Only recently, three-dimensional direct numerical simulations (DNS) with detailed chemistry have become possible. These types of simulations will have an important impact on combustion science because of the data they provide. Obtaining similar data sets through experimental characterization is very challenging and requires joint measurements of a multitude of chemical species concentrations in addition to temperature and velocity fields. Gruber et al. (J. Fluid Mech., vol. 658, 2010, pp. 5–32) have performed a detailed chemistry DNS to understand the physics of flame/wall interactions. They found that flames interact with streamwise vortical structures close to the wall, and that these structures can push the flame towards or away from the wall. The flames get extinguish when they are too close to the wall. Interestingly, the extinction process actually causes an order-of-magnitude increase in heat release, and therefore, strongly amplifies wall heat transfer.

A novel method for performing spectral analysis of a fluid flow solely based on snapshot sequences from numerical simulations or experimental data is presented by Schmid (J. Fluid Mech., 2010, this issue, vol. 656, pp. 5–28). Dominant frequencies and wavenumbers are extracted together with dynamic modes which represent the associated flow structures. The mathematics underlying this decomposition is related to the Koopman operator which provides a linear representation of a nonlinear dynamical system. The procedure to calculate the spectra and dynamic modes is based on Krylov subspace methods; the dynamic modes reduce to global linear eigenmodes for linearized problems or to Fourier modes for (nonlinear) periodic problems. Schmid (2010) also generalizes the analysis to the propagation of flow variables in space which produces spatial growth rates with associated dynamic modes, and an application of the decomposition to subdomains of the flow region allows the extraction of localized stability information. For finite-amplitude flows this spectral analysis identifies relevant frequencies more effectively than global eigenvalue analysis and decouples frequency information more clearly than proper orthogonal decomposition.

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

New large-eddy simulations of flow over a flexible plant canopy by Dupont et al. (J. Fluid Mech., 2010, this issue, vol. 652, pp. 5–44) have produced apparently paradoxical results. Work over the last three decades had suggested that turbulent eddies could ‘lock onto’ to the waving frequency of uniform cereal canopies. Their new simulations contradict this view, although a resolution may lie in the essentially three-dimensional nature of the instability process that generates the dominant eddies above plant canopies.

Direct numerical simulations are rapidly becoming one of the most important techniques to examine the dynamics of multiphase flows. Lucci, Ferrante & Elghobashi (J. Fluid Mech., 2010, this issue, vol. 650, pp. 5–55) address several fundamental issues for spherical particles in isotropic turbulence. They show the importance of including the finite size of the particles and discuss how particles of a size comparable to the largest length scale at which viscosity substantially affects the turbulent eddies (i.e. the Taylor microscale) always increase the dissipation of turbulent kinetic energy.

Significant advances have been made in applying ideas from nonlinear dynamical systems theory to flows which exhibit sequences of bifurcations in the transition to turbulence. Moreover, the recent discoveries of finite-amplitude states in linearly stable flows holds great promise for a breakthrough in our understanding transition in shear flows. Tsukahara, Tillmark & Alfredsson (J. Fluid Mech., 2010, this issue, vol. 648, pp. 5–33) study a novel variant of a classical shear flow by adding global rotation. The competition between the induced body force and shear-induced instabilities leads to the discovery of a rich and beautiful tapestry of transition sequences.

Receptivity is the process which describes how environmental disturbances (such as gusts, acoustic waves or wall roughness) are filtered by a boundary layer and turned into downstream-growing waves. It is closely related to the identification of initial conditions for the disturbances and requires knowledge of the characteristics of the specific external forcing field. Without such a knowledge, it makes sense to focus on worst case scenarios and search for those initial states which maximize the disturbance amplitude at a given downstream position, and hence to identify upper bounds on growth rates, which will be useful in predicting the transition to turbulence. This philosophical approach has been taken by Tempelmann, Hanifi & Henningson (J. Fluid Mech., 2010, vol. 646, pp. 5–37) in a remarkably complete parametric study of ‘optimal disturbances’ for a model of the flow over a swept wing; they pinpoint the crucial importance both of the spatial variation of the flow and of non-modal disturbances, even when the flow is ‘supercritical’ and hence subject to classical ‘normal mode’ instabilities.

Many insects and spiders can travel on the water surface by rapid synchronized movements of the legs. It has been found that frictional forces, capillary waves and the creation of water jets and eddies beneath the fluid surface are all involved in the mechanisms of propulsion used by these creatures. Elaborate adaptations of the body structure mediate the wetting and de-wetting of the body surface to provide support and differential adhesion. Flow visualization as well as theoretical modelling have led to an understanding of the mechanisms invoked by water striders and spiders for water walking with a variety of gaits and speeds.

Rarely do intra-cellular flows amount to much: cells are small, and so are their Reynolds numbers. The extraordinarily large cells of the Characean algae provide a fascinating counter-example, as their geometry precludes the standard methods of distributing food and waste. van de Meent et al. (J. Fluid Mech., 2010, this issue, vol. 642, pp. 5–14) present nuclear magnetic resonance (NMR) velocimetry measurements of the fluid flow within individual living cells, which agree quantitatively with their fluid mechanical model and confirm a long-standing hypothesis. In addition to biomimetic parallels with microfluidic labs on chips, this work showcases NMR velocimetry as an under-appreciated but immensely powerful technique. The non-invasive tracer-free high-resolution flow measurements it enables – even in opaque and heterogeneous fluids – should find wide application.

Taylor's hypothesis, relating temporal to spatial fluctuations in turbulent flows is investigated using powerful numerical computations by del Álamo & Jiménez (J. Fluid Mech., 2009, this issue, vol. 640, pp. 5–26). Their results cast doubt on recent interpretations of bimodal spectra in relation to very large-scale turbulent structures in experimental measurements in turbulent shear flows.

A finite-amplitude propagating wave induces a drift in fluids. Understanding how drifts produced by many waves disperse pollutants has broad implications for geophysics and engineering. Previously, the effective diffusivity was calculated for a random set of small-amplitude surface and internal waves. Now, this is extended by Bühler & Holmes-Cerfon (J. Fluid Mech., 2009, this issue, vol. 638, pp. 5–26) to waves in a rotating shallow-water system in which the Coriolis force is accounted for, a necessary step towards oceanographic applications. It is shown that interactions of finite-amplitude waves affect particle velocity in subtle ways. An expression describing the particle diffusivity as a function of scale is derived, showing that the diffusivity can be substantially reduced by rotation.

The addition of even minute amounts of a polymer to a liquid can modify some of its properties drastically, like the ways in which jets of the liquid break into droplets or the dynamics of dripping droplets at an orifice. The elasticity conferred by the polymers can delay the separation of the drops considerably, which hesitate between falling or running back to the orifice, ‘gobbling’ along their way the thread to which they are attached. Other free-surface flows are also of a hesitant nature.

Vortex-induced vibration of solid structures has been known since ancient times, and remains a very important problem of fluid mechanics. Experimental studies of the vortex-induced vibration of circular cylinders have provided many fundamental insights. Recent extremely carefully controlled forced vibration experiments by Morse & Williamson (J. Fluid Mech., 2009, this issue, vol. 634, pp. 5–39), generating finely resolved data sets, are providing a fresh understanding of the mechanisms involved, especially for ocean structures with very low mass and damping.

Recent work has developed a beautiful model system for studying the energy focusing and heating power of collapsing bubbles. The bubble is effectively one-dimensional and the collapse and heating can be quantitatively measured. Thermal effects are shown to play an essential role in the time-dependent dynamics.

Turbulent flows near walls have been the focus of intense study since their first description by Ludwig Prandtl over 100 years ago. They are critical in determining the drag and lift of an aircraft wing for example. Key challenges are to understand the physical mechanisms causing the transition from smooth, laminar flow to turbulent flow and how the turbulence is then maintained. Recent direct numerical simulations have contributed significantly towards this understanding.