We present detailed experiments on transient growth of turbulent spots induced by external forcing in plane Couette-Poiseuille flow, which are studied in the framework of linear of transient growth. The experimental investigation is supplemented with full theoretical analysis. We compare quantitatively the experimental and theoretical results, including maximal gain and the time at which it occurs. We also present the limits of validity for the application of the linear theory at high amplitude perturbation and Reynolds number, showing experiments with self-sustained states.
We experimentally and numerically investigate the temporal aspects of turbulent spots spreading in a plane Couette flow for transitional Reynolds numbers between 300 and 450. Spot growth rate, spot advection rate and large-scale flow intensity are measured as a function of time and Reynolds number. All these quantities show similar dynamics clarifying the role played by large-scale flows in the advection of the turbulent spot. The contributions of each possible growth mechanism: growth induced by large scale advection or growth by destabilization, are discussed for the different stages of the …
The proliferation of turbulence in subcritical wall-bounded shear flows involves spatially localised coherent structures. Turbulent spots correspond to finite-time nonlinear responses to pointwise disturbances and are regarded as seeds of turbulence during transition. The rapid spatial decay of the turbulent fluctuations away from a spot is accompanied by large-scale flows with a robust structuration. The far field velocity field of these spots is investigated numerically using spectral methods in large domains in four different flow scenarios (plane Couette, plane Poiseuille, Couette-Poiseuil…
We investigate the growth in the spanwise direction of turbulent spots invading a laminar flow in a plane Couette flow. Direct Numerical Simulation is used to track the nucleation of streaks during the spot growth. Experiment and direct numerical simulation allow us to study the velocity of the spot fronts and of the vortices observed at the spots' edges. All these results show that two mechanisms are involved when turbulent spots grow: a formerly proposed local growth occurring at the spot spanwise tips but also in comparable proportion a global growth induced by large-scale advection identif…
Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear stability analysis to a turbulent swirling jet undergoing a control parameter transient. The flow undergoes a transition from a non-vortex breakdown state to a state with a strong recirculation bubble and the associated global mode. High-speed Particle Image Velocimetry (PIV) measurements are the basis for a local linear stability analysis of the temporarily e…
Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow -- the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotempor…
It has been reported that a fully localized turbulent band in channel flow becomes sustained when the Reynolds number is above a threshold. Here we show evidences that turbulent bands are of a transient nature instead. When the band length is controlled to be fixed, lifetimes of turbulent bands appear to be stochastic and exponentially distributed, a sign of a memoryless transient nature. Besides increasing with the Reynolds number, the mean lifetime also strongly increases with the band length. Given that the band length always changes over time in real channel flow, this size dependence may …
We present a new experimental set-up that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We carry out the first experimental results in the transitional regime for this flow. Using flow visualization we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures …
We find an instability resulting in generation of large-scale vorticity in a fast rotating small-scale turbulence or turbulent convection with inhomogeneous fluid density along the rotational axis in anelastic approximation. The large-scale instability causes excitation of two modes: (i) the mode with dominant vertical vorticity and with the mean velocity being independent of the vertical coordinate; (ii) the mode with dominant horizontal vorticity and with the mean momentum being independent of the vertical coordinate. The mode with the dominant vertical vorticity can be excited in a fast rot…
Influence of statistically stationary, homogeneous, and isotropic turbulence on the mean area of a passive self-propagating front and, hence, on the rate of fluid consumption by the front is analysed in the case of asymptotically high turbulent Reynolds number $Re_L$ and asymptotically high ratio of the Kolmogorov velocity to a constant speed $u_0$ of the front. By considering an early stage of the front evolution, the mean (over the studied early stage) front area and consumption velocity $\bar{u}_T$ are analytically determined. The analysis shows that the mean $\bar{u}_T$ is proportional to …
For channel flow at subcritical Reynolds numbers ($Re<5772$), a laminar-to-turbulent transition can emerge due to a large transient amplification in the kinetic energy of small perturbations, resulting in an increase in drag at the walls. The objectives of the present study are three-fold: (1) to study the nonlinear effects on transient energy growth, (2) to design a feedback control strategy to prevent this subcritical transition, and (3) to examine the control mechanisms that enable transition suppression. We investigate transient energy growth of linear optimal disturbance in plane Poiseuil…
The breakup of an interface into a cascade of droplets and their subsequent coalescence is a generic problem of central importance to a large number of industrial settings such as mixing, separations, and combustion. We study the breakup of a liquid jet introduced through a cylindrical nozzle into a stagnant viscous phase via a hybrid interface-tracking/level-set method to account for the surface tension forces in a three-dimensional Cartesian domain. Numerical solutions are obtained for a range of Reynolds (Re) and Weber (We) numbers. We find that the interplay between the azimuthal and strea…
Transient energy growth of flow perturbations is an important mechanism for laminar-to-turbulent transition that can be mitigated with feedback control. Linear quadratic optimal control strategies have shown some success in reducing transient energy growth and suppressing transition, but acceptable worst-case performance can be difficult to achieve using sensor-based output feedback control. In this study, we investigate static output feedback controllers for reducing transient energy growth of flow perturbations within linear and nonlinear simulations of a sub-critical channel flow. A static …
In the article the authors present a numerical method for modelling a laminar-turbulent transition in magnetohydrodynamic flows. The equations in the small magnetic Reynolds numbers approach is considered. Speed, pressure and electrical potential are decomposed to the sum of the state values and the finite amplitude perturbations. A solver based on the Nectar++ framework is described. The authors suggest to use of small-length local disturbances as a transition trigger. They can be imposed by blowing or electrical enforcing. The stability of the Hartmann flow and the flow in the bend are consi…
In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study the localized turbulence in pipe flow numerically and elucidate a state space structure that gives rise to transient chaos. Starting from the basin boundary separating laminar and turbulent flow, we identify transverse homoclinic orbits, the presence of which necessitates a homoclinic tangle and chaos. A direct consequence of the homoclinic tangle is the fractal nature of the laminar-turbulent boundary…
Nuclear burning plays a key role in a wide range of astrophysical stellar transients, including thermonuclear, pair instability, and core collapse supernovae, as well as kilonovae and collapsars. Turbulence is now understood to also play a key role in these astrophysical transients. Here we demonstrate that turbulent nuclear burning may lead to large enhancements above the uniform background burning rate, since turbulent dissipation gives rise to temperature fluctuations, and in general the nuclear burning rates are highly sensitive to temperature. We derive results for the turbulent enhanceme…
Despite the nonlinear nature of wall turbulence, there is evidence that the energy-injection mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities from mean-flow inflection points, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in simplified theories and conceptual arguments. Whether the flow follows a…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Melentiev Energy Systems Institute of Siberian Branch of Russian Academy of Sciences（俄罗斯科学院西伯利亚分院梅连季耶夫能源系统研究所）
Turbulent state of spectrally stable shear flows may be developed and sustained according to the bypass scenario of transition. If it works in non-magnetised boundless and homogeneous quasi-Keplerian flow, transiently growing shearing vortices should supply turbulence with energy. Employing the large shearing box approximation, as well as a set of global disc models, we study the optimal growth of the shearing vortices in such a flow in the whole range of azimuthal length-scales, $λ_y$, as compared to the flow scale-height, $H$. It is shown that with the account of the viscosity the highest po…
