To propose efficient and better designs for small swimming and flying unmanned vehicles, understanding of the unsteady mechanisms to generate lift and thrust forces at low Reynolds numbers is of key importance. Fluid flowing over these vehicles interact nonlinearly with the structure and carries great complexities. Recently, due to interest in biomimicking flying (micro-air vehicles) and swimming robots (underwater vehicles), industry has shown keen interest in production of these vehicles. To design effective control of these vehicles, thorough understanding of its unsteady aerodynamics and underlying phenomena is required. In this study, we focus upon coupling the numerical simulations with the tools of nonlinear dynamics. We decompose this whole study into two parts;​ aerodynamics and hydrodynamics.

In the first part, we investigate the bifurcations occurring in the flows over oscillating airfoils at low Reynolds numbers. Investigation of mechanism responsible for the generation of unsteady forces pose challenges due to wide spectrum of parameters that are involved in its dynamics. Both experimental and currently available numerical techniques require costly resources in terms of time and money. Considering this fact, we also develop non-linear reduced-order models for unsteady aerodynamic forces produced by plunging, pitching, and flapping airfoils. Observing similarity in the character of unsteady forces generated by pitching, and plunging airfoils, we propose an equivalence criteria to obtain the aerodynamic forces of same magnitude or order. We also demonstrate that deflection of the wake for large Strouhal numbers is a result of strong quadratic nonlinearity.

With the lessons learnt from the nonlinear analysis/interaction of flapping airfoils, we investigate the hydrodynamics of fish swimming in the second part of this dissertation. We consider a single fish and two fish in tandem performing traveling-wave like motion, known as undulation. In case of tandem configuration, we numerically simulate the flow while both fish undulate asynchronously. We quantify the drafting and inverse-drafting effects using time-averaged drag coefficients. We also explain physical mechanisms which are responsible for hydrodynamic advantage/disadvantage to upstream and downstream fish. To further enhance our understanding related to the instability mechanisms in the wakes of undulating bodies, we compute the symmetry/asymmetry of parent and combined modes. We apply the symmetry principles, already established for drag-producing wakes of bluff bodies, to the thrust-producing wakes of undulating fish. We conclude that thrust producing wakes also follow the same symmetry principles.

This research addresses the coupling of techniques/tools of nonlinear mechanics with computational fluid dynamics to explore important features of complex flows around oscillating and undualating bodies.