Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLagrangian and Eulerian accelerations in turbulent stratified shear flows
146
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Lagrangian (LA) and Eulerian Acceleration (EA) properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable stratification are studied using direct numerical simulations. The Richardson number is varied from $Ri=0$, corresponding to unstratified shear flow, to $Ri=1$, corresponding to strongly stratified shear flow. The probability density functions (pdfs) of both LA and EA have a stretched-exponential shape and they show a strong and similar influence on the Richardson number. The extreme values of the EA are stronger than those observed for the LA. Geometrical statistics explain that the magnitude of the EA is larger than its Lagrangian counterpart due to the mutual cancellation of the Eulerian and convective acceleration, as both vectors statistically show an anti-parallel preference. A wavelet-based scale-dependent decomposition of the LA and EA is performed. The tails of the acceleration pdfs grow heavier for smaller scales of turbulent motion. Hence the flatness increases with decreasing scale, indicating stronger intermittency at smaller scales. The joint pdfs of the LA and EA indicate a trend to stronger correlations with increasing Richardson number and at larger scales of the turbulent motion. A consideration of the terms in the Navier--Stokes equation shows that the LA is mainly determined by the pressure-gradient term, while the EA is dominated by the nonlinear convection term.
rate research
Read More
A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian) velocity increments. The universal nature of the intermittency phenomenon as observed in experimental measurements and numerical simulations is shown to be fully taken into account by the multiscale picture proposed by the multifractal formalism, and its extensions to the dissipative scales and to the Lagrangian framework. The article is devoted to the presentation of these arguments and to their comparisons against empirical data. In particular, explicit predictions of the statistics, such as probability density functions and high order moments, of the velocity gradients and acceleration are derived. In the Eulerian framework, at a given Reynolds number, they are shown to depend on a single parameter function called the singularity spectrum and to a universal constant governing the transition between the inertial and dissipative ranges. The Lagrangian singularity spectrum compares well with its Eulerian counterpart by a transformation based on incompressibility, homogeneity and isotropy and the remaining constant is shown to be difficult to estimate on empirical data. It is finally underlined the limitations of the increment to quantify accurately the singular nature of Lagrangian velocity. This is confirmed using higher order increments unbiased by the presence of linear trends, as they are observed on velocity along a trajectory.
We present in this article a novel Lagrangian measurement technique: an instrumented particle which continuously transmits the force/acceleration acting on it as it is advected in a flow. We develop signal processing methods to extract information on the flow from the acceleration signal transmitted by the particle. Notably, we are able to characterize the force acting on the particle and to identify the presence of a permanent large-scale vortex structure. Our technique provides a fast, robust and efficient tool to characterize flows, and it is particularly suited to obtain Lagrangian statistics along long trajectories or in cases where optical measurement techniques are not or hardly applicable.
In linearly stable shear flows at moderate Re, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge of chaos, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories we provide evidence, that the edge of chaos separates state space not globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.
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 spatiotemporal phenomena observed in transition, from spot growth to turbulent bands and uniform turbulence. The model substantially reduces the cost of simulating intermittent turbulent structures while maintaining the essential physics and a direct connection to the Navier-Stokes equations. We demonstrate the generic nature of this process by introducing stress-free equivalent flows for plane Poiseuille and pipe flows which again capture the turbulent-laminar structures seen in transition.
A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. The measurements were conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. The stereoscopic particle tracking velocimetry results in three component tracks of position, velocity and acceleration of the tracer particles within the vertically-oriented jet with a Taylor-based Reynolds number $mathcal R_lambda simeq 230$. Analysis is performed at seven locations from 15 diameters up to 45 diameters downstream. Eulerian analysis is first carried out to obtain critical parameters of the jet and relevant scales, namely the Kolmogorov and large turnover (integral) scales as well as the energy dissipation rate. Lagrangian statistical analysis is then performed on velocity components stationarised following methods inspired by Batchelor (textit{J. Fluid Mech.}, vol. 3, 1957, pp. 67-80) which aim to extend stationary Lagrangian theory of turbulent diffusion by Taylor to the case of self-similar flows. The evolution of typical Lagrangian scaling parameters as a function of the developing jet is explored and results show validation of the proposed stationarisation. The universal scaling constant $C_0$ (for the Lagrangian second-order structure function), as well as Eulerian and Lagrangian integral time scales are discussed in this context. $C_0$ is found to converge to a constant value (of the order of $C_0 = 3$) within 30 diameters downstream of the nozzle. Finally, the existence of finite particle size effects are investigated through consideration of acceleration dependent quantities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
