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We focus on plane Poiseuille flow where an incompressible fluid is pushed between two parallel plates by maintaining a constant bulk velocity. Plane Poiseuille flow is a canonical wall-bounded shear flow where a subcritical transition to turbulence is observed. Assuming periodic boundary conditions in streamwise and spanwise directions, we classify invariant subspaces of the plane Poiseuille flow up to half-box shifts. Exploiting the interplay between symmetries and dynamics, we find new finite amplitude traveling wave solutions in some invariant subspaces, far below the linear stability threshold.

Planning and adapting to future coastal ocean conditions requires accurate coastal ocean predictions of the nutrient, pollutant, heat and sediment transport. As coastal ocean turbulence is often driven by relatively small scale processes such as high-frequency internal waves and submesocale eddies that are not captured in most regional ocean models turbulence parameterisation is challenging Using a combination of process-based field campaigns and long-term monitoring data we have characterised the relationship between diapycnal mixing and diverse external forcings and differing flow regimes on the Australian northwest shelf. We show that the overall diapycnal mixing is dominated by relatively rare but energetic mixing events. We observe that the semi-diurnal barotropic tide, the spring-neap tidal variability, and the seasonal variability in stratification all affect the magnitude of diapycnal mixing and its vertical distribution.

Atmosphere and ocean dynamics are dictated by balanced flows, such as mesoscale eddies, but determining a precise balanced state remains challenging in the presence of its nonlinear coupling with the unbalanced flows, such as internal gravity waves. The spontaneous loss of balance, resulting in nonlinear internal wave generation, challenges the existence of an invariant balanced state from a mathematical perspective, and at the same time has physical implications for the energy cycle of the atmosphere and ocean.

In this talk, I will discuss the recent progress in deriving and quantifying the balanced state in geophysical flows from nonlinear flow decomposition as well as the comparison of balanced states from different mathematical approaches: higher order balance and optimal balance . This decomposition is applied to varied oceanic regimes in a suite of idealized models to quantify spontaneous wave generation and assess its role in the energy cycle relative to other mechanisms. To ...