Energy Transfer to Resonant Zonal Rossby Modes in Two-Dimensional Turbulence on a Rotating Sphere

The transfer of energy by the nonlinear interaction of Rossby waves in two-dimensional turbulence on a rotating sphere was investigated in this study. Although it has been suggested that three-wave resonant interaction dominates nonlinear interactions when the rotation rate of the sphere is sufficiently high, resonant interactions do not transfer energy to zonal Rossby waves, resulting in the nonresonant interaction of Rossby waves being responsible for the generation of zonal flows [Reznik, Piterbarg, and Kartashova, Dyn. Atmos. Oceans 18, 235 (1993); Obuse and Yamada, Phys. Rev. Fluids 4, 024601 (2019)]. The resonant and nonresonant interactions of Rossby waves were investigated in this study, and it was found that although energy is transferred to the zonal Rossby modes by the nonresonant three-wave interaction of Rossby waves, the target of this nonresonant energy transfer is only the resonant zonal Rossby waves

Linear stability of steady zonal jet flows induced by a small-scale forcing on a plane

We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999). It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets

Three-wave resonant interactions and zonal flows in two-dimensional Rossby-Haurwitz wave turbulence on a rotating sphere

This paper addresses three-wave resonant interactions of Rossby-Haurwitz waves in two-dimensional turbulence on a rotating sphere. Zonal modes are often omitted from the "resonant wave set" even when they satisfy the conditions for three-wave resonant interactions, as they do not transfer any energy to other modes in a resonant manner. However, the presence of zonal flows induces phase shifts in other modes, and it is not at all clear that their influence is negligible. Since it is expected that three-wave resonant interactions govern the entire dynamics of turbulence if the rotation rate of the sphere is sufficiently high, by analogy with the theorem regarding three-wave resonant interactions of Rossby waves on a beta plane with sufficiently large beta previously proven by Yamada and Yoneda [Physica D 245, 1 (2013)], an appropriate definition of the resonant wave set was determined by comparing the time evolution of several wave sets on a rapidly rotating sphere. It was found that zonal waves of the form Y-l(m=0) exp(i omega t) with odd l, where Y(l)(m )are the spherical harmonics, should be considered for inclusion in the resonant wave set to ensure that the dynamics of the resonant wave set determine the overall dynamics of the turbulence on a rapidly rotating sphere. Consequently, it is suggested that the minimal resonant wave set that must be considered in the discussion of the three-wave interaction of Rossby-Haurwitz waves is the set consisting of nonzonal resonant waves and zonal waves of the form Y-l(0) exp(icot) with odd l

Comparative Gene Analysis Focused on Silica Cell Wall Formation: Identification of Diatom-Specific SET Domain Protein Methyltransferases

Silica cell walls of diatoms have attracted attention as a source of nanostructured functional materials and have immense potential for a variety of applications. Previous studies of silica cell wall formation have identified numerous involved proteins, but most of these proteins are species-specific and are not conserved among diatoms. However, because the basic process of diatom cell wall formation is common to all diatom species, ubiquitous proteins and molecules will reveal the mechanisms of cell wall formation. In this study, we assembled de novo transcriptomes of three diatom species, Nitzschia palea, Achnanthes kuwaitensis, and Pseudoleyanella lunata, and compared protein-coding genes of five genome-sequenced diatom species. These analyses revealed a number of diatom-specific genes that encode putative endoplasmic reticulum-targeting proteins. Significant numbers of these proteins showed homology to silicanin-1, which is a conserved diatom protein that reportedly contributes to cell wall formation. These proteins also included a previously unrecognized SET domain protein methyltransferase family that may regulate functions of cell wall formation-related proteins and long-chain polyamines. Proteomic analysis of cell wall-associated proteins in N. palea identified a protein that is also encoded by one of the diatom-specific genes. Expression analysis showed that candidate genes were upregulated in response to silicon, suggesting that these genes play roles in silica cell wall formation. These candidate genes can facilitate further investigations of silica cell wall formation in diatoms

β平面上2次元乱流における東西流の長期的振る舞いの漸近解析

京都大学0048新制・課程博士博士(理学)甲第16588号理博第3700号新制||理||1537(附属図書館)29263京都大学大学院理学研究科数学・数理解析専攻(主査)教授 岡本 久, 教授 向井 茂, 教授 國府 寛司学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDA

Long-time asymptotic states of forced two-dimensional barotropic incompressible flows on a rotating sphere

This study re-examines a long-time asymptotic state of a two-dimensional barotropic incompressible flow with a small-scale, Markovian random forcing on a rotating sphere. Numerical simulations with different rotation rates of the sphere and different wavenumbers of the forcing are performed from zero initial condition. The integration time is extended to around 100–500 times that of the previous study by Nozawa and Yoden [Phys. Fluids 9, 2081 (1997)] . At an early stage of the time integration, a multiple zonal-band structure or a structure with westward circumpolar jets emerges. However, in the course of time development, a multiple zonal-band structure is found to appear in all cases. The multiple zonal-band structure then enters quasisteady state, showing little energy increase with nearly steady energy spectrum. This is followed by a sudden merger/disappearance of the jets, accompanying an energy increase, and at the final stage of the time integration, a zonal-band structure with only two or three jets is realized in all cases. The characteristic total wavenumber of this asymptotic state is far lower than the Rhines wavenumber of the zonal flow, which suggests that the inverse energy cascade is not totally stopped by the β effect

Effect of turbulence on zonal jet flows in equivalent-barotropic quasi-geostrophic model

The linear stability of zonal flows superposed upon a sinusoidal, slightly supercritical background flow in an equivalent-barotropic quasi-geostrophic model on a $\beta$ plane is investigated using asymptotic analysis. Consistent with results of full numerical simulations, all the steady isolated zonal jet solutions were found to be linearly unstable, and specifically, the mode independent of longitudinal direction was found to be most unstable, even when the amplitude equation of the zonal flows has longitudinal dependence. References K. Obuse, S. Takehiro and M. Yamada, Long-time asymptotic states of forced two-dimensional barotropic incompressible flows on a rotating sphere. Phys. Fluids 22:156601, 2010. doi:10.1063/1.3407652 R. K. Scott and L. M. Polvani, Forced-dissipative shallow-water turbulence on the sphere and the atmospheric circulation of the giant planets. J. Atmos. Sci. 64:3158–3176, 2007. doi:10.1175/JAS4003.1 A. J. Manfroi and W. R. Young, Slow evolution of zonal jets on the beta plane. J. Atmos. Sci. 56:784–800, 1999. doi:10.1175/1520-0469(1999)056<0784:SEOZJO>2.0.CO;2 K. Obuse, S. Takehiro and M. Yamada, Linear stability of steady zonal jet flows induced by a small-scale forcing on a $\beta$ plane. Physica D 240:1825–1834, 2011. doi:10.1016/j.physd.2011.08.009 S. Takehiro, M. Odaka, K. Ishioka, M. Ishiwatari, Y.-Y. Hayashi and SPMODEL Development Group, A series of hierarchical spectral models for geophysical fluid dynamics. Nagare Multimedia, 2006. http://www.nagare.or.jp/mm/2006/spmodel