Transient growth, edge states, and repeller in rotating solid and fluid.

Area of Science:

• Fluid dynamics
• Solid mechanics
• Wave dynamics

Background:

• Classical solid rotation exhibits transient energy growth under specific inertia conditions.
• Rotating fluids display similar dynamics in energy transfer between inertial waves.

Purpose of the Study:

• To investigate large transient energy growth and relaxation oscillations in rotating solids and fluids.
• To understand the underlying mechanisms of energy transfer in these systems.

Main Methods:

• Analysis of perturbation energy growth in solid rotation.
• Application of triadic resonance conditions to inertial waves in rotating fluids.
• Identification of conserved quantities like energy and helicity.

Main Results:

• Transient energy growth occurs when unstable axis inertia approaches stable axis inertia.
• Relaxation oscillations arise from energy transfer to unstable axes or waves.
• These phenomena are linked to conserved energy and helicity, particularly when waves have similar helicities and energies, and a third wave has vanishing frequency.

Conclusions:

• The study reveals surprising transient dynamics in rotating systems.
• Energy transfer and oscillations are explained by conserved quantities and specific wave interactions.
• The findings have implications for understanding wave dynamics in various physical problems involving conserved energy and pseudomomentum.