We use asymptotic and numerical methods to explore the effects of boundaries in two contrasting fluid regimes. We first describe static equilibria in rectangular channels that are perturbed by isolated ridges/grooves or scattered bump protrusions/intrusions. We solve the Young-Laplace equation to quantify the sensitivity of the meniscus shape to the perturbations using a combination of numerical computations and asymptotic techniques. We show that the total pressure difference over the meniscus (and therefore the mean curvature) can be found without solving the Young-Laplace equation. Perturbations can induce long-range curvature of the contact line, which matches onto the contact line of a droplet with the same mean curvature as the meniscus. We use this information to choose specific combinations of perturbations to engineer contact line shapes. We further present an asymptotic description of nonlinear equilibrium and travelling-wave solutions of the Navier-Stokes equations in incompressible unsteady and compressible parallel boundary-layer flows. The solutions take the form of self-sustaining vortex-wave interaction-type states, known as free-stream coherent structures. The interaction produces streaky disturbances that can grow exponentially due to interaction with the base flow. An unsteady base flow strongly affects the time evolution of the structures, and they can only persist for a finite time. Meanwhile the velocity disturbance field for compressible parallel flows in the subsonic and moderate supersonic regimes also drives a passive thermal field. The maximum amplitude of the resulting disturbances depends on the Mach number and the Prandtl number.