One of the important processes that affect large-scale ocean circulation, and its influence on the climate, is oceanic mixing. It dissipates the global energy input from winds and tides, thereby affecting the circulation and transport of scalar properties. Flow instabilities and nonlinear wave interactions are two essential pathways that lead to mixing by transfer of energy to smaller scales. Recent studies have also highlighted the contribution of particles and swimming marine organisms to oceanic mixing through Darwinian drift. We study three different problems concerning the three pathways aforementioned. As a first step, we investigate the spectrum of waves present in a two-dimensional, finite-depth fluid layer with a free surface. In linear theory, a viscous fluid supports two capillary-gravity waves and a class of countably infinite purely decaying (viscous) modes. Treating this as a linear initial value problem, we study the role of the viscous modes in representing disturbances at and far away from the free surface. An important problem in the parametrization of the upper-ocean mixed layer is the generation of surface waves by the wind. A mechanism of instability is investigated by Miles (1957), considering a quasi-laminar velocity profile in the air blowing over an inviscid, quiescent water layer of infinite extent. We study the effect of water-layer depth, surface velocity, and viscosity on the Miles' instability by considering an experimentally observed flow-reversal velocity profile in the water.

In deep-ocean, mixing due to breaking internal waves is essential for maintaining abyssal stratification and in the transport of nutrients and planktons. Triadic resonance is one of the prominent mechanisms leading to internal wave dissipation. Resonant generation of superharmonic waves occurs when two primary waves of the same frequency excite a secondary wave at twice the frequency. In an inviscid, uniformly-stratified fluid between two parallel plates, the resonance between three discrete internal wave modes occurs when they satisfy a modenumber condition along with horizontal wavenumber and frequency conditions. Using asymptotic theory and numerical methods, we study the necessity of the modenumber condition in the presence of shear and identify resonant interactions over a wide range of Richardson numbers and primary wave frequencies. The relative importance of different resonant interactions is being studied using amplitude evolution equations. In the last part of this work, we study the transport of finite-sized, anisotropic particles in linear wave fields. Recent studies considering the transport of particles regarded the translation and orientation dynamics as decoupled although their finite size and anisotropy indicate that they are coupled. The disturbance flow field generated by a settling sphere in uniformly stratified ambient and the corresponding Darwin drift is also being studied.