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Abstract
Classical theories of continuum mechanics - hydrodynamics and elasticity - rely on symmetries, such as isotropy, time-reversal invariance, or mirror symmetry. These are obeyed by familiar fluids such as air or water. Yet, many systems in soft matter do not satisfy these constraints. In this thesis, I develop a theoretical fluid mechanics framework to describe the consequences of these broken symmetries on fluid flow. Concretely, I consider chiral fluids, such as fluids composed of spinning particles or driven by a magnetic field. These fluids, described by a modified Navier-Stokes equation, exhibit additional “odd” viscosity coefficients, which do not dissipate energy. I reveal the significant impact odd viscosity can have on fluid flow in three dimensions across a range of Reynolds numbers. In the low Reynolds number limit, sedimenting particles in a chiral fluid generate a rotating flow that is absent in usual fluids; in turn, this flow affects how immersed particles respond to forces and torques. At intermediate Reynolds numbers, odd viscosity reshapes the vortex structure of the wake of a sphere and modifies the bifurcations that govern this transitional regime. At high Reynolds numbers, the non-dissipative nature of odd viscosity disrupts the energy cascade that occurs in fully developed turbulent flows, leading to pattern formation with a tunable scale. This work on chiral fluids uncovers a whole new world of phenomena stemming from broken microscopic symmetries and provides a solid ground for describing and harnessing chiral soft matter systems across all scales.