Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations.A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett-Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky-Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime.The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.

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Three-dimensional flow structure and aerodynamic loading on a revolving wing Phys. Fluids 25, 034101 (2013) On the interaction of shock waves and sound waves in transonic buffet flow Phys. Fluids 25, 026101 (2013) Thermochemical nonequilibrium modeling of a low-power argon arcjet wind tunnel J. Appl. Phys. 113, 053304 (2013) Biomimetic flow control based on morphological features of living creatures Phys. Fluids 24, 121302 (2012) Study of mechanisms and factors that influence the formation of vortical wake of a heaving airfoil Forward flights of a bilaterally symmetrically flapping butterfly modeled as a fourlink rigid-body system consisting of a thorax, an abdomen, and left and right wings are numerically simulated. The joint motions of the butterflies are adopted from experimental observations. Three kinds of the simulations, distinguished by ways to determine the position and attitude of the thorax, are carried out: a tethered simulation, a prescribed simulation, and free-flight simulations. The upward and streamwise forces as well as the wake structures in the tethered simulation, where the thorax of the butterfly is fixed, reasonably agree with those in the corresponding tethered experiment. In the prescribed simulation, where the thoracic trajectories as well as the joint angles are given by those observed in a free-flight experiment, it is confirmed that the butterfly can produce enough forces to achieve the flapping flights. Moreover, coherent vortical structures in the wake and those on the wings are identified. The generation of the aerodynamic forces due to the vortical structures are also clarified. In the free-flight simulation, where only the joint angles are given as periodic functions of time, it is found that the free flight is longitudinally unstable because the butterfly cannot maintain the attitude in a proper range. Focusing on the abdominal mass, which largely varies owing to feeding and metabolizing, we have shown that the abdominal motion plays an important role in periodic flights. The necessity of control of the thoracic attitude for periodic flights and maneuverability is also discussed. C 2013 American Institute of Physics. [http://dx.

We perform direct numerical simulations of dynamic equations of decaying gravity waves on infinite-depth water. Power-law behaviour of the wave action spectrum and structure functions of the surface elevation is obtained. These power laws agree with the prediction of the weak turbulence theory. The probability density function (p.d.f.) of the surface elevation is close to the Gaussian distribution around the mean value which seems to be consistent with the random phase approximation. However, the p.d.f. deviates weakly from the Gaussian in the tail region. This deviation is significant and can be amplified by taking the Laplacian. In addition, intermittency and breakdown of the weak turbulence theory are discussed.

The spectral energy density of the internal waves in the open ocean is considered. The Garrett and Munk spectrum and the resonant kinetic equation are used as the main tools of the study. Evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is not in fact slow are reported. Instead, nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with the viewpoint expressed in papers by C. H. McComas and P. Mü ller, and by P. Mü ller et al., which regards the Garrett and Munk spectrum as an approximate stationary state of the resonant kinetic equation. It also puts the self-consistency of a resonant kinetic equation at a serious risk. The possible reasons for and resolutions of this paradox are explored. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. Consequently, this inclusion shows a tendency of improving of self-consistency of the kinetic equation approach.

Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical simulations according to the Föppl-von Kármán equation, and successfully reproduced the variability of the energy spectra by changing the magnitude of external force systematically. When the total energies in wave fields are small, the energy spectra are close to a statistically steady solution of the kinetic equation in the weak turbulence theory. On the other hand, in large-energy wave fields, another self-similar spectrum is found. Coexistence of the weakly nonlinear spectrum in large wavenumbers and the strongly nonlinear spectrum in small wavenumbers are also found in moderate energy wave fields.

Vertical variation in leaf gas exchange characteristics of trees grown in a lowland dipterocarp forest in Peninsular Malaysia was investigated. Maximum net photosynthetic rate, stomatal conductance, and electron transport rate of leaves at the upper canopy, lower canopy, and forest floor were studied in situ with saturated condition photosynthetic photon flux density. The dark respiration rate of leaves at the various heights was also studied. Relationships among gas exchange characteristics, and also with nitrogen content per unit leaf area and leaf dry matter per area were clearly detected, forming general equations representing the vertical profile of several important parameters related to gas exchange. Numerical analysis revealed that the vertical distribution of gas exchange parameters was well determined showing both larger carbon gain for the whole canopy and at the same time positive carbon gain for the leaves of the lowest layer. For correct estimation of gas exchange at both leaf and canopy scales using multi-layer models, it is essential to consider the vertical distribution of gas exchange parameters with proper scaling coefficients.

Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At the intermediate rotation rates, bistability of these two statistically steady states is observed. Such hysteretic behavior is also observed for the variation of the amplitude of an external force.Formation of columnar structures parallel to a rotation axis is one of the most fundamental and distinctive phenomena in flows subject to rotation. The emergence of columnar vortices in the rotating turbulence makes a threedimensional (3D) flow into a quasi-two-dimensional (Q2D) flow. The Taylor-Proudman theorem has succeeded in explaining the cylindrical flow in laboratory experiments and field observations in terms of the Taylor column. However, the theorem cannot describe transitions between the Q2D and 3D flows, because energy is exchanged between the Q2D mode and the 3D mode by nonlinear mechanisms [1]. The energy transfers to the Q2D modes were demonstrated by an instability analysis [2] and weak-turbulence theory in the large-rotation limit [3]. The Coriolis term breaks the parity invariance of the governing equation of the flow, and introduces a scale-independent time scale which induces two-dimensionalization at larger scales more effectively. Therefore, the Coriolis effect originates cyclone-anticyclone asymmetry with enhanced stretching of cyclonic vorticity and destabilization of anticyclonic one due to the centrifugal instability and the vortex tilting [4].To classify the flow properties in rotating systems, the Rossby number Ro, which is the ratio between the linear and nonlinear time scales, has been used [5]. Note that though various definitions of Ro are used in literature, the following facts are independent of its detailed definition. When the Coriolis force is weak relative to turbulence, i.e., Ro ≫ 1, the 3D Kolmogorov turbulence is obtained. When Ro ∼ 1, only cyclonic vortices appear at large scales, and the flow becomes Q2D. When Ro ≪ 1, both cyclonic and anticyclonic vortices appear, and the flow fields are almost completely two-dimensionalized. The transitions between the Q2D turbulence and the 3D turbulence by changing the system's rotation rate Ω were numerically studied [6]. It was reported that Ro-dependence of turbulent statistics is not monotonic in the range Ro ∼ 1, where the coherent vortices and inertial waves at small wave numbers and the turbulence at large wave numbers coexist [7,8]. The two-dimensionalization and the cyclone-anticyclone asymmetry depend on the external forces and the boundary conditions (e.g., Ref.[9]).Recently, Ref.[10] reported a phase diagram for statistically st...