On the frequency selection mechanism of the low-Re flow around rectangular cylinders

In the flow past elongated rectangular cylinders at moderate Reynolds numbers, vortices shedding from the leading- and trailing-edge corners are frequency locked by the impinging leading-edge vortex instability. The present work investigates how the chord-based Strouhal number varies with the aspect ratio of the cylinder at a Reynolds number (based on the cylinder thickness and the free-stream velocity) of $Re=400$ , i.e. when locking is strong. Several two-dimensional, nonlinear simulations are run for rectangular and D-shaped cylinders, with the aspect ratio ranging from $1$ to $11$ , and a global linear stability analysis of the flow is performed. The shedding frequency observed in the nonlinear simulations is predicted fairly well by the eigenfrequency of the leading eigenmode. The inspection of the structural sensitivity confirms the central role of the trailing-edge vortex shedding in the frequency locking, as already assumed by other authors. Surprisingly, however, the stepwise increase of the Strouhal number with the aspect ratio reported by several previous works is not fully reproduced. Indeed, with increasing aspect ratio, two distinct flow behaviours are observed, associated with two flow configurations where the interaction between the leading- and trailing-edge vortices is different. These two configurations are fully characterised, and the mechanism of selection of the flow configuration is discussed. Lastly, for aspect ratios close to the jump between two consecutive shedding modes, the Strouhal number is found to present hysteresis, implying the existence of multiple stable configurations. Continuing the lower shedding-mode branch by increasing the aspect ratio, we found that the periodic configuration loses stability via a Neimark–Sacker bifurcation leading to different Arnold tongues. This hysteresis can explain, at least partially, the significant scatter of existing experimental and numerical data.

3D structure of single and multiple vortices in a flow under rotation

In this paper, we analyze the 3D structure of vortices developed in a rotating cylinder nonhomogeneously heated from below, when the rotation rate is increased. The analysis has been done by using nonlinear simulations. For a fixed Rayleigh number, the rotation rate is the bifurcation parameter. At low rotation rates, one single vortex is developed. When the rotation on the system is increased, another coexistent vortex appears at mid-levels in the cell. If the rotation is high enough, multiple-vortex structures with three or four vortices are developed at different heights. For larger rotation, complex multiple vortices appear with a chaotic behavior. A force balance analysis permits to study the role of the forces being determinant.

Secondary instability in thin film flows under an inclined plane: growth of lenses on spatially developing rivulets

The response of a thin film flowing under an inclined plane, modelled using the lubrication equation, is studied. The flow at the inlet is perturbed by the superimposition of a spanwise-periodic steady modulation and a decoupled temporally periodic but spatially homogeneous perturbation. As the consequence of the spanwise inlet forcing, the so-called rivulets grow downstream and eventually reach a streamwise-invariant state, modulated along the direction perpendicular to the flow. The linearized dynamics in the presence of a time-harmonic inlet forcing shows the emergence of a time-periodic flow characterized by drop-like structures (so-called lenses) that travel on the rivulet. The spatial evolution is rationalized by a weakly non-parallel stability analysis. The occurrence of the lenses, their spacing and thickness profile, is controlled by the inclination angle, flow rate, and the frequency and amplitude of the time-harmonic inlet forcing. The faithfulness of the linear analyses is verified by nonlinear simulations. The results of the linear simulations with inlet forcing are combined with the computations of nonlinear travelling lenses solutions in a double-periodic domain to obtain an estimate of the dripping length, for a large range of conditions.

Nonlinear Simulations of GravityWave Tunneling and Breaking over Auckland Island

Horizontally dispersing gravity waves with horizontal wavelengths of 30 – 40 km were observed at mesospheric altitudes over Auckland Island by the airborne advanced mesospheric temperature mapper during a DEEPWAVE research flight on 14 July 2014. A 3D nonlinear compressible model is used to determine which propagation conditions enabled gravity wave penetration into the mesosphere and how the resulting instability characteristics led to widespread momentum deposition. Results indicate that linear tunneling through the polar night jet enabled quick gravity wave propagation from the surface up to the mesopause, while subsequent instability processes reveal large rolls that formed in the negative shear above the jet maximum and led to significant momentum deposition as they descended. This study suggests that gravity wave tunneling is a viable source for this case and other deep propagation events reaching the mesosphere and lower thermosphere.

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ion temperature gradient (ITG), trapped electron mode (TEM) and electron temperature gradient (ETG) modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermodiffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.