Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling

Acute mountain sickness.

Acute mountain sickness (AMS) is a clinical syndrome occurring in otherwise healthy normal individuals who ascend rapidly to high altitude. Symptoms develop over a period ofa few hours or days. The usual symptoms include headache, anorexia, nausea, vomiting, lethargy, unsteadiness of gait, undue dyspnoea on moderate exertion and interrupted sleep. AMS is unrelated to physical fitness, sex or age except that young children over two years of age are unduly susceptible. One of the striking features ofAMS is the wide variation in individual susceptibility which is to some extent consistent. Some subjects never experience symptoms at any altitude while others have repeated attacks on ascending to quite modest altitudes. Rapid ascent to altitudes of 2500 to 3000m will produce symptoms in some subjects while after ascent over 23 days to 5000m most subjects will be affected, some to a marked degree. In general, the more rapid the ascent, the higher the altitude reached and the greater the physical exertion involved, the more severe AMS will be. Ifthe subjects stay at the altitude reached there is a tendency for acclimatization to occur and symptoms to remit over 1-7 days

A Tale of Waves and Eddies in a Sea of Rotating Turbulence

In this thesis, we investigate several properties of rotating turbulent flows. First, we ran several computer simulations of rotating turbulent flows and performed statistical analysis of the data produced by an established computational model using Large Eddy Simulations (LES). This enabled us to develop deeper phenomenological understanding of such flows, e.g. the effect of anisotropic injection in the power laws of energy and helicity spectral densities, development of shear in specific rotating flows and evidence of wave-vortex coupling. This served as a motivation for detailed theoretical investigations. Next, we undertook a theoretical study of nonlinear resonant wave interactions to deduce new understanding of rotating flow dynamics. The latter analysis pertained to the highly anisotropic regime of rotating flows. To the best of our knowledge, the application of wave-turbulence theory to asymptotically reduced equations in the limit of rapidly rotating hydrodynamic flows is presented here for the first time and aims to further our understanding of highly anisotropic turbulent flows. A coupled set of equations, known as the wave kinetic equations, for energy and helicity is derived using a novel symmetry argument in the canonical description of the wave field sustained by the flow. A modified wave turbulence schematic is proposed and includes scaling law solutions of the flow invariants that span a hierarchy of slow manifold regions where slow inertial waves are in geostrophic balance with non-linear advection processes. A brief summary of the key findings of this thesis is presented in Table 1

Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves

Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant k ⊥ cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases

A Hamiltonian model of the Fibonacci quasicrystal using non-local interactions: simulations and spectral analysis

This article presents a Hamiltonian architecture based on vertex types and empires for demonstrating the emergence of aperiodic order in one dimension by a suitable prescription for breaking translation symmetry. At the outset, the paper presents different algorithmic, geometrical, and algebraic methods of constructing empires of vertex configurations of a given lattice. These empires have non-local scope and form the building blocks of the proposed lattice model. This model is tested via Monte Carlo simulations beginning with randomly arranged N tiles. The simulations clearly establish the Fibonacci configuration, which is a one-dimensional quasicrystal of length N, as the final relaxed state of the system. The Hamiltonian is promoted to a matrix operator form by performing dyadic tensor products of pairs of interacting empire vectors followed by a summation over all permissible configurations. A spectral analysis of the Hamiltonian matrix is performed and a theoretical method is presented to find the exact solution of the attractor configuration that is given by the Fibonacci chain as predicted by the simulations. Finally, a precise theoretical explanation is provided which shows that the Fibonacci chain is the most probable ground state. The proposed Hamiltonian is a mathematical model of the one dimensional Fibonacci quasicrystal

Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space

We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford’s geometric algebra. Consequently, we establish a connection between a three-dimensional icosahedral seed, a six-dimensional (6D) Dirichlet quantized host and a higher dimensional lattice structure. The 20G, owing to its icosahedral symmetry, bears the signature of a 6D lattice that manifests in the Dirichlet integer representation. We present an interpretation whereby the three-dimensional 20G can be regarded as the core substratum from which the higher dimensional lattices emerge. This emergent geometry is based on an induction principle supported by the Clifford multi-vector formalism of three-dimensional (3D) Euclidean space. This lays a geometric framework for understanding several physics theories related to S U ( 5 ) , E 6 , E 8 Lie algebras and their composition with the algebra associated with the even unimodular lattice in R 3 , 1 . The construction presented here is inspired by Penrose’s three world model

Alimentação de porcas gestantes e lactantes com dietas contendo saponinas Feeding sows in gestation and lactation with diets containing saponins

Foi realizado um experimento para avaliar o desempenho de porcas e suas leitegadas alimentadas com dietas que continham saponinas. Trinta porcas geneticamente homogêneas foram distribuídas em dois tratamentos, dieta testemunha e dieta testemunha com adição de 160ppm de fontes de saponinas. O delineamento utilizado foi o de blocos ao acaso, tendo como fator de bloqueamento a ordem de parto. Nas porcas, foram avaliados: o consumo de ração, características das fezes (cor e textura) e escore corporal. Nos leitões, foram avaliados: número de nascidos vivos, nascidos mortos, mumificados; pesos ao nascer e ao desmame e mortalidade na lactação. Não foram encontradas diferenças na cor das fezes das fêmeas. Na textura, as fezes das fêmeas que receberam a dieta com a adição de saponinas foram cerca de 11% mais duras (P<0,05). Na última semana de lactação, as fêmeas alimentadas com a adição de saponinas apresentaram um escore corporal 12% superior (P<0,05) às fêmeas controle. Não foram encontradas diferenças (P>0,05) nos leitões em relação as variáveis nascidos vivos, nascidos mortos e mumificados. Os leitões das fêmeas que receberam dietas contendo saponinas foram mais pesados (P<0,05) ao nascer (1,2 x 1,4kg) e ao desmame (5,5x 5,9kg). Porcas alimentadas nos últimos 10 dias de gestação e na lactação com dietas contendo 160ppm de saponinas têm melhor escore corporal no final da lactação e suas leitegadas são mais pesadas ao nascer e ao desmame.<br>An experiment was carried out to study the effect of saponins on sows and their piglets performances. Thirty genetically homogeneous sows were distributed in two treatments: one control diet (CD) and a CD plus 160ppm of saponins. The experimental design was a completely randomized block. The studied variables in sows were feed supply, fecal characteristics (color and texture) and corporal score. In the piglets the studied variables were mummified fetuses, stillborn, born alive and total born, birth and weaning weights. Were not found differences in color in sows feces. The fecal texture for sows that received diets with saponins was about 11% more solid (P<0.05). In the end of nursing the sows fed with saponins presented a corporal score 12% higher (P<0.05), compared to the control females. The piglets of sows that received diets with saponins presented higher weights on birth (1.2 x 1.4kg) and at weaning (5.5 x 5.9kg) weights, both at P<0.05. Sows fed in the last 10 days of gestation and during the nursing period with diets containing 160ppm of saponins, had better corporal score in the end of nursing and their piglets had higher birth and weaning weights