Wave turbulence in the two-layer ocean model

This paper looks at the two-layer ocean model from a wave turbulence perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It turns out that energy is transferred via local triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale. From there it is then transferred to the large-scale barotropic modes via a nonlocal inverse transfer. Using scale separation a sys- tem of coupled equations were obtained for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. It is found that this transfer is mostly anisotropic and mostly to the zonal component

Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame

We analyze the interaction of plane '+'-polarized gravitational waves with a Fabry-Perot cavity in the local Lorentz frame of the cavity input mirror outside of the range of long-wave approximation with the force of radiation pressure taken into account. The obtained detector response signal is represented as a sum of two parts: (i) the phase shift due to displacement of the movable mirror under the influence of gravitational wave and the force of light pressure, and (ii) the phase shift due to direct interaction of gravitational wave with light wave inside the cavity. We obtain formula for the movable mirror law of motion paying close attention to the phenomena of optical rigidity, radiative friction and direct coupling of gravitational wave to light wave. Some issues concerning the detection of high-frequency gravitational waves and the role of optical rigidity in it are discussed. We also examine in detail special cases of optical resonance and small detuning from it and compare our results with the known ones.Comment: 17 pages, 9 figures; corrected references [7,8,34], added 2 new references (currently [35,36]), added comments on (i) relativistic corrections, (ii) detector angular pattern, (iii) quantized electromagnetic field, increased font in figure

Weak Alfvén-wave turbulence revisited

Weak Alfvénic turbulence in a periodic domain is considered as a mixed state of Alfvén waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed, and, indeed, none is found. If the 2D modes are not directly forced, k−2 and k−1 spectra are found for the Alfvén waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar, and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagating Alfvén waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved

A model for rapid stochastic distortions of small-scale turbulence

We present a model describing the evolution of the small-scale Navier–Stokes turbulence due to its stochastic distortion by much larger turbulent scales. This study is motivated by numerical findings (Laval et al. Phys. Fluids vol. 13, 2001, p. 1995) that such interactions of separated scales play an important role in turbulence intermittency. We introduce a description of turbulence in terms of the moments of $k$-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko et al. Phys. Rev. E vol. 68, 2003, 0266311). Working with the $k$-space moments allows us to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the small-scale two-dimensional turbulence shows that the Fourier moments take their Gaussian values in the energy cascade range whereas the enstrophy cascade is intermittent. In three dimensions, we show that the statistics of turbulence wavepackets deviates from Gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centred at its origin and having one large, one neutral and one small axis with the velocity field pointing parallel to the smallest axis

On fundamental diffraction limitation of finesse of a Fabry-Perot cavity

We perform a theoretical study of finesse limitations of a Fabry-Perot (FP) cavity occurring due to finite size, asymmetry, as well as imperfections of the cavity mirrors. A method of numerical simulations of the eigenvalue problem applicable for both the fundamental and high order cavity modes is suggested. Using this technique we find spatial profile of the modes and their round-trip diffraction loss. The results of the numerical simulations and analytical calculations are nearly identical when we consider a conventional FP cavity. The proposed numerical technique has much broader applicability range and is valid for any FP cavity with arbitrary non-spherical mirrors which have cylindrical symmetry but disturbed in an asymmetric way, for example, by tilt or roughness of their mirrors.Comment: 15 pages, 10 figure

Optical Gravitational Wave Antenna with Increased Power Handling Capability

Fundamental sensitivity of an optical interferometric gravitational wave detector increases with increase of the optical power which, in turn, limited because of the opto-mechanical parametric instabilities of the interferometer. We propose to optimize geometrical shape of the mirrors of the detector to reduce the diffraction-limited finesse of unessential optical modes of the interferometer resulting in increase of the threshold of the opto-mechanical instabilities and subsequent increase of the measurement sensitivity. Utilizing parameters of the LIGO interferometer we found that the proposed technique allows constructing a Fabry-Perot interferometer with round trip diffraction loss of the fundamental mode not exceeding $5$~ppm, whereas the loss of the first dipole as well as the other high order modes exceed $1,000$~ppm and $8,000$~ppm, respectively. The optimization comes at the price of tighter tolerances on the mirror tilt stability, but does not result in a significant modification of the optical beam profile and does not require changes in the the gravity detector read-out system. The cavity with proposed mirrors is also stable with respect to the slight modification of the mirror shape.Comment: 5 pages, 4 figure

Is Sustainable Development of Deserts Feasible?

Hot deserts that presently cover about one-fifth of the land area of our planet are rapidly devouring more and more arable lands mostly due to anthropogenic causes. We propose an interdisciplinary approach to revitalizing and commercializing hot deserts, which is based on systems thinking and Russian and NASA space technology experience in designing life-support systems for long-duration flights. We formulate ten principles for the design of sustainable life support systems in deserts, which can make the development of the deserts feasible. It is discussed how the principles can be employed to design and operate desert’s eco-industrial parks with greenhouses in which the transpired and evaporated moisture is collected and condensed. The potential benefits of setting up the eco-industrial parks in deserts include the slowdown and eventual reversal of the desertification trend, the migration of many industrial production facilities from mild-climate regions to deserts, the increased availability of potable water and food in deserts, the development of poor African countries, and the emergence of new investment markets