Session ES: Rotating Flows II

High order structure functions and intermittency in decaying rotating turbulence

Longitudinal and transverse velocity structure functions are measured in a decaying rotating turbulence experiment by means of Particle Image Velocimetry (PIV). Turbulence is generated by rapidly towing a grid through the fluid, providing an initial state which is approximately homogeneous and isotropic. During the self-similar decay of turbulence, before the Ekman timescale, structure functions up to order 8 show well-defined power laws in the inertial range. For moderate Rossby numbers, the exponent of the second-order longitudinal structure function, $\zeta_2$, is found to increase in time, in agreement with the steepening of the power spectrum, but the normalized higher-order exponents, $\zeta_p / \zeta_2$, remain close to those of the intermittent non-rotating case (She-Leveque model). For smaller Rossby numbers, a slight departure of $\zeta_p / \zeta_2$ from the intermittent curve is observed, although it remains far from the non-intermittent linear prediction $\zeta_p / \zeta_2 = p/2$. These results are compared to recent experiments and simulations of forced rotating turbulence.   

Steroscopic PIV measurements in electromagnetically forced rotating turbulence

A novel laboratory experiment has been set up for studying effects of rotation on (inhomogeneous) turbulence. Rotating turbulence plays an important role in fields as diverse as engineering, geophysics, and astrophysics. Three-dimensional turbulence is generated near the bottom of a square fluid container using electromagnetic forcing. Typical Taylor-based Reynolds numbers are of the order of 150-200. A stereoscopic PIV technique is used for quantifying the two-dimensionalisation by rotation. From the many results, we mention here the linear scaling of the structure function exponents in presence of rotation, as reported recently by Baroud et al. [Phys. Rev. Lett. 88, 4501 (2002)]. The scaling is anomalous with respect to the theoretical prediction for self-similar homogeneous isotropic turbulence.   

Large Eddy Simulation and Measurements of Turbulent Rotor-Stator Flows

Comparisons between large eddy simulation (LES) and velocity measurements have been performed for the turbulent flow in a real shrouded rotor-stator configuration. To investigate turbulent flow regimes, LES numerical results (Spectral Vanishing Viscosity technique) and experimental data have been favourably compared for a large range of rotational Reynolds number 10$^{5}\le $Re=$\Omega $b$^{2}$/$\nu \le $10$^{6}$ in an annular cavity of curvature parameter Rm = (b + a)/(b- a) = 1$.$8 and of aspect ratio G = (b-a)/h = 5, where a and b are respectively the inner and outer radii of the rotating disk and $h $is the interdisk spacing. All the characteristics of 3D turbulent boundary layers have been found and coherent structures have been shown under the form of annuli or spiral arms.   

Saturation of the Magnetorotational Instability

An analytical theory is presented [1,2] that describes asymptotically exactly the process of nonlinear saturation of the magnetorotational instability in a strongly nonlinear regime. The theory is applied to a model problem employing a linear shear flow in a uniformly rotating channel, and can be extended to annular domains. The theory shows that the instability saturates by modifying the shear responsible for it, and that both viscous and ohmic dissipation are required to achieve saturation. The theory also describes the approach from small amplitude perturbations to the final strongly nonlinear saturated state. Possible applications to recent laboratory experiments as well as to accretion disks will be discussed. \newline \newline [1] E. Knobloch and K. Julien, Phys. Fluids 17, 094106 (2005). \newline [2] K. Julien and E. Knobloch. J. Math. Phys. 48, 065405 (2007)   

Numerical simulations of magneto-rotational turbulence in cylindrical geometry.

Inspired by the puzzle of anomalous angular momentum transport in accretion discs, direct numerical simulations of magneto-rotational turbulence are performed in cylindrical Couette geometry. We show that in strongly supercritical regimes, the flows act as efficient dynamos and the turbulence persists even in the absence of an externally imposed magnetic field. The mechanism responsible for the saturation amplitude of the turbulence involves both an increase in dissipation and a modification of the background rotational profile. The angular momentum transport is enhanced from its collisional value by a factor of the order the Reynolds number of the fluctuating velocity. Despite approximate equipartition between the velocity and magnetic fluctuations, the transport is mostly associated with the Maxwell stresses due to correlation of the magnetic fluctuations induced by their kinematic interaction with the background rotational shear.   

Modulated rotating convection

Recent experiments in rotating convection have shown that the spatio-temporal bulk convective state with K\"uppers-Lortz dynamics can be suppressed by small amplitude modulations of the rotation rate. The resultant axisymmetric pulsed target patterns were observed to develop into axisymmetric modulated traveling roll states as the modulation amplitude and Rayleigh number were increased. Using the Navier--Stokes--Boussinesq equations with physical boundary conditions, we are able to numerically reproduce the experimental results and gain physical insight into the responsible mechanism, and relate onset of the traveling roll state to a saddle-node on an invariant circle bifurcation.   

Wall-attached convection in rotating annular cavities

Rayleigh-B\'{e}nard convection is investigated in rotating annular cavities using three-dimensional spectral solutions of the basic equations in the Boussinesq-Oberbeck approximation. At moderate rotation rates, convection modes attached to the sidewalls set in at values of the Rayleigh number significantly below the value of the onset of convection in an infinitely extended layer. In this work, we investigate the linear and nonlinear dynamics of these sidewall modes at intermediate rotation rates $\Omega =60$ and $\Omega =180$ and in the case of annular cavities of aspect ratio $\Gamma (\equiv \Delta R/d)=1.5$, where $\Delta R=R_o -R_i $ and $d$ is the height of the cavity. As the mean radius decreases from $R_m =2.2$ to $1.4$, the wall-mode convection does no longer set in along the inner cylinder because of the circumference becomes small compared to the expected mode-wavelength. Then, axisymmetric convection rolls occurs travelling slowly in the radial direction.