Session ES: Rotating Flows

Lagrangian statistics in rotating turbulence

Background rotation becomes important when the ratio of the nonlinear acceleration over the Coriolis force becomes small enough. The Coriolis force has an anisotropic effect on the flow, and leads to the formation of columnar vortex structures and Ekman boundary layers close to the horizontal no-slip boundaries. The first aim of this work is to feed the fundamental investigation of turbulence with experimental data, giving further insight into the anisotropic effects of rotation on turbulent particle-pair dispersion and quantifying this anisotropy through the comparison of the horizontal (normal to the rotation axis) dispersion and the reduced vertical one, together with some other relevant manifestations of anisotropy. A series of experiments of electromagnetically forced turbulence ($Re_{\lambda}\sim 150$) is performed in a confined tank put on a rotating table and the Rossby number is varied between 1 and 0.08. A 3D-PTV technique is used to extract trajectories in a volume comparable with the integral scale of the flow and with space- and time-resolutions adequate to resolve the Kolmogorov scales.   

Twisted wake of a sphere in rotating fluid

The Taylor-Proudman theorem has simple and interesting consequences, illustrating the fact that rotating fluids exhibit a range of phenomena not found in non-rotating fluids. The principal phenomenon of these is the formation of Taylor Columns. The phenomena occur if there are relative motions between a flow in a strongly rotating system and an obstacle in the flow. In our research, effect of the background rotation on the wake of flow past a solid sphere has been studied experimentally. The sphere is hung in a rotating tank filled with water. While the sphere is towed along the centre line of the rotation, the wake region was chased with a digital video camera and a light sheet that illuminates the area. The experiments were performed in various range of the Rossby number. The visualization from the same inertia frame yields striking results. Twisting columnar flow, which looks quite similar to Taylor Column, visualized in the wake of a sphere in rotating fluid. Taking PTV (Particle Tracking Velocimetry) analysis, velocity fields of the flow were obtained. With the help of the results, discussions about the development of the twisted columnar flow and its structure will have been taken place in the conference.   

Gravitationally forced surface waves in a rotating cylinder

A thin layer of fluid, flowing axially along the inner surface of a horizontal rotating cylinder is subjected to a periodic forcing due to the gravitational acceleration. Since the frequency of the forcing lies within the critical range ($[0,\,2 \Omega]$) for which the inviscid problem is of a hyperbolic nature, the solution which in this case may be obtained on closed form displays a characteristic ``Mach wave''-like behavior.   

Experimental Study of Energy Transfer by Inertial Waves During the Build up of Turbulence in a Rotating System

We study the transition from fluid at rest to turbulence in a rotating water cylinder. We show that the energy, injected at a given height, is carried by inertial wave packets through the volume. These waves serve as the main energy transport mechanism and even when they are of large amplitude, they propagate in velocities consistent with those calculated form linearized theory. Nonlinear energy transport is governed by a second time scale, which depends on the velocity of the flow. It, thus, takes place only at long times and allows for the observed extended linear behavior. The observed linear effects that are unique to rotating flows can, therefore, highly impact energy transfer, distribution and statistics, even at high Reynolds numbers. Such effects are of special importance when considering rotating turbulent fields that are driven by intermittent energy sources.   

Direct Numerical Simulation and Coherent Vortex Extraction of sheared and rotating turbulent flow

The effect of rotation on the structure and dynamics of homogeneous sheared turbulence is investigated using direct numerical simulation (PoF, 20, 045103 (2008)). We consider shear flow without rotation, with moderate and with strong rotation, where the rotation axis is either parallel or anti-parallel to the mean flow vorticity. For moderate rotation an anti-parallel configuration increases the growth of the turbulent kinetic energy for a limited range of rotation ratios, while the parallel case reduces the growth as compared to the non-rotating case. For strong rotation energy decay is observed and linear effects dominate. Flow visualizations show that the inclination angle of vortical structures depends on the rotation rate and orientation and that the inclination angle is related to the growth of the turbulent kinetic energy. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. The coherent part preserves the vortical structures using only a few percent of the degrees of freedom, while the incoherent part was found to be structureless and of dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, indicating an increased coherency of the flow. Restarting the DNS with the filtered fields confirms that the coherent component preserves the temporal dynamics of the total flow.   

Modeling the effects of system rotation on the turbulent heat fluxes

A new model is proposed for accounting for the effects of system rotation on the turbulent scalar fluxes. The model is based on extension to rotating frames of an explicit, algebraic model derived using tensor representation theory. The outcome is a rational model which allows for the turbulent scalar fluxes to depend on the details of the turbulence field and on the gradients of both the mean velocity and temperature. Such dependence, which is absent from conventional gradient-transport models, is required by the exact equations governing the transport of the heat fluxes. An a priori assessment of the model is performed using results from Direct Numerical Simulations of heated flows in channels rotated about their streamwise, spanwise and wall-normal axes. The results are generally in close agreement with the DNS but some important differences remain. The reasons for these are discussed. Further assessment is carried out by actual computations of heated flow in a channel rotated about a spanwise axis with suction through one wall and blowing through the opposite wall. Comparisons are made with experimental data and with results from a complete scalar-flux transport model. Conclusions are drawn from these results, and from a variety of other flows with system rotation, streamline curvature and swirl.   

Laminarization mechanisms in rotating channel flow

The influence of moderate rotation rate on turbulent channel flow is that the turbulence is suppressed on the stable side and augmented on the unstable side because of the Coriolis force. When the rotation increases the turbulent region becomes restricted to an increasingly thin zone near the unstable wall. For a rotation rate, $Ro>3$ (normalized by bulk velocity and channel height) inviscid linear theory yields a stable laminar flow (Bradshaw JFM 1969) and a recent DNS study (Grundestam et al., JFM 2008) indicates that the turbulent flow laminarizes for $Ro$ slightly below 3. By including viscous effects in a novel linear stability analysis the critical $Ro$ has been identified for different $Re$ and has been verified by DNS. The most unstable modes are tilted slightly oblique streamwise vortices clearly visible in the DNS. TS waves are unaffected by rotation and are always unstable for supercritical $Re$ but with a different length scale and an interesting interaction with the other modes.   

Numerical and mathematical approaches to analyses of water-circulator-induced flow in ponds

Pollution and muddiness of natural and artificial reservoirs that are used to supply water irrigation have become important problems in recent years. A rotating propeller operating at low speed set on a lake surface is proposed because it is expected that the device can induce vertical circulating flow by the centrifugal force. Although various experiments have shown clearly that the water quality in a lake is improved by operation of such equipment, the flow mechanism is not fully understood. This study is intended to characterize vertical circulating flow resulting from the propeller's action. To survey such a fluid motion numerically and mathematically in simple systems, the flow induced by the top boundary condition which forces a horizontal rotating flow is investigated here. Simulations of flows created by the top boundary condition are carried out to obtain steady-state solutions with various Reynolds numbers and aspect ratios.   

Rayleigh-Taylor instability in rotating volcanic umbrellas

We study the shape of an expanding volcanic umbrella that is turbulent and is rotating about a vertical axis though the center of the umbrella. We argue that the centrifugal forces associated with the rotation of the umbrella trigger a turbulent variant of the Rayleigh--Taylor instability. As a manifestation of this instability, the edge of the umbrella becomes wavy. As a test case, we consider the wavy umbrella from the climactic eruption of Mount Pinatubo on June 15, 1991.   

Premixed laminar flame propagation in a rotating vessel

Combustion in a swirling flow is devoted to burn lean mixture in spark ignition engines since it provides fuel economy and exhaust emission reduction. Therefore it is important to know the flame behavior under centrifugal forces. The flame in a rotating gas is modified by an aerodynamic mechanism due to action of centrifugal forces instead the laminar burning velocity due to chemical kinetics. The paper deals with important characteristics of eddy combustion mechanism such as: flame shape and propagation as a function of the rotation rate. Therefore pictures captured by a video camera are treated with the image processing toolbox from Matlab in order to establish the main characteristics of the flame kernel of a mixture propane -- air at different rotation rates ranging from 500 to 4000 rpm. It is observed that the flame propagates along the rotation axis and that the extinguishing of the flame is involved with the heat losses as soon the flame reaches the wall of the chamber. In addition, the flame shape is quite similar to the intrusion head of a light fluid penetrating into a stagnated heavy fluid.