This article presents a broad overview of the fluid mechanics of the human cardiovascular system. Beginning in the heart, we travel through the main features of our circulation to highlight important functions and diseases where fluid mechanics plays a central role. Of particular focus is the role of computational modelling in uncovering the dynamic flow phenomenon throughout our body, its association with cardiovascular disease mechanisms and progression and its importance in clinical treatment planning. We also emphasize the multiscale nature of the cardiovascular system, and associated challenges. The main aim of this review is to highlight progress and ongoing challenges in our understanding of cardiovascular haemodynamics, as well as the future outlook for translating the current state-of-the-art to widespread clinical application and improved patient outcomes.

Inviscid models for vortex rings and dipoles are constructed using nested patches of vorticity. These models constitute more realistic approximations to experimental vortex rings and dipoles than the single-contour models of Norbury and Pierrehumbert, and nested contour dynamics algorithms allow their simulation with low computational cost. In two dimensions, nested-contour models for the analytical Lamb dipole are constructed. In the axisymmetric case, a family of models for vortex rings generated by a piston–cylinder apparatus at different stroke ratios is constructed from experimental data. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circulation or shed vorticity into a tail, depending on the perturbation size. A change in the behaviour of the model vortex rings is identified at a stroke ratio of three, when it is found that the maximum relative perturbation size vortex rings can accept becomes approximately constant. We hypothesise that this change in response is related to pinch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings. In particular, we suggest that a perturbation response-based framework can be useful in understanding vortex formation in biological flows.