Stratified flows are ubiquitous. The atmosphere and ocean are two common examples of naturally stratified fluid bodies. In both, the density varies continuously in the vertical direction (hence "stratified"), supporting the formation of internal gravity waves (IGWs). The discontinuous density change at the interface of two fluids (for example, the air-sea interface) can also support the formation of surface gravity waves (SGWs). Beyond stratification, the intricate interplay within the atmosphere-ocean system involves a multitude of influencing factors. These encompass effects like shear flows in the air and water layers, as well as the effect of vertically migrating organisms on the surrounding fluid, among numerous others. Given the intricacy of considering all these factors simultaneously, our study focuses on three distinct sets of factors, with density stratification serving as the common factor among all three.
In the first problem, we consider a finite-depth air-water two-layer shear flow. Here, the stratification is discontinuous because of the sharp density change at the interface of water and air. Owing to shear flow, this system is prone to two inviscid instabilities that occur due to the interaction of the surface wave with the shear flow in the air and water layers: Miles' and rippling instabilities, respectively. The generation of the SGWs is a crucial part of the upper ocean dynamics, which affects the exchange of momentum, mass, and heat across the interface. Therefore, we study the relative importance of these inviscid instabilities in generating SGWs. Considering the specific case of an experimentally observed flow-reversal profile in the water layer and an exponential velocity profile in the air layer, we see that the Rayleigh equation can be solved analytically for both air and water layers. Further, comparing our results with those of experiments in the literature, we show that over specific parameter regimes, the rippling instability growth rates are more than the Miles' instability and match well with the experimental results. A viscous numerical stability study is also performed and indicates a fundamental change in the energy input mechanism between inviscid and viscous versions of the Miles instability.

In the second problem, we neglect the air layer and consider the effect of shear flow in nonlinear interactions of IGWs in a uniformly stratified water layer bounded by rigid walls at the top and bottom. In the ocean interior, IGWs are generated by the action of tides and winds, transport the energy to farther locations from their generation sites, and dissipate into the bulk through nonlinear processes. Although various generation mechanisms of IGWs are known, their dissipation mechanisms still need to be better understood. Hence, we study how the background shear flow modifies the nonlinear interactions, in particular triadic resonance interactions, among IGW modes. Using a weakly nonlinear theory for a monochromatic set of IGW modes, we derive governing equations for the amplitude of the super-harmonic term. Solving these equations in a wide parameter space, we show that additional resonances can be observed in the presence of arbitrarily weak shear that are otherwise non-existent in the absence of shear. Using a weak-shear asymptotic theory, we show that this is because the number of conditions that need to be satisfied for resonance (vertical and horizontal wavenumber conditions and a frequency condition) reduces even in the presence of arbitrarily weak shear. This increases the number of resonances significantly.

In the final problem, we study the disturbance flow field of particulate matter migrating vertically in a linearly stratified fluid. Vertically migrating organisms in the ocean drag large amounts of fluid along. This is suggested to contribute to large-scale oceanic mixing and is termed "biogenic mixing." Hence, we study the disturbance flow field of a vertically moving organism modeled as a rigid sphere. This problem is characterized by the presence of three forces, namely viscous, buoyancy, and inertia. In the regime where viscous forces are first comparable to the buoyancy forces, we extend the analytical expressions derived in the previous literature and describe additional flow features of the reverse-jet region that were previously overlooked. Our analysis reveals a tertiary screening length that eliminates the reverse-jet, other than the primary and secondary screening lengths known previously. The complete flow picture described in this study has implications in calculating the drift volume induced by vertically translating particulate matter and, consequently, in quantifying the biogenic mixing.