Andrey I. Aleksyuk

We examine the mechanisms responsible for the onset of the three-dimensional mode B instability in the wake behind a circular cylinder. We show that it is possible to explicitly account for the stabilising effect of spanwise viscous diffusion and then demonstrate that the remaining mechanisms involved in this short-wavelength instability are preserved in the limit of zero wavelength. Using the resulting simplified equations, we show that perturbations in different fluid particles interact only through the in-plane viscous diffusion which turns out to have a destabilising effect. We also show that in the presence of viscous diffusion, the closed trajectories which had been conjectured to play a crucial role in the onset of the mode B instability are not actually a prerequisite for the growth of mode B type perturbations. We combine these observations to identify the three essential ingredients for the development of the mode B instability: (i) the amplification of perturbations in the braid regions due to the stretching mechanism; and the spreading of perturbations through (ii) viscous diffusion, and (iii) cross-flow advection which transports fluid between the two braid regions on either side of the cylinder. Finally, we develop a simple criterion that allows the prediction of the regions where three-dimensional short-wavelength perturbations are amplified by the stretching mechanism. The approach used in our study is general and has the potential to give insights into the onset of three-dimensionality via short-wavelength instabilities in other flows.

We study the onset of the three-dimensional mode A instability in the near wake behind a circular cylinder. We show that long-wavelength perturbations organise in a time-shifting pattern such that the in-plane velocity in each streamwise slice corresponds to the base flow solution at shifted times. This observation introduces an additional unifying characteristic for certain mode A type instabilities. We then analyse the mechanisms which control the growth or decay of these perturbations and highlight the crucial role played by the tilting mechanism which operates via non-local interactions in a manner similar to Biot–Savart induction. We characterise its domain of influence using a Green's function-based approach which allows us to rationalise the non-trivial dependence of the growth rate on the spanwise wavenumber. We connect this behaviour to the subtle balance between the local growth of the perturbations as they are swept along by the flow and the feedback on the perturbations that are generated during the next period of the time-periodic base flow. Finally, we discuss generalisations of our findings to other types of flows.

The total enthalpy of a uniform flow is redistributed behind a thermally insulated body such that a considerable cooling of fluid in terms of total temperature occurs near the wake centreline. This energy separation phenomenon is also observed after time averaging and can lead to the recovery temperature at the rear part of the body becoming lower than the static temperature of the incoming flow (the Eckert–Weise effect). By the numerical solution of the Navier–Stokes equations, the present work studies energy separation in the wake, the Eckert–Weise effect and their sensitivity on the flow interference behind side-by-side cylinders. The considered distances between the cylinders cover the key regimes of interference: single, bistable and coupled vortex streets. The first and second regimes amplify the efficiency of energy separation in the wake and the intensity of the Eckert–Weise effect, respectively. In the developed wake, a clear relation between the vortex structure and the total enthalpy redistribution is demonstrated as well as a limitation on the intensity of this redistribution imposed by the deficit of velocity. The connection of the Eckert–Weise effect with the vortex formation process is clarified. Among the mechanisms changing the total enthalpy in fluid particles, the non-stationarity of pressure defines the averaged distribution: the decrease of pressure in forming vortices is mainly responsible for the cooling of fluid behind the body. The balance with the heating of the rear surface by the involvement of fluid from the sides defines the intensity of the effect.

Flows of two immisible fluids are considered taking into account the capillary and gravity forces. The flow is described using a viscous incompressible fluid model within a two-dimensional formulation. The Navier–Stokes equations are solved numerically by an extended finite-element method, which allows for the presence of a strong discontinuity on the interface. The interface location is tracked using the level set method. This approach makes it possible to study flows with a varying topology of the interface. The calculation results are presented for the problems of a rising 2D bubble, development of the Rayleigh–Taylor instability, and a film flowing down a vertical wall in an extended region.

The objective of this study was to provide the most accurate presentation of the behavior of a disastrous rain flood, which had resulted in destruction of a dam, casualties, and significant...

Regions with reduced and increased values of total enthalpy are observed in a time-averaged flow behind a bluff body. This energy redistribution takes place both in the vortex formation region and in the developed vortex wake. The present paper focuses on studying the effect of the structure of a vortex street on the intensity of energy redistribution. Two approaches are used. The first one is direct numerical simulation of the flow behind a transversely oscillating cylinder, which is known for a variety of vortex patterns in the wake. The simulations are based on a finite element solution of the Navier-Stokes equations for a compressible perfect viscous gas. The second approach is based on simplified point vortex models for infinite periodic vortex streets, which contain a finite number of vortex chains in equilibrium. It turns out that these simple models make it possible to obtain satisfactory qualitative results, particularly if a more precise approximation of velocity fields in the vortex cores (Rankine vortices) is implemented. It is shown that the effect of energy redistribution significantly depends on the vortex structure, namely the mutual arrangement of the vortices and their intensities. The estimates of the energy separation efficiency in the time-averaged flow are obtained for the general case of an arbitrary number of chains. A more detailed analysis is performed for vortex streets with 2, 3, and 4 vortex chains.