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14:00   Wall Bounded Turbulence 2 14:00 15 mins #141 Dynamics and evolution of Turbulent Taylor rolls Francesco Sacco, Rodolfo Ostilla-Mónico, Roberto Verzicco Abstract: In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor-Couette flow, the fluid motion developing in the gap between two concentric cylinders rotating at different angular velocity, is not an exception, and toroidal Taylor rolls have been observed from the early development of the flow up to the fully turbulent regime. In this manuscript we show that under the generic name of ``Taylor rolls'' there is a wide variety of structures that differ for the vorticity distribution within the cores, the way they are driven and their effects on the mean flow. We relate the rolls at high Reynolds numbers not to centrifugal instabilities, but to a combination of shear and anti-cyclonic rotation, showing that they are preserved in the limit of vanishing curvature and can be better understood as a pinned cycle which shows similar characteristics as the self-sustained process of shear flows. By analyzing the effect of the computational domain size, we show that this pinning is not a product of numerics, and that the position of the rolls is governed by a random process with the space and time variations depending on domain size. 14:15 15 mins #96 Turbulence: the view from the wall Miguel Encinar, Javier Jimenez Abstract: In this work we focus on the reconstruction of the velocity components in the logarithmic layer from wall measurements only, using linear stochastic estimation. We found that the reconstructions are reasonably accurate up to $y/h \approx 0.3$, and that the eddies that can be reconstructed are those "attached" in the sense of Townsend 14:30 15 mins #151 A realizable turbulence model for the Reynolds stress based on the square root tensor Kazuhiro Inagaki, Taketo Ariki, Fujihiro Hamba Abstract: To perform a numerical simulation of high-Reynolds-number turbulent flows, the Reynolds-averaged Navier-Stokes (RANS) modeling is still useful approach. The previous study proposed a turbulence modeling for the Reynolds stress based on the square root tensor in which the realizability conditions are always satisfied. Using this technique, we propose a realizable model for the Reynolds stress involving quartic nonlinearity on the velocity gradient. The performance of the present model is discussed in basic turbulent flows. 14:45 15 mins #270 Statistics of streamline geometry in wall-bounded turbulence Rina Perven, Joseph Klewicki, Jimmy Philip Abstract: The pdf file attached 15:00 15 mins #471 Hierarchy of vortices in a developed turbulent boundary layer Susumu Goto, Yutaro Motoori Abstract: We conduct the DNS of a developed turbulent boundary layer to reveal the concrete image of the hierarchy of coherent vortices and its generation mechanism. Our DNS shows that, in the logarithmic layer, large-scale vortices are directly created by mean-flow stretching, whereas small-scale ones seem to be sustained by a kind of energy cascade due to the vortex stretching by larger-scale vortices. 15:15 15 mins #441 How invariant solutions support the formation of oblique turbulent-laminar stripes Tobias M. Schneider, Florian Reetz Abstract: Transitional shear flows in spatially extended wall-bounded geometries form patterns of coexisting laminar and turbulent regions. Most prominent are regular turbulent-laminar stripes with large-scale wavelengths and a non-obvious oblique orientation against the direction of the laminar base flow. The mechanism behind the formation of oblique stripe patterns has puzzled scientists for almost 6 decades. Recent advances in computational methods not only allow to efficiently simulate stripes [1] but also to construct exact invariant solutions of the Navier-Stokes equations that resemble the oblique stripe pattern (Fig. 1). We present a set of invariant solutions of plane Couette flow, including equilibrium solutions and periodic orbits, that have the geometric characteristics of the oblique stripe pattern. These invariant solutions emerge via saddle-node, pitchfork and Hopf bifurcations at low Reynolds numbers Re < 300. At Re = 350, where stripes are observed as a stable pattern, these weakly unstable invariant solutions form a dynamical network supporting the patterned turbulence. The invariant solutions exist over a limited range of pattern angles suggesting a selection mechanism for the observed oblique orientation of turbulent-laminar stripes. 15:30 15 mins #365 A ONEDIMENSIONAL EXAMPLE OF THE CONTRASTING BEHAVIOUR OF LAMINAR AND TURBULENT FLOW Paolo Luchini Abstract: It is an experimental and numerical fact, although perhaps not a widely known one, that the turbulent incarnation of plane Poiseuille flow has a \emph{higher} velocity than turbulent Couette flow for the same value of the wall shear stress. Equivalently, it exhibits a higher velocity profile when represented in wall units. This difference was interpreted in \cite{PRL,EJMB} as a wake function induced by the pressure gradient, which must be summed to the universal logarithmic law in a framework of matched asymptotic expansions. This presentation is to point out that this turbulent behaviour is strikingly opposite to laminar behaviour, where in wall units the velocity profile of Poiseuille flow is everywhere \emph{lower} than in Couette flow, as depicted in Figure \ref{pgcomp} for an arbitrarily chosen Reynolds number $\Re_\tau=1000$. This at first sight counterintuitive contrapposition is coherent with one that was observed by Russo and Luchini \cite{RL}, during the direct numerical simulation of a turbulent channel flow perturbed by an external force profile $F(z)$ with zero mean. There we found that a zero-resultant force produces a flow rate which not only is nonzero, but astonishingly has opposite direction in laminar and in turbulent flow. We deduced that the concept of a local turbulent diffusion, or eddy viscosity, which likens turbulent transport to a space-varying classical viscosity, should perhaps be adopted with more caution than it frequently is in dealing with boundary perturbations to a parallel flow \cite{BH}. Figure \ref{pgcomp} in fact provides an even simpler piece of evidence of the same phenomenon. Let us assume that the difference $\delta u=u_P(z)-u_C(z)$ between Poiseuille and Couette velocity is described by an eddy-viscosity model of the mixing-length variety; it would then have to obey the Reynolds-averaged equation \begin{equation} \left[\nu_T(z)\delta u_z\right]_z = p_x/\rho \label{eq1} \end{equation} where $\nu_T(z)$ is the eddy viscosity. With the boundary conditions $\delta u(0)=\delta u_z(0)=0$, the solution $\delta u$ of (\ref{eq1}) for a favourable, negative pressure gradient and any positive eddy viscosity is bound to be negative, just as it is when viscosity is constant in laminar flow, whereas the true turbulent $\delta u$ displayed in Figure \ref{pgcomp} is positive. Therefore the conclusion attained by Russo and Luchini \cite{RL} with reference to a zero-mean volume force applies just as well to the mean pressure gradient: the widespread mixing-length model \eqref{eq1} is an oversimplification and fails to capture the observed onedimensional physics.