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Register a new userForced linear shear flows with rotation: rotating Couette-Poiseuille flow, its stability and astrophysical implications
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We explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions suitable for the systems under consideration, the background plane shear flow and, hence, accretion disk velocity profile modifies to parabolic flow, which is plane Poiseuille flow or Couette-Poiseuille flow, depending on the frame of reference. In the presence of rotation, plane Poiseuille flow becomes unstable at a smaller Reynolds number under pure vertical as well as threedimensional perturbations. Hence, while rotation stabilizes plane Couette flow, the same destabilizes plane Poiseuille flow faster and forced local accretion disk. Depending on the various factors, when local linear shear flow becomes Poiseuille flow in the shearing box due to the presence of extra force, the flow becomes unstable even for the Keplerian rotation and hence turbulence will pop in there. This helps in resolving a long standing problem of sub-critical transition to turbulence in hydrodynamic accretion disks and laboratory plane Couette flow.
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Turbulent plane Poiseuille and Couette flows share the same geometry, but produce their flow rate owing to different external drivers, pressure gradient and shear respectively. By looking at integral energy fluxes, we pose and answer the question of which flow performs better at creating flow rate. We define a flow {em efficiency}, that quantifies the fraction of power used to produce flow rate instead of being wasted as a turbulent overhead; {em effectiveness}, instead, describes the amount of flow rate produced by a given power. The work by Gatti emph{et al.} (emph{J. Fluid Mech.} vol.857, 2018, pp. 345--373), where the constant power input (CPI) concept was developed to compare turbulent Poiseuille flows with drag reduction, is here extended to compare different flows. By decomposing the mean velocity field into a laminar contribution and a deviation, analytical expressions are derived which are the energy-flux equivalents of the FIK identity. These concepts are applied to literature data supplemented by a new set of direct numerical simulations, to find that Couette flows are less efficient but more effective than Poiseuille ones. The reason is traced to the more effective laminar component of Couette flows, which compensates for their higher turbulent activity. It is also observed that, when the fluctuating fields of the two flows are fed with the same total power fraction, Couette flows dissipate a smaller percentage of it via turbulent dissipation. A decomposition of the fluctuating field into large and small scales explains this feature: Couette flows develop stronger large-scale structures, which alter the mean flow while contributing less significantly to dissipation.
We consider the effect of stratification on systematic, large-scale flows generated in anelastic convection. We present results from three-dimensional numerical simulations of convection in a rotating plane layer in which the angle between the axis of rotation and gravity is allowed to vary. This model is representative of different latitudes of a spherical body. We consider two distinct parameter regimes: (i) weakly rotating and (ii) rapidly rotating. In each case, we examine the effect of stratification on the flow structure and heat transport properties focussing on the difference between Boussinesq and anelastic convection. Furthermore, we show that regimes (i) and (ii) generate very different large-scale flows and we investigate the role stratification has in modifying these flows. The stratified flows possess a net helicity not present in the Boussinesq cases which we suggest, when combined with the self-generated shear flows, could be important for dynamo action.
We reveal and investigate a new type of linear axisymmetric helical magnetorotational instability which is capable of destabilizing viscous and resistive rotational flows with radially increasing angular velocity, or positive shear. This instability is double-diffusive by nature and is different from the more familiar helical magnetorotational instability, operating at positive shear above the Liu limit, in that it works instead for a wide range of the positive shear when ${rm (i)}$ a combination of axial/poloidal and azimuthal/toroidal magnetic fields is applied and ${rm (ii)}$ the magnetic Prandtl number is not too close to unity. We study this instability first with radially local WKB analysis and then confirm its existence using a global stability analysis of the magnetized flow between two rotating cylinders with conducting or insulating boundaries. From an experimental point of view, we also demonstrate the presence of the new instability in a magnetized viscous and resistive Taylor-Couette flow with positive shear for such values of the flow parameters, which can be realized in upcoming experiments at the DRESDYN facility. Finally, this instability might have implications for the dynamics of the equatorial parts of the solar tachocline and dynamo action there, since the above two necessary conditions for the instability to take place are satisfied in this region. Our global stability calculations for the tachocline-like configuration, representing a thin rotating cylindrical layer with the appropriate boundary conditions -- conducting inner and insulating outer cylinders -- and the values of the flow parameters, indicate that it can indeed arise in this case with a characteristic growth time comparable to the solar cycle period.
Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At the intermediate rotation rates, bistability of these two statistically steady states is observed. Such hysteretic behavior is also observed for the variation of the amplitude of an external force.
We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this communication. Although literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by $We = n^2+k^2-1$, is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here, $We = rho Omega^2 a^3/gamma$ is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with $Omega$ being the angular velocity of the rigidly rotating column, $a$ the column radius, $rho$ the density of the fluid, and $gamma$ the surface tension coefficient; $k$ and $n$ denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the $We-k$ plane. For all $n >1$, the viscously unstable region, corresponding to $We > n^2+k^2-1$, contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the $We$ axis, persists for $n= 1$. This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.
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