Two-dimensional turbulence on the surface of a sphere

1978 ◽  
Vol 87 (2) ◽  
pp. 305-319 ◽  
Author(s):  
Cha-Mei Tang ◽  
Steven A. Orszag
Keyword(s):  
Energy Transfer ◽  
Spectral Methods ◽  
Large Scale ◽  
Spherical Geometry ◽  
Numerical Results ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Constants Of Motion ◽  
Cartesian Geometry ◽  
Back Transfer

Large-scale atmospheric flow shares certain attributes with two-dimensional turbulence. In this paper, we study the effect of spherical geometry on two-dimensional turbulence.Energy transfer is multi-component in spherical geometry in contrast to energy transfer among triads of wave vectors in Cartesian geometry. It follows that energy transfer is more local in spherical than in Cartesian geometry. Enstrophy transfer to higher wavenumbers in spherical geometry is less than enstrophy transfer to higher wavenumbers in Cartesian geometry. Since both energy and enstrophy are inviscid constants of motion, the back transfer of energy is also less in spherical than in Cartesian geometry. Therefore, with a finite viscosity, enstrophy decays more slowly in spherical geometry than in Cartesian geometry. Here these conjectures are tested numerically by spectral methods. The numerical results agree well with the conjectures.

scholarly journals Two-dimensional turbulence on a sphere

2022 ◽  
Vol 933 ◽  
Author(s):  
Erik Lindborg ◽  
Arne Nordmark
Keyword(s):  
Energy Transfer ◽  
Spherical Harmonic ◽  
Spherical Geometry ◽  
Polar Axis ◽  
Spectral Energy ◽  
Harmonic Space ◽  
Two Dimensional ◽  
Optimal Test ◽  
Viscous Term ◽  
Divergent Flow

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

scholarly journals A Modified Spectral Methods for Large-Scale UnconStrained

2018 ◽  
Vol 29 (1) ◽  
pp. 127
Author(s):  
Basim A. Hassan ◽  
Haneen A. Alashoor
Keyword(s):  
Unconstrained Optimization ◽  
Spectral Methods ◽  
Large Scale ◽  
Optimization Problems ◽  
Numerical Results ◽  
Unconstrained Optimization Problems ◽  
Globally Convergent ◽  
Descent Condition

A modified spectral methods for solving unconstrained optimization problems based on the formulae are derived which are given in [4, 5]. The proposed methods satisfied the descent condition. Moreover, we prove that the new spectral methods are globally convergent. The Numerical results show that the proposed methods effective by comparing with the FR-method.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

Solution‐Processed Large‐Scale Concentric‐Ring Laser on Two‐Dimensional Ruddlesden–Popper Perovskites Thin Films

2021 ◽  
pp. 2100193
Author(s):  
Peng Liu ◽  
Bingqian Zhang ◽  
Qing Liao ◽  
Guifen Tian ◽  
Chunling Gu ◽  
...  
Keyword(s):  
Thin Films ◽  
Ring Laser ◽  
Large Scale ◽  
Two Dimensional ◽  
Concentric Ring ◽  
Solution Processed

Large-scale visualization of dispersion of liquid-exfoliated two-dimensional nanosheets

2021 ◽  
Author(s):  
Xingyu Cui ◽  
Wen ying Shi ◽  
Chao Lu
Keyword(s):  
Aqueous Solution ◽  
Large Scale ◽  
Fluorescence Microscope ◽  
Visualization Method ◽  
Two Dimensional ◽  
Non Invasive

An ultrafast, non-invasive and large-scale visualization method has been developed to evaluate the dispersion of two-dimensional nanosheets in aqueous solution with fluorescence microscope by formation of excimers from improvement of...

scholarly journals Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles.

Soft Matter ◽  
2021 ◽  
Author(s):  
Claudio Maggi ◽  
Matteo Paoluzzi ◽  
Andrea Crisanti ◽  
Emanuela Zaccarelli ◽  
Nicoletta Gnan
Keyword(s):  
Phase Separation ◽  
Critical Point ◽  
Computer Simulations ◽  
Large Scale ◽  
Universality Class ◽  
Critical Behaviour ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Active Particles ◽  
Two Dimensional Model

We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the systems critical behaviour close to the critical point...

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