Long-time simulations of the Kelvin-Helmholtz instability using an adaptive vortex method.

Area of Science:

• Fluid dynamics
• Nonlinear physics
• Computational physics

Background:

• The Kelvin-Helmholtz instability is a fundamental phenomenon in fluid dynamics.
• Understanding interface evolution under shear flow is crucial for various applications.
• Previous models often lacked the resolution to capture late-time dynamics.

Purpose of the Study:

• To investigate the nonlinear evolution of interfaces in density-stratified fluids under parallel shear flow.
• To explore the late-time dynamics of the Kelvin-Helmholtz instability using advanced computational methods.
• To analyze the development of secondary instabilities and resulting structures.

Main Methods:

• Utilized the vortex sheet model for interface dynamics.
• Employed long-time computations with the point vortex method.
• Implemented an adaptive point insertion procedure for enhanced resolution.
• Applied a high-order shock-capturing scheme to the vortex method.

Main Results:

• Successfully simulated chaotically distorted interfaces of the Kelvin-Helmholtz instability with high resolution.
• Observed the evolution of a secondary instability at late times.
• Documented the distortion of the internal rollup structure.
• Confirmed the eventual development into a disordered structure.

Conclusions:

• The Kelvin-Helmholtz instability in stratified fluids is characterized by secondary instabilities and eventual structural disorder.
• Adaptive and high-order numerical methods are effective for simulating complex fluid instabilities.
• The study provides insights into the late-stage evolution of shear flow instabilities.