long-time growth rates of distance moments and a negative senior Lyapunov exponent.
• Derived the exact Cramér function and confirmed its satisfaction of the fluctuation relation despite time irreversibility.
• In 2D, obtained a positive Lyapunov exponent and asymptotic growth rates for fast and slow strain limits, identifying a singular quasideterministic limit.

Conclusions:

• The telegraph noise model provides valuable insights into fluid particle dispersion, offering a balance between simplicity and realism.
• The findings highlight the distinct behaviors of particle separation in 1D and 2D flows and under different strain rates.
• The study demonstrates the applicability of fluctuation relations even with time-irreversible strain statistics.