Fluid Deformation in Random Unsteady Flow

2025/10/02 by Lester, Daniel, Dentz, Marco
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.2510.01668

Abstract

Fluid deformation controls myriad processes including mixing and dispersion, development of stress in complex fluids, droplet breakup and emulsification, fluid-structure interaction, chemical reactions and biological activity. We develop a simple stochastic model for fluid deformation in random unsteady flows such as homogeneous isotropic turbulence. We show that although the Lagrangian velocity process is non-Markovian and non-Fickian, temporal decorrelation due to the unsteady nature of the flow renders the evolution of the Lagrangian velocity gradient tensor to be Fickian. Application of a coordinate transform renders the velocity gradient tensor upper triangular, eliminating vortical rotation and decoupling principal stretches from shear deformations, leading to a stochastic model of fluid deformation as a simple Brownian process. We develop closed-form expressions for the evolution of the Cauchy-Green tensor and show that the finite-time Lyapunov exponents are Gaussian distribution. Application of this model to DNS calculations of forced isotropic turbulence at Taylor-scale Reynolds number Re_λ≈ 433, confirms the underlying model assumptions and provides excellent agreement with theoretical results.

Citations

• Immersed Methods for Fluid–Structure Interaction
• The Lagrangian Deformation Structure of Three-Dimensional Steady Flow

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