Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Objective determination of feature resolution in two sea surface temperature analyses

Considerable effort is presently being devoted to producing high-resolution sea surface temperature (SST) analyses with a goal of spatial grid resolutions as low as 1 km. Because grid resolution is not the same as feature resolution, a method is needed to objectively determine the resolution capability and accuracy of SST analysis products. Ocean model SST fields are used in this study as simulated “true” SST data and subsampled based on actual infrared and microwave satellite data coverage. The subsampled data are used to simulate sampling errors due to missing data. Two different SST analyses are considered and run using both the full and the subsampled model SST fields, with and without additional noise. The results are compared as a function of spatial scales of variability using wavenumber auto- and cross-spectral analysis. The spectral variance at high wavenumbers (smallest wavelengths) is shown to be attenuated relative to the true SST because of smoothing that is inherent to both analysis procedures. Comparisons of the two analyses (both having grid sizes of roughly ) show important differences. One analysis tends to reproduce small-scale features more accurately when the high-resolution data coverage is good but produces more spurious small-scale noise when the high-resolution data coverage is poor. Analysis procedures can thus generate small-scale features with and without data, but the small-scale features in an SST analysis may be just noise when high-resolution data are sparse. Users must therefore be skeptical of high-resolution SST products, especially in regions where high-resolution (~5 km) infrared satellite data are limited because of cloud cover.

Changing HRM systems in two Russian oil companies: Western hegemony or Russian spetsifika?

We contrast attempts to introduce what were seen as sophisticated Western-style human resource management (HRM) systems into two Russian oil companies – a joint venture with a Western multinational corporation (TNK-BP) and a wholly Russian-owned company (Yukos). The drivers for Western hegemony within the joint venture, heavily influenced by expatriates and the established HRM processes introduced by the Western parent, were counteracted to a significant degree by the Russian spetsifika – the peculiarly Russian way of thinking and doing things. In contrast, developments were absorbed faster in the more authoritarian Russian-owned company. The research adds to the theoretical debate about international knowledge transfer and provides detailed empirical data to support our understanding of the effect of both organizational and cultural context on the knowledge-transfer mechanisms of local and multinational companies. As the analysis is based on the perspective of senior local nationals, we also address a relatively under-researched area in the international HRM literature which mostly relies on empirical data collected from expatriates and those based solely in multinational headquarters.