Topology of rotating stratified fluids with and without background shear flow

Abstract

Poincaré-gravity modes described by the shallow water equations in a rotating frame have non-trivial topology, providing a new perspective on the origin of equatorially trapped Kelvin and Yanai waves. We investigate the topology of rotating shallow water equations and continuously stratified primitive equations in the presence of a background sinusoidal shear flow. The introduction of a background shear flow not only breaks the Hermiticity and homogeneity of the system but also leads to instabilities. We show that singularities in the phase of the Poincaré waves of the unforced shallow-water equations and primitive equations persist in the presence of shear. Thus the bulk Poincaré bands have non-trivial topology and we expect and confirm the persistence of the equatorial waves in the presence of shear along the equator where the Coriolis parameter $f$ changes sign.

References in corpus (37)

• Topological Insulators
• Topological insulators and superconductors
• Edge states and topological invariants of non-Hermitian systems
• Topological phases of non-Hermitian systems
• Topological Acoustics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Acoustic topological insulator and robust one-way sound transport
• Topological Band Theory for Non-Hermitian Hamiltonians
• Topological States and Adiabatic Pumping in Quasicrystals
• Anomalous edge state in a non-Hermitian lattice
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Topological mechanics of gyroscopic metamaterials
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Three-Dimensional Topological Insulators
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Observation of novel edge states in photonic graphene
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Experimental Observation of Large Chern numbers in Photonic Crystals
• Topological Phases of Sound and Light
• Topological Origin of Equatorial Waves
• Symmetry-protected multifold exceptional points and their topological characterization
• Topological Sound and Flocking on Curved Surfaces
• Wave-Mean Flow Interactions in the Atmospheric Circulation of Tidally Locked Planets
• Topological Gaseous Plasmon Polariton in Realistic Plasma
• Topological phases and bulk-edge correspondence of magnetized cold plasmas
• L lines, C points and Chern numbers: understanding band structure topology using polarization fields
• Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
• Topological phase in plasma physics
• Wave topology brought to the coast
• Nontrivial topology in the continuous spectrum of a magnetized plasma
• Topological protection can arise from thermal fluctuations and interactions
• Tutorial: Topology, waves, and the refractive index