Quasi-two-dimensional hydrodynamics and problems of two-dimensional turbulence

Area of Science:

• Fluid dynamics
• Hydrodynamics
• Turbulence theory

Background:

• Traditional 2-D hydrodynamic models derived from 3-D Navier-Stokes equations possess inherent limitations.
• Simulating 2-D turbulence using standard 2-D equations is problematic due to the absence of a Kolmogorov dissipation scale and reverse energy flux.

Purpose of the Study:

• To address the principal problems in quasi-two-dimensional (Q2-D) hydrodynamics.
• To develop corrected 2-D motion equations that accurately describe real hydrodynamic processes.
• To provide a valid framework for simulating 2-D turbulence.

Main Methods:

• Incorporating the vertical structure of Q2-D flow to refine 2-D hydrodynamic equations.
• Developing an alternative approach to simulate 2-D turbulence by introducing a natural external scale.
• Verifying the applicability of the refined Q2-D approach through laboratory experiments.

Main Results:

• Accounting for vertical flow structure eliminates "genetic" defects in formal 2-D idealizations of 3-D Navier-Stokes equations.
• Corrected 2-D motion equations adequately describe real hydrodynamic processes under specific conditions.
• The alternative approach introduces a natural external scale for 2-D turbulence, dependent on system properties.

Conclusions:

• The refined Q2-D hydrodynamic model offers a more accurate representation of fluid dynamics.
• The proposed method for 2-D turbulence simulation overcomes limitations of existing models.
• Large-scale vortex dynamics in 2-D turbulence are shown to be universal at high Reynolds numbers, independent of domain specifics.