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In an earlier paper we had developed a method for computing the effective energy transfer between any two Fourier modes in fluid or magnetohydrodynamic (MHD) flows. This method is applied to a pseudo-spectral, direct numerical simulation (DNS) study of energy transfer in the quasi-steady state of 2-D MHD turbulence with large scale kinetic forcing. Two aspects of energy transfer are studied: the energy fluxes, and the energy transfer between different wavenumber regions (shells).The picture of energy fluxes that emerges is quite complex -there is a forward cascade of magnetic energy, an inverse cascade of kinetic energy, a flux of energy from the kinetic to the magnetic field, and a reverse flux which transfers the energy back to the kinetic from the magnetic. The energy transfer between different wave number shells is also complex -local and nonlocal transfers often possess opposing features, i.e., energy transfer between some wave number shells occurs from kinetic to magnetic, and between other wave number shells this transfer is reversed. The net transfer of energy is from kinetic to magnetic. The results obtained from the flux studies and the shell-to-shell energy transfer studies are consistent with each other. * In magnetohydrodynamic (MHD) turbulence several scales interact amongst themselves and energy is transferred between them. This transfer plays an important role in the generation of magnetic fields. In this paper we study the energy transfer in two-dimensional(2-D) MHD turbulence. The MHD and Navier Stokes equations show that energy is transferred, in spectral space, to a mode k from modes p and q such that the three wave numbers satisfy the condition k + p + q = 0. In an earlier paper (we will refer to this paper as Paper I) [1] we had introduced the idea of effective energy transfer between a pair of modes within a triad by the mediation of the third mode, and found the formulae for computing these transfers. In this paper we have applied this method to study energy transfer in 2-D MHD turbulence.In fluid turbulence the dynamics of energy transfer has been well studied. In 3-D fluid turbulence the kinetic energy is transferred from large scales to small scales, whereas in two dimensions there is an inverse cascade of kinetic energy from small scales to large scales [2]. For MHD turbulence there have been various phenomenological [3][4][5], analytical [6][7][8][9][10][11][12][13], and numerical studies [14-23] to investigate energy spectra, energy cascade rates, etc. Contrary to fluid turbulence, the direct numerical simulations (DNS) of MHD turbulence show that the total energy is transferred from large scales to small scales both in 2-D as well as 3-D turbulence [19,24]. There have been theoretical predictions of the magnitude and directions of only a few of the various fluxes [6,12,8].Magnetohydrodynamic turbulence is sometimes described in terms of the Elsasser variables z ± = u ± b. It has been a basic assumption of the phenomenologies for MHD turbulence that the energies associated with z ± a...

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Π(u), we demonstrate that, for stably stratified flows, the kinetic energy spectrum E(u)(k)∼k(-11/5), the potential energy spectrum E(θ)(k)∼k(-7/5), and Π(u)(k)∼k(-4/5) are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence E(u)(k) follows Kolmogorov's spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Π(u)(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Π(u)(k) and E(u)(k)∼k(-5/3) for a narrow band of wave numbers.

We employ detailed numerical simulations to probe the mechanism of flow reversals in twodimensional turbulent convection. We show that the reversals occur via vortex reconnection of two attracting corner rolls having same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to this flow reconfiguration. The flow configurations during the reversals have been analyzed quantitatively using large-scale modes. Using these tools, we also show why flow reversals occur for a restricted range of Rayleigh and Prandt numbers.PACS numbers: 47.55. 47.27.De Several experiments [1][2][3][4][5][6][7][8] and numerical simulations [8][9][10][11][12] on turbulent convection exhibit "flow reversals" in which the probes near the lateral walls of the container show random reversals (also see review articles [13]). These reversals have certain similarities with magnetic field reversals in dynamo and Kolmogorov flow [7]. Researchers typically study convection in a controlled setup called "Rayleigh-Bénard convection" in which a fluid confined between two plates is heated from below and cooled at the top. The two nondimensional numbers used to characterize the flow are the Rayleigh number (Ra), which is the ratio of the buoyancy term and the diffusive term, and the Prandtl number (Pr), which is the ratio of the kinematic viscosity and the thermal diffusivity. Cioni et al. [4] performed convection experiments on mercury, water, and helium gas in a cylindrical geometry and observed reversals for Ra > 10 8 . Sugiyama et al. [8] and Vasiliev and Frick [5] studied reversals in a rectangular box with water. No reversal was observed for a cubical box (aspect ratio 1), but a quasi two-dimensional box (aspect ratio ≤ 0.2) exhibits reversals for a band of Rayleigh and Prandtl numbers [8]. Surprisingly, a cubical box containing mercury shows reversals [7], indicating a strong role played by the Prandtl number and geometry in the reversal dynamics.Several theoretical models have been invoked to explain flow reversals. Benzi and Verzicco [9] and Sreenivasan et al. [14] used stochastic resonance, while Arajuo et al.[15] employed low-dimensional models with noise to explain reversals. Brown and Ahlers [3] and Mishra et al. [11] showed that in a cylindrical geometry, the flow reversals are induced by a rotation or cessation of large-scale flow structures. For two-dimensional box geometry, Sugiyama et al.[8] relate the flow reversal to the growth of the corner rolls due to the plume detachments from the boundary layers. Chandra and Verma [12] studied the reversals quantitatively by representing flow structures as Fourier modes and showed that during the reversals, the amplitude of the first Fourier mode (k x = 1, k y = 1) becomes very small, while the Fourier mode (k x = 2, k y = 2) gains strength. The growth of the secondary modes at the expense of the primary modes is akin to the cessation-led reversals reported by Brown and Ahlers [3] and Mishra et al. [11], ...

Based on direct numerical simulations and symmetry arguments, we show that the large-scale Fourier modes are useful tools to describe the flow structures and dynamics of flow reversals in Rayleigh-Bénard convection (RBC). We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the "cessation-led" reversals observed earlier in experiments and numerical simulations. We find anomalous fluctuations in the Nusselt number during the reversals. Using the structures of the RBC equations in the Fourier space, we deduce two symmetry transformations that leave the equations invariant. These symmetry transformations help us in identifying the reversing and non-reversing Fourier modes.PACS numbers: 47.55. 47.27.De, Many experiments [1][2][3][4][5][6][7] and numerical simulations [5,[8][9][10] on turbulent convection reveal that the velocity field of the system reverses randomly in time (also see review articles [11]). This phenomenon, known as "flow reversal", remains ill understood. This process gains practical importance due to its similarities with the magnetic field reversals in geodynamo and solar dynamo [12]. In this letter, we study the dynamics and symmetries of flow reversals in turbulent convection using the large-scale Fourier modes of the velocity and temperature fields.The experiments and simulations performed to explore the nature of flow reversals are typically for an idealized convective system called Rayleigh-Bénard convection (RBC) in which a fluid confined between two plates is heated from below and cooled at the top. Detailed measurements show that the first Fourier mode vanishes abruptly during some reversals [3,4]. These reversals are referred to as "cessation-led". Recently Sugiyama et al. [5] performed RBC experiments on water in a quasi two-dimensional box, and observed flow reversals with the flow profile dominated by a diagonal large-scale roll and two smaller secondary rolls at the corners. They attribute the flow reversals to the growth of the two smaller corner rolls as a result of plume detachments from the boundary layers.Several theoretical studies performed to understand reversals in RBC provide important clues. Broadly, these works involve either stochasticity (e.g., "stochastic resonance" [8, 13]), or low-dimensional models with noise [14,15]. Mishra et al.[10] studied the large-scale modes of RBC in a cylindrical geometry and showed that the dipolar mode decreases in amplitude and the quadrupolar mode increases during the cessation-led reversals. Regarding dynamo, low-dimensional models constructed using the large-scale modes and symmetry arguments reproduced dynamo reversals successfully [7,16].The theoretical models described above only focus on the large-scale modes. Here too, they provide limited information about these modes due to small number of measuring probes. In this letter we compute large-scale and intermediate-scale Fourier modes accurately using the complete flow profile. This helps us ...