Stabilizing and destabilizing effects of a solid-body rotation on quasi-two-dimensional shear layers (original) (raw)

Rotating free-shear flows. Part 2. Numerical simulations

Journal of Fluid Mechanics, 1995

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Rt), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor-Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.

Experiments on a barotropic rotating shear layer. Part 1. Instability and steady vortices

Journal of Fluid Mechanics, 1999

The barotropic shear layer in a rotating fluid is studied in a laboratory experiment. Through the rotation of circular sections in the base and lid of a circular tank relative to a background rotation of the entire system, a vertical layer of strong horizontal shear develops, the Stewartson layer. Above a critical shear, the shear layer breaks up through barotropic instability, which is an inertial instability. The flow then develops a string of vortices along the shear zone. It will be shown that the transition from an axisymmetric flow to regular vortices occurs through a Hopf bifurcation. Subsequent transitions to more complex flows, such as modulated vortices, chaos and highly irregular flow, will be presented briefly, while the main points of this paper are the primary instability, steady vortices and their nonlinear dynamics. Among the issues discussed is the sensitivity of the flow to the direction of the differential shear. The experimental data will be used to test the abil...

The structure of a turbulent free shear layer in a rotating fluid

Journal of Fluid Mechanics, 1992

An experimental investigation has been carried out on the effects of rotation on the development and structure of turbulence in a free shear layer, oriented so that its mean vorticity is parallel or antiparallel to the system vorticity. The effective local Rossby number extended down to about 1/3. The experimental methods were hydrogen-bubble flow visualization and hot-film anemometry.In summarizing the results we refer to stabilized flow when the system vorticity has the same sign as the shear vorticity and destabilized and subsequently restabilized when it has the opposite sign (Tritton 1992). The roller eddy pattern, familiar in non-rotating flow, was observed in all stabilized flows, but was almost completely disrupted by even weak destabilization. Notable features of the quantitative results were: reorientation by Coriolis effects of the Reynolds stress tensor (inferred from the ratio of the cross-stream to longitudinal turbulence intensity and the normalized shear stress); cha...

Anisotropy and cyclone-anticyclone asymmetry in decaying rotating turbulence

arXiv (Cornell University), 2009

The effect of a background rotation on the decay of homogeneous turbulence produced by a grid is experimentally investigated. Experiments have been performed in a channel mounted in the large-scale 'Coriolis' rotating platform, and measurements have been carried out in the planes normal and parallel to the rotation axis using particle image velocimetry. After a short period of about 0.4 tank rotation where the energy decays as t −6/5 , as in classical isotropic turbulence, the energy follows a shallower decay law compatible with t −3/5 , as dimensionally expected for energy transfers governed by the linear timescale Ω −1. The crossover occurs at a Rossby number Ro ≃ 0.25, without noticeable dependence with the grid Rossby number. After this transition, anisotropy develops in the form of vertical layers where the initial vertical velocity remains trapped. These layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, producing significant horizontal gradient of vertical velocity which eventually become unstable. After the Ro ≃ 0.25 transition, the vertical vorticity field first develops a cyclone-anticyclone asymmetry, reproducing the growth law of the vorticity skewness, S ω (t) ≃ (Ωt) 0.7 , reported by Morize, Moisy & Rabaud [Phys. Fluids 17 (9), 095105 (2005)]. At larger time, however, the vorticity skewness decreases and eventually returns to zero. The present results indicate that the shear instability of the vertical layers contribute significantly to the re-symmetrisation of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the initial conditions in the decay of rotating turbulence.

Experiments on instability of columnar vortex pairs in rotating fluid

Geophysical & Astrophysical Fluid Dynamics, 2002

We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exceeds unity. The vortex pair consisting of a cyclonic and an anticyclonic vortex is induced by a rotating flap in a fluid which is itself initially in a state of solid-body rotation. The anticyclonic vortex is then subject to either centrifugal or elliptical instability, depending on whether its initial ellipticity is small or large, while the cyclone always remains stable. The experimental results demonstrate that the perturbations due to centrifugal instability have a typical form of toroidal vortices of alternating sign (rib vortices). The perturbations due to elliptical instability are of the form of sinuous deformation of the vortex filament in the plane of maximal stretching which corresponds to the plane of symmetry for the vortex pair. The initial perturbations in both cases are characterized by a definite wave number in the vertical direction. The characteristics of the unstable anticyclone are determined by the main nondimensional parameter of the flow -the Rossby number. The appearance of both centrifugal and elliptical instabilities are in accord with the predictions of theoretical criteria for these cases.

Rotating free-shear flows. I. Linear stability analysis

Physics of Fluids A: Fluid Dynamics, 1993

Using linear stability analysis, the instability characteristics are examined of both planar wakes and mixing layers subjected to rigid-body rotation with axis of rotation perpendicular to the plane of the ambient flow. In particular, the tendency of rotation to stabilize or destabilize three-dimensional motions is addressed. In the inviscid limit the results are consistent with the criterion established by Pedley [J. Fluid Mech. 35, 97 (1969)] and Bradshaw [J. Fluid Mech. 36, 177 (1969)]. Cyclonic rotation and strong anticyclonic rotation tend to stabilize three-dimensional motions, whereas weaker anticyclonic rotation (Ro≳1) acts to destabilize these motions. This latter instability is in the form of streamwise rolls, similar to previous results obtained for boundary layer and channel flows. It is found that this instability is stronger than the coexisting Kelvin–Helmholtz instability for roughly the range 1.5<Ro<8, and its effect is maximum for Ro≂2. For the case of constan...

Coherent structures in rotating three-dimensional turbulence

Journal of Fluid Mechanics, 1994

Numerical simulations investigating the formation and stability of quasi-two-dimensional coherent vortices in rotating homogeneous three-dimensional flow are described. In a numerical study of shear flows Lesieur, Yanase & Métais (1991) found that cyclones (respectively anticyclones) with |ω2D| ∼O(2Ω), where ω2Dis the vorticity and Ω is the rotation rate, are stabilized (respectively destabilized) by the rotation. A study of triply periodic pseudo-spectral simulations (643) was undertaken in order to investigate the vorticity asymmetry in homogeneous turbulence. Specifically, we examine (i) the possible three-dimensionalization of initially two-dimensional vortices and (ii) the emergence of quasi-two-dimensional structures in initially-isotropic three-dimensional turbulence. Direct numerical simulations of the Navier—Stokes equations are compared with large-eddy simulations employing a subgridscale model based on the second-order velocity structure function evaluated at the grid sep...

Shear-layer instability in a rotating system

Journal of Flow Visualization …, 2007

The shear-layer instability in the flow over a rotating disk with a free surface is investigated experimentally by flow visualizations for a large range of the flow control parameters: the aspect ratio G of the cavity, the rotationnal Reynolds number Re and the radius ratio s between the inner and outer radii of the rotating disk. This instability develops along the cylindrical shroud as sharp-cornered polygonal patterns characterized by the number of vortices m. This number m can be scaled by considering an Ekman number based on the water depth, which confirms that the shroud boundary layer is of Stewartson type. The appearance threshold of the first polygonal mode is constant by considering the mixed Reynolds number introduced by Niino and Misawa (1984) based on both the water depth at rest and the rotating disk radius. For large values of s, the instability patterns appear along the hub as small stationary cells.

Evolution of a turbulent cloud under rotation

Localized patches of turbulence frequently occur in geophysics, such as in the atmosphere and oceans. The effect of rotation, Ω, on such a region (a 'turbulent cloud') is governed by inhomogeneous dynamics. In contrast, most investigations of rotating turbulence deal with the homogeneous case, although inhomogeneous turbulence is more common in practice. In this paper, we describe the results of 512 3 direct numerical simulations (DNS) of a turbulent cloud under rotation at three Rossby numbers (Ro), namely 0.1, 0.3 and 0.5. Using a spatial filter, fully developed homogeneous turbulence is vertically confined to the centre of a periodic box before the rotation is turned on. Energy isosurfaces show that columnar structures emerge from the cloud and grow into the adjacent quiescent fluid. Helicity is used as a diagnostic and confirms that these structures are formed by inertial waves. In particular, it is observed that structures growing parallel to the rotation axis (upwards) have negative helicity and those moving antiparallel (downwards) to the axis have positive helicity, a characteristic typical of inertial waves. Two-dimensional energy spectra of horizontal wavenumbers, k ⊥ , versus dimensionless time, 2Ωt, confirm that these columnar structures are wavepackets which travel at the group velocities of inertial waves. The kinetic energy transferred from the turbulent cloud to the waves is estimated using Lagrangian particle tracking to distinguish between turbulent and 'wave-only' regions of space. The amount of energy transferred to waves is 40 % of the initial at Ro = 0.1, while it is 16 % at Ro = 0.5. In both cases the bulk of the energy eventually resides in the waves. It is evident from this observation that inertial waves can carry a significant portion of the energy away from a localized turbulent source and are therefore an efficient mechanism of energy dispersion.

Velocity profiles of cyclones and anticyclones in a rotating turbulent flow

Physics of Fluids

Strong rotation makes an underlying turbulent flow quasi-two-dimensional that leads to the upscale energy transfer. Recent numerical simulations show that under certain conditions, the energy is accumulated at the largest scales of the system, forming coherent vortex structures known as condensates. We analytically describe the interaction of a strong condensate with weak small-scale turbulent pulsations and obtain an equation that allows us to determine the radial velocity profile U (r) of a coherent vortex. When external rotation is fast, the velocity profiles of cyclones and anticyclones are identical to each other and are well described by the dependence U (r) ∝ ±r ln(R/r), where R is the transverse size of the vortex. As the external rotation decreases, this symmetry disappears: the maximum velocity in cyclones is greater and the position of the maximum is closer to the axis of the vortex in comparison with anticyclones. Besides, our analysis shows that the size R of the anticyclone cannot exceed a certain critical value, which depends on the Rossby and Reynolds numbers. The maximum size of the cyclones is limited only by the system size under the same conditions. Our predictions are based on the linear evolution of turbulent pulsations on the background of the coherent vortex flow and are accompanied by estimates following from the nonlinear Navier-Stokes equation.