Nonlinear Planetary Electromagnetic Vortex Structures in the Ionospheric F-Layer

A study is made of the dynamics of planetary-scale electromagnetic waves in the F-layer of the ionosphere. It is shown that, in this layer, a new branch of large-scale magneto-ionospheric wave perturbations is generated under the action of the latitudinal variations of the geomagnetic field, which are a constant property of the ionosphere. The waves propagate along the parallels with phase velocities of tens to hundreds of km/s. The pulsations of the geomagnetic field in the waves can be as strong as several tens of nT. A possible self-localization effect is revealed: these waves may form nonlinear localized solitary vortices moving either westward or eastward along the parallels with velocities much higher than the phase velocities of the linear waves. The characteristic dimension of a vortex is about 10⁴ km or even larger. The magnetic fields generated by vortex structures are one order of magnitude stronger than those in linear waves. The vortices are long-lived formations and may be regarded as elements of strong structural turbulence in the ionosphere. The properties of the wave structures under investigation are very similar to those of ultralow-frequency perturbations observed experimentally in the ionosphere at middle latitudes.     

How to perform measurements in a hovering animal's wake: physical modelling of the vortex wake of the hawkmoth, Manduca sexta

The vortex wake structure of the hawkmoth, Manduca sexta, was investigated using a vortex ring generator. Based on existing kinematic and morphological data, a piston and tube apparatus was constructed to produce circular vortex rings with the same size and disc loading as a hovering hawkmoth. Results show that the artificial rings were initially laminar, but developed turbulence owing to azimuthal wave instability. The initial impulse and circulation were accurately estimated for laminar rings using particle image velocimetry; after the transition to turbulence, initial circulation was generally underestimated. The underestimate for turbulent rings can be corrected if the transition time and velocity profile are accurately known, but this correction will not be feasible for experiments on real animals. It is therefore crucial that the circulation and impulse be estimated while the wake vortices are still laminar. The scaling of the ring Reynolds number suggests that flying animals of about the size of hawkmoths may be the largest animals whose wakes stay laminar for long enough to perform such measurements during hovering. Thus, at low advance ratios, they may be the largest animals for which wake circulation and impulse can be accurately measured.     

Vortex electron dynamics in a high-current plasma lens

An analytic study is made of the following problems: the instability of a plasma against the excitation of vortex turbulence, the turbulence saturation amplitude, the types and spatial structures of the nascent vortices, and their nonlinear growth rates in an electrostatic plasma lens for focusing high-current ion beams.     

Unsteady flow field around a human hand and propulsive force in swimming

Much effort has been undertaken for the estimation of propulsive force of swimmers in the front crawl. Estimation is typically based on steady flow theory: the so-called quasi-steady analysis. Flow fields around a swimmer, however, are extremely unsteady because the change direction of hand produces unsteady vortex motions. To evaluate the force correctly, it is necessary to know the unsteady properties determined from the vortex dynamics because that unsteadiness is known to make the force greater. Unsteady flow measurements were made for this study using a sophisticated technique called particle image velocimetry (PIV) in several horizontal planes for subjects swimming in a flume. Using that method, a 100 time-sequential flow fields are obtainable simultaneously. Each flow field was calculated from two particle images using the cross-correlation method. The intensity of vortices and their locations were identified. A strong vortex was generated near the hand and then shed by directional change of the hand in the transition phase from in-sweep to out-sweep. When the vortex was shed, a new vortex rotating in the opposite direction around the hand was created. The pair of vortices induced the velocity component in the direction opposite to the swimming. Results of this study show that the momentum change attributable to the increase in this velocity component is the origin of thrust force by the hand.     

Vortex interactions with flapping wings and fins can be unpredictable

As they fly or swim, many animals generate a wake of vortices with their flapping fins and wings that reveals the dynamics of their locomotion. Previous studies have shown that the dynamic interaction of vortices in the wake with fins and wings can increase propulsive force. Here, we explore whether the dynamics of the vortex interactions could affect the predictability of propulsive forces. We studied the dynamics of the interactions between a symmetrically and periodically pitching and heaving foil and the vortices in its wake, in a soap-film tunnel. The phase-locked movie sequences reveal that abundant chaotic vortex-wake interactions occur at high Strouhal numbers. These high numbers are representative for the fins and wings of near-hovering animals. The chaotic wake limits the forecast horizon of the corresponding force and moment integrals. By contrast, we find periodic vortex wakes with an unlimited forecast horizon for the lower Strouhal numbers (0.2–0.4) at which many animals cruise. These findings suggest that swimming and flying animals could control the predictability of vortex-wake interactions, and the corresponding propulsive forces with their fins and wings.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

Nonlinear Wave Structures and Plasma−Dust Effects in the Earth’s Atmosphere

The interaction of charged dust grains with nonlinear vortical structures in the Earth’s atmosphere is analyzed. Certain aspects of the atmosphere?ionosphere interaction, in particular, mechanisms for the appearance of dust grains at ionospheric altitudes, are discussed. It is shown that, at certain altitudes, there are regions in the wavenumber space in which conditions leading to the excitation of acoustic?gravity waves are satisfied. The interaction of nonlinear acoustic?gravity waves with dust grains of meteoric origin at ionospheric altitudes, which leads to the mixing and redistribution of dust grains over the region where vortices exist, is investigated. The possibility of formation of vertical and horizontal dust flows in dusty ionospheric plasma as a result of modulational instability is analyzed. The dynamics of dust grains in dust devils frequently arising in the atmosphere above well-heated surfaces is modeled. The vortical structure of such a dust devil is characterized by a reduced pressure in the center, which facilitates the lifting of small dust grains from the surface. The formulated model is used to calculate the trajectories of dust grains in dust devils with allowance for the influence of the electric field generated in the vortex by colliding dust grains. The calculations show that dust devils play an important role in the transport of dust grains.     

Three-dimensional diastolic blood flow in the left ventricle

Three-dimensional blood flow in a human left ventricle is studied via a computational analysis with magnetic resonance imaging of the cardiac motion. Formation, growth and decay of vortices during the myocardial dilation are analyzed with flow patterns on various diametric planes. They are dominated by momentum transfer during flow acceleration and deceleration through the mitral orifice. The posterior and anterior vortices form an asymmetric annular vortex at the mitral orifice, providing a smooth transition for the rapid inflow to the ventricle. The development of core vortex accommodates momentum for deceleration and for acceleration at end diastolic atrial contraction. The rate of energy dissipation and that of work done by viscous stresses are small; they are approximately balanced with each other. The kinetic energy flux and the rate of work done by pressure delivered to blood from ventricular dilation is well balanced by the total energy influx at the mitral orifice and the rate change of kinetic energy in the ventricle.     

Renewable fluid dynamic energy derived from aquatic animal locomotion

Aquatic animals swimming in isolation and in groups are known to extract energy from the vortices in environmental flows, significantly reducing muscle activity required for locomotion. A model for the vortex dynamics associated with this phenomenon is developed, showing that the energy extraction mechanism can be described by simple criteria governing the kinematics of the vortices relative to the body in the flow. In this way, we need not make direct appeal to the fluid dynamics, which can be more difficult to evaluate than the kinematics. Examples of these principles as exhibited in swimming fish and existing energy conversion devices are described. A benefit of the developed framework is that the potentially infinite-dimensional parameter space of the fluid-structure interaction is reduced to a maximum of eight combinations of three parameters. The model may potentially aid in the design and evaluation of unsteady aero- and hydrodynamic energy conversion systems that surpass the Betz efficiency limit of steady fluid dynamic energy conversion systems.     

Electrical instability in cardiac muscle: phase singularities and rotors

A dynamical system is "excitable" at some stage in its behavior (e.g. at a rest state or while it is nearly at rest prior to a spontaneous event) if a small, but not too small, stimulus of the right kind elicits an immediate big reaction that eventually leads back to the original state. During this return to excitability a typical system is not excitable. An excitable system need not have an attracting rest state; a spontaneous oscillator can be excitable, too, as is common in biological and in chemical excitable kinetics. In a medium characterized by such excitable dynamics at every point, the excitation can propagate as a travelling pulse. Undamaged cardiac muscle shares with other excitable media certain features of such pulse propagation in two and three dimensions. Among the new electrophysiological phenomena thus anticipated are paired mirror-image vortices ("rotors") organized around phase singularities. These should arise in the myocardium near the intersection of a moving critical contour of phase in the normal cycle of excitation and recovery with a momentary critical contour of local stimulus strength. Such intersections, and the corresponding aftermath of paired rotors, should only occur following certain combinations of stimulus size and stimulus timing. Plotting those combinations on a "vulnerability diagram", one delineates a domain for creation of rotors (corresponding to tachycardia) surrounded on all sides by a halo of combinations at which just a few repetitive responses follow stimulation. The experiments called for to check these implications have now been carried out in the special case of electrically-induced tachycardia in healthy canine ventricle. They support the two-dimensional theory, so a new experiment is suggested to demonstrate wholly intramural three-dimensional vortex filaments.     

Molecular dynamics simulations of ion channels formed by bundles of amphipathic α-helical peptides

Ion channels may be formed by self-assembly of amphipathic α-helical peptides into parallel helix bundles. The transbilayer pores formed by such peptides contain extended columns of water molecules, the properties of which may differ from those of water in its bulk state. The de novo designed peptides of DeGrado et al., which contain only leucine and serine residues, are considered as a simple example of such channels. Molecular dynamics simulations of peptide helix bundles with water molecules within and at the mouths of their pores are used to refine such models and to investigate the properties of intra-pore water. The translational and rotational mobility of water molecules within the pores are reduced relative to bulk water. Furthermore, intra-pore waters orient themselves with their dipoles anti-parallel to the helix dipoles, as do the hydroxyl groups of serine residues. Comparison of approximate predictions of ionic conductances with experimental values provides support for the validity of these models. Received: 23 April 1996 / Accepted: 7 August 1996     

The observed range for temporal mean-variance scaling exponents can be explained by reproductive correlation

The mean-variance scaling relationship known as Taylor's power law has been well documented empirically over the past four decades but a general theoretical explanation for the phenomenon does not exist. Here we provide an explanation that relates empirical patterns of temporal mean-variance scaling to individual level reproductive behavior. Initially, we review the scaling behavior of population growth models to establish theoretical limits for the scaling exponent b that is in agreement with the empirically observed range (1≤b≤2). We go on to show that the degree of reproductive covariance among individuals determines the scaling exponent b. Independent reproduction results in an exponent of one, while completely correlated reproduction results in the upper limit of two. Intermediate exponents, which are common empirically, can be generated through the decay of reproductive covariance with increasing population size. Finally, we describe how the link between reproductive correlation and the scaling exponent provides a way to infer properties of individual-level reproductive behavior, such as the relative influence of demographic stochasticity, from a macroecological pattern.     

Vortex shedding as a precursor of turbulent electrical activity in cardiac muscle.

In cardiac tissue, during partial blockade of the membrane sodium channels, or at high frequencies of excitation, inexcitable obstacles with sharp edges may destabilize the propagation of electrical excitation waves, causing the formation of self-sustained vortices and turbulent cardiac electrical activity. The formation of such vortices, which visually resembles vortex shedding in hydrodynamic turbulent flows, was observed in sheep epicardial tissue using voltage-sensitive dyes in combination with video-imaging techniques. Vortex shedding is a potential mechanism leading to the spontaneous initiation of uncontrolled high-frequency excitation of the heart.     

A review of fish swimming mechanics and behaviour in altered flows

Fishes suspended in water are subject to the complex nature of three-dimensional flows. Often, these flows are the result of abiotic and biotic sources that alter otherwise uniform flows, which then have the potential to perturb the swimming motions of fishes. The goal of this review is to highlight key studies that have contributed to a mechanistic and behavioural understanding of how perturbing flows affect fish. Most of our understanding of fish behaviour in turbulence comes from observations of natural conditions in the field and laboratory studies employing controlled perturbations, such as vortices generated in the wake behind simple geometric objects. Laboratory studies have employed motion analysis, flow visualization, electromyography, respirometry and sensory deprecation techniques to evaluate the mechanisms and physiological costs of swimming in altered flows. Studies show that flows which display chaotic and wide fluctuations in velocity can repel fishes, while flows that have a component of predictability can attract fishes. The ability to maintain stability in three-dimensional flows, either actively with powered movements or passively using the posture and intrinsic compliance of the body and fins, plays a large role in whether fish seek out or avoid turbulence. Fish in schools or current-swept habitats can benefit from altered flows using two distinct though not mutually exclusive mechanisms: flow refuging (exploiting regions of reduced flow relative to the earth frame of reference) and vortex capture (harnessing the energy of environmental vortices). Integrating how the physical environment affects organismal biomechanics with the more complex issue of behavioural choice requires consideration beyond simple body motions or metabolic costs. A fundamental link between these two ways of thinking about animal behaviour is how organisms sense and process information from the environment, which determines when locomotor behaviour is initiated and modulated. New data are presented here which show that behaviour changes in altered flows when either the lateral line or vision is blocked, showing that fish rely on multi-modal sensory inputs to negotiate complex flow environments. Integrating biomechanics and sensory biology to understand how fish swim in turbulent flow at the organismal level is necessary to better address population-level questions in the fields of fisheries management and ecology.     

A tree swaying in a turbulent wind: a scaling analysis

A tentative scaling theory is presented of a tree swaying in a turbulent wind. It is argued that the turbulence of the air within the crown is in the inertial regime. An eddy causes a dynamic bending response of the branches according to a time criterion. The resulting expression for the penetration depth of the wind yields an exponent which appears to be consistent with that pertaining to the morphology of the tree branches. An energy criterion shows that the dynamics of the branches is basically passive. The possibility of hydrodynamic screening by the leaves is discussed.     

Flow patterns around cocoons and pupae of black flies of the genusSimulium (Diptera : Simuliidae)

Flow patterns around structurally different cocoons and pupae of five species ofSimulium Latreille are described. Three features of the flow pattern common to all cocoons are; 1) a solenoidal vortex around the cocoon, 2) upward flow anterior (downstream) to the cocoon, and 3) one or two pairs of spiral-shaped vortices, which either touch or envelop the fill filaments of the pupa. The solenoidal vortex and the upward-spiralling, downstream vortices are common features of flow patterns around most bluff bodies submerged in a boundary layer. The proximity of the vortices to the fill filaments of all pupae suggests that these vortices are associated with gaseous exchange at the gill filaments.     

A formulation for calculating the translational velocity of a vortex ring or pair

Cephalopods, among other marine animals, use jet propulsion for swimming. A simple actuator is designed to loosely mimic pulsatile jet formation in squid and jellyfish. The actuator is comprised of a cavity with an oscillating diaphragm and an exit orifice. Periodic oscillation of the diaphragm results in the formation of an array of vortex rings and eventually could generate a periodic pulsatile jet. A general formulation for calculating the velocity of a steadily translating vortical structure in two-dimensional and axi-symmetric shear flows is presented. This technique is based on taking the variational derivative of an energetic function at its critical point. This technique is general, applicable to vortices in liquid and gas media, with no limitation on the relative size of the vortex core. The technique is then implemented to estimate the translational velocity of a vortex ring in a Helmholtz vortex ring generator.     

Role of diastolic vortices in flow and energy dynamics during systolic ejection

MRI-based computational fluid dynamics simulations were performed in the left ventricles of two adult porcine subjects with varying physiological states (before and after an induced infarction). The hypothesis that diastolic vortices store kinetic energy and assist systolic ejection was tested, by performing systolic simulations in the presence and absence of diastolic vortices. The latter was achieved by reinitializing the entire velocity field to be zero at the beginning of systole. A rudimentary prescribed motion model of a mitral valve was included in the simulations to direct the incoming mitral jet towards the apex. Results showed that the presence or absence of diastolic vortex rings had insignificant impact on the energy expended by walls of the left ventricles for systolic ejection for both the porcine subjects, under all physiological conditions. Although substantial kinetic energy was stored in diastolic vortices by end diastole, it provided no appreciable savings during systolic ejection, and most likely continued to complete dissipation during systole. The role of diastolic vortices in apical washout was investigated by studying the cumulative mass fraction of passive dye that was ejected during systole in the presence and absence of vortices. Results indicated that the diastolic vortices play a crucial role in ensuring efficient washout of apical blood during systolic ejection.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

The interpretation of site-directed mutagenesis experiments by linear free energy relations

Fersht and co-workers have applied a linear free energy relation (Br?nsted equation) to analyze site-directed mutagenesis experiments involving the enzyme tyrosyl-tRNA synthetase and have suggested that the Br?nsted exponent is linearly correlated with the value of the reaction coordinate at the transition state. We point out that when the mutants differ solely through the formation or deletion of a hydrogen bond away from the reaction center, a linear free energy relation is expected only in limiting cases for which the Br?nsted relation exponent is 0, 1 or infinity. The results may be correlated with a conformational coordinate but not with the development of the reaction coordinate per se.