Long waves in streamwise varying shear flows: new mechanisms for a weakly nonlinear instability

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics
• Wave Propagation

Background:

• Shear flows are fundamental in fluid dynamics, often exhibiting marginal stability.
• Understanding wave dynamics in such flows is crucial for predicting transition phenomena.
• Weakly nonlinear instability is a key mechanism for turbulence onset.

Purpose of the Study:

• To investigate the weakly nonlinear dynamics of long waves in streamwise-varying shear flows.
• To identify the governing equations and emergent instability mechanisms.
• To elucidate the transition pathway to finite-amplitude states.

Main Methods:

• Derivation of a variable-coefficient Boussinesq equation.
• Analysis of nonmodal and modal instabilities.
• Examination of local flow stability characteristics.

Main Results:

• The dynamics are accurately described by a variable-coefficient Boussinesq equation.
• Emergence of new nonmodal or modal instabilities is demonstrated.
• These instabilities facilitate the achievement of amplitude thresholds for nonlinear instability.

Conclusions:

• Variable-coefficient Boussinesq equations are key for understanding these dynamics.
• Emergent instabilities provide natural pathways for transition to finite-amplitude states.
• This work advances the understanding of flow stability and transition mechanisms.