13:30
Instability and Transition 4
Chair: Martin Oberlack
13:30
15 mins
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Direct versus noise-induced optimal transitions for a model shear flow
Marina Pausch, Bruno Eckhardt
Abstract: The transition from laminar to turbulent flow in parallel shear flows like pipe flow or plane Couette flow is not due to a linear instability of the laminar profile but requires finite amplitude perturbations. The perturbations have to be strong enough that they cross the boundary to the basin of attraction of the turbulent regime.
We use a 2-dimensional model of the transition to turbulence to explore the underlying phase space structure for optimal perturbations with respect to three different criteria: the energy of the initial condition, the energy dissipation of the initial condition and the amplitude of noise in a noise-induced transition. We find that the optimal transition states are different, but that the scaling with Reynolds number is the same in all three cases. Implications for full simulations will be discussed.
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13:45
15 mins
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Stereoscopic PIV measurement in laminar rotating plane Couette flow
Takuya Kawata, P. Henrik Alfredsson
Abstract: Plane Couette flow with spanwise system rotation shows structures of streamwise-oriented roll cells that arise due to the instability by the Coriolis force when the system rotation is in the opposite direction to the mean flow vorticity.
The momentum transport caused by such roll cell structures makes the flow tend to exhibit zero absolute vorticity.
In the present study, stereoscopic PIV measurements in the rotating plane Couette flow were carried out in order to further illuminate the vortex structures and transport phenomena in this flow.
The Reynolds stresses and some terms of its transport equation were evaluated to discuss the transport phenomena caused by the coherent structure.
Furthermore, the wall shear stress was evaluated based on the measurement results of the Reynolds and viscous shear stresses and its variation with the system rotation rate is also presented.
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14:00
15 mins
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Turbulent bursts and linear instabilities in rotating channel flow
Geert Brethouwer
Abstract: Recurring bursts of turbulence are observed in DNS of rotating channel flow
for a range of Reynolds numbers and rotation rates. The bursts are caused
by a linear instability and happen in a weakly to strongly turbulent environment.
In some cases turbulence or other flow fluctuations can slow down the instability.
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14:15
15 mins
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An Analytical Criterion for Centrifugal Instability in Non-Axisymmetric Vortices
David Nagarathinam, Sameen A, Manikandan Mathur
Abstract: Non-axisymmetric vortices are ubiquitous in nature; examples include polar vortices in planets, the giant red spot in Jupiter, tornadoes and cyclones on Earth, mesoscale eddies in the ocean. Turbulent flows are furthermore known to be dominated by small- and large-scale vortex structures. Owing to the wide range of applications, knowledge of conditions under which a given vortex becomes unstable is beneficial. Here, the centrifugal instability of two-dimensional, non-axisymmetric vortices in the presence of an axial flow $(w)$ and a background rotation $(\Omega_z)$ is studied using the local stability approach. The local stability approach, based on geometric optics and similar in formulation to the rapid distortion theory \cite{bib:godeferd2001}, considers the evolution of shortwavelength perturbations along streamlines in the base flow. This approach, developed by Lifschitz $\&$ Hameiri \cite{bib:lifschitz1991}, is particularly useful for base flows for which a global stability analysis is computationally expensive. A sufficient criterion for centrifugal instability in an axisymmetric vortex with $(w)$ and $(\Omega_z)$ is first derived by analytically solving the local stability equations for wave vectors that are periodic upon evolution around a closed streamline. This criterion is then heuristically extended to non-axisymmetric vortices and written in terms of integral quantities on a streamline. The criterion is then shown to be accurate in describing centrifugal instability over a reasonably large range of parameters that specify Stuart vortices and Taylor-Green vortices.
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14:30
15 mins
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Turbulent bands in a planar shear flow without walls
Matthew Chantry, Laurette S. Tuckerman, Dwight Barkley
Abstract: The banded structure of turbulence is observed immediately beyond transition in shear flows with two unconstrained directions (e.g. TCF, PCF, PPF). Yet despite its ubiquitous nature, the mechanisms underpinning bands are not understood to the level of localized turbulence in pipe flow. To this aim we investigate turbulent bands in Waleffe flow, a sinusoidal shear flow, U(y)=sin(pi/2 * y), with stress-free boundary conditions at y=+-1. The existence of turbulent bands in this system demonstrates that walls are not necessary to induce the phenomenon. The sinusoidal nature of the base forcing means the dominant features of bands can be viewed through a small number of Fourier modes in y. Utilizing this simple dependence we examine the emergence of turbulent bands from uniform turbulence.
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14:45
15 mins
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Influence of Magnetic Diffusion on Short-Wavelength Magnetic Buoyancy Instability
Marek Grądzki, Krzysztof Mizerski
Abstract: Magnetic buoyancy instability (MBI) is believed to plays an important role in the evolution of magnetic fields in astrophysical objects. In the Sun large-scale toroidal magnetic field is probably generated in the tachocline – a thin region of strong radial shear, between radiative and convective zones. Observations indicate that this field rises the surface and create active regions. MBI is a probable mechanism for this phenomenon. Magnetic and thermal diffusivity are parameters of solar plasma which could be important for dynamics of MBI. Here we consider preliminary case which include only magnetic dissipation. The singular perturbation methods are used to find difference with case without any dissipation.
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15:00
15 mins
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Unstable periodic motion in large eddy simulation of homogeneous, isotropic turbulence
Lennaert van Veen, Yasuda Tatsuya, Susumu Goto, Genta Kawahara
Abstract: We study unstable, time-periodic solutions in Large Eddy Simulation (LES) of Homogeneous, Isotropic Turbulence (HIT). The
turbulence is forced at large spatial scales by an external body force which induces four vortex columns in a
rectangular domain with periodic boundary conditions. The dissipation range dynamics is represented by the
Smagorinsky model. Both the kinematic viscosity and the Smagorinsky constant are used as a homotopy parameters connecting steady, laminar flow
to turbulent inertial range dynamics. We find several families of periodic solutions, some bifurcating from the
steady flow and some filtered from more turbulent dynamics, and attempt to track these solutions to the limit of
fully developed turbulence.
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15:15
15 mins
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DIFFERENTIAL DIFFUSIVE INSTABILITIES OF MISCIBLE TWO-LAYER STRATIFICATIONS IN POROUS MEDIA AND HELE-SHAW CELLS
Shyam Sunder Gopalakrishnan, Jorge Carballido-Landeira, Anne De Wit, Bernard Knaepen
Abstract: In porous media, a stratification of a given solution on top of another miscible solution can be buoyantly unstable because
of an unstable density stratification or because of differential diffusive effects. The former is the well known Rayleigh–Taylor (RT)
mechanism wherein the interface is destabilized by the denser solution overlying a less dense one in the gravity field. Whereas the latter
is of particular interest in the field of oceanography, when the upper solution is less dense than the lower one with the lower component
diffusing faster than the upper one, resulting in a double diffusive (DD) instability. Similarly, a diffusive-layer convection (DLC)
instability has also been observed for a stable density stratification with the upper solute diffusing faster than the lower one. Though
the literature on differential diffusion effects is pretty vast, very few studies have managed to establish a connection, both qualitatively
and quantitatively, between numerical simulations and experimental observations, which is the basis of the present study. We report
our findings in a broad parameter range where the instability mechanism could be triggered by an unstable density stratification or due
to differential diffusive effects, or even both, resulting in mixed modes.
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