Employing a poloidal-toroidal projection technique, a multi-scale analysis of resonant wave triads in columnar vortices is performed to obtain the governing equations of the triadically coupled wave amplitudes. For inviscid flows, we establish that resonance between neutral, smooth waves is conservative, and the temporal evolution of wave amplitudes is either bounded or explosively unstable based on the signs of the triad's interaction coefficients. Assessing the onset of weakly nonlinear instabilities through the pseudoenergy criterion introduced by Cairns (1979, J. Fluid Mech., vol. 92), we use the large-axial-wavenumber asymptotic approach by Le Dizes and Lacaze (2005, J. Fluid Mech., vol. 542) to evaluate each triad member's pseudoenergy and argue against the possibility of explosive conservative three-wave resonance involving only regular Kelvin waves. Additionally, extending our investigation to specific vortices, such as the Lamb-Oseen vortex and the Batchelor vortex, we find that triadic resonance among their neutral modes consistently results in bounded behaviour.

Design-by-Morphing (DbM) is a novel design methodology that creates a search space for topology optimization. Traditional design techniques often impose geometric constraints and, sometimes, the designer’s biases on the design space, which restricts the novelty of the designs and allows for only small local changes. On the contrary, we show in this paper that DbM does not impose such restrictions on the design space, thus allowing for a radical and expansive search space with only a few design parameters. We compare DbM with other methods in the case of design space generation for 2D airfoils and find that DbM can reconstruct the entire UIUC database with >99.5% accuracy. Furthermore, using a bi-objective genetic algorithm, we optimize the airfoil designs created by DbM to maximize both the lift-over-drag ratio, CLDmax, and stall angle tolerance, ∆α, which results in a Pareto-front of innovative airfoils that exhibit substantial improvements in both objectives.

We present Design-by-Morphing (DbM), a novel design methodology applicable to creating a search space for topology optimization of 2D airfoils. Most design techniques impose geometric constraints and sometimes designers' bias on the design space itself, thus restricting the novelty of the designs created, and only allowing for small local changes. We show that DbM methodology does not impose any such restrictions on the design space and allows for extrapolation from the search space, thus granting truly radical and large search space with a few design parameters. In comparison to other shape design methodologies, we apply DbM to create a search space for 2D airfoils. We optimize this airfoil shape design space for maximizing the lift-over-drag ratio, $CLD_{max}$, and stall angle tolerance, $\Delta \alpha$. Using a bi-objective genetic algorithm to optimize the DbM space, it is found that we create a Pareto-front of radical airfoils exhibiting remarkable properties for both objectives.