Intermittency of three-dimensional perturbations in a point-vortex model.

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Nonlinear Dynamics

Background:

• Three-dimensional (3D) instabilities in two-dimensional (2D) flows remain poorly understood, hindering progress in turbulence theory.
• Existing theoretical models often fail to capture the complex dynamics of these instabilities.

Purpose of the Study:

• To propose a novel, energy-conserving model for 3D instabilities on 2D flows.
• To investigate the behavior of these instabilities across different evolutionary stages: linear, passive-nonlinear, and fully nonlinear.
• To provide a new framework for analyzing complex simulation data and guiding theoretical development.

Main Methods:

• Development of a simplified model coupling a regularized 2D point-vortex flow with localized 3D perturbations ('ergophages').
• Analysis of the linear regime, focusing on ergophage amplitude growth, instantaneous growth rates, and Lévy flight dynamics.
• Investigation of the passive-nonlinear regime, characterizing Lévy on-off intermittency and its statistical properties.
• Exploration of the fully nonlinear regime, examining feedback effects on the 2D flow and vortex temperature.

Main Results:

• The linear regime exhibits fluctuating growth rates and Lévy flight behavior of ergophage amplitudes.
• A new phenomenon termed 'Lévy on-off intermittency' is identified in the passive-nonlinear regime.
• In the fully nonlinear regime, strong ergophage activity disrupts the 2D flow condensate, leading to a zero-temperature state.

Conclusions:

• The proposed model offers a valuable new perspective on 3D instabilities in 2D flows.
• The findings are crucial for interpreting direct numerical simulations (DNS) and advancing theoretical understanding.
• The model's energy-conserving nature and identified intermittency provide a foundation for future research in fluid dynamics.