The Impact of Divergence Tilt and Meridional Flow for Cross-Equatorial Eddy Momentum Transport in Gill-Like Settings

This work investigates the sensitivity of the cross-equatorial eddy momentum flux and its rotational and divergent components to Hadley cell strength in simple variants of the Gill problem. An expression is derived linking the divergent momentum flux to the mean meridional wavenumber weighted by the spectrum of divergent eddy kinetic energy, supporting the relation between divergence phase tilt and momentum flux suggested by a previous study. Newtonian cooling makes the divergence tilt eastward moving away from the equator as observed, but this tilt is also sensitive to the Hadley cell. As the divergence tilt is enhanced in the downstream direction of the flow, wave propagation increases along that direction when the Hadley cell strengthens. The meridional flow also plays a second, important role for cross-equatorial propagation. With no Hadley cell, inviscid Sverdrup balance requires perfect compensation between the divergent and rotational momentum fluxes at the equator. The model can only produce cross-equatorial propagation when Sverdrup balance is violated, which in the linear, nearly inviscid limit requires vorticity advection by the mean flow. As the Hadley cell attenuates the geopotential tilt imparted by the divergent forcing, the compensation by the rotational momentum flux is reduced. The linear model can reproduce reasonably well previous nonlinear results by Kraucunas and Hartmann when linearized about their zonal-mean climatologies. The sensitivity of the cross-equatorial momentum fluxes to Hadley cell strength in these solutions is dominated by changes in the divergent flux and consistent with diagnosed changes in the divergence tilt.

A comparative study of quaternionic rotational Dirac equation and its interpretation

In this study, we develop the generalized Dirac-like four-momentum equation for rotating spin-1/2 particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists of the rotational energy and angular momentum of particle and antiparticle. Accordingly, we also discuss the four-vector form of quaternionic relativistic mass, moment of inertia and rotational energy-momentum in Euclidean space-time. The quaternionic four-angular momentum, (i.e. the rotational analogy of four-linear momentum) predicts the dual energy (rest mass energy and pure rotational energy) and dual momentum (linear-like momentum and pure rotational momentum). Further, the solutions of quaternionic rotational Dirac energy-momentum are obtained by using one-, two- and four-component of quaternionic spinor. We also demonstrate the solutions of quaternionic plane wave equation which gives the rotational frequency and wave propagation vector of Dirac particles and antiparticles in terms of quaternionic form.

Effects of Abdominal Rotation on Jump Performance in the Ant Gigantiops destructor (Hymenoptera, Formicidae)

Synopsis Jumping is an important form of locomotion, and animals employ a variety of mechanisms to increase jump performance. While jumping is common in insects generally, the ability to jump is rare among ants. An exception is the Neotropical ant Gigantiops destructor (Fabricius 1804) which is well known for jumping to capture prey or escape threats. Notably, this ant begins a jump by rotating its abdomen forward as it takes off from the ground. We tested the hypotheses that abdominal rotation is used to either provide thrust during takeoff or to stabilize rotational momentum during the initial airborne phase of the jump. We used high speed videography to characterize jumping performance of G. destructor workers jumping between two platforms. We then anesthetized the ants and used glue to prevent their abdomens from rotating during subsequent jumps, again characterizing jump performance after restraining the abdomen in this manner. Our results support the hypothesis that abdominal rotation provides additional thrust as the maximum distance, maximum height, and takeoff velocity of jumps were reduced by restricting the movement of the abdomen compared with the jumps of unmanipulated and control treatment ants. In contrast, the rotational stability of the ants while airborne did not appear to be affected. Changes in leg movements of restrained ants while airborne suggest that stability may be retained by using the legs to compensate for changes in the distribution of mass during jumps. This hypothesis warrants investigation in future studies on the jump kinematics of ants or other insects.

The Role of the Divergent Circulation for Large-Scale Eddy Momentum Transport in the Tropics. Part II: Dynamical Determinants of the Momentum Flux

This paper investigates the coupling between the rotational and divergent circulations aiming to explain the observations that show that the tropical eddy momentum flux is due to correlations between divergent eddy meridional velocities and rotational eddy zonal velocities. A simple linear model in which the observed eddy divergence field is used to force the vorticity equation can reproduce quite well the observed tropical eddy momentum flux. The eddy momentum flux in the model shows little sensitivity to the basic-state winds and is mainly determined by the characteristics of the divergent forcing. Vortex stretching and divergent advection of planetary vorticity produce eddy momentum flux contributions with the same sign but the former forcing dominates. It is shown that the main factor affecting the direction of the eddy momentum flux response to both forcings is the meridional tilt of the divergence phase lines, albeit with an opposite sign to the classical relation between rotational momentum flux and streamfunction phase tilt. How this divergent structure is determined remains an open question.

A Study of Weight-Based Compensation for Asymmetric Upper Limb Growth Secondary to Pre-Pubertal Operative Humeral Epiphyseal Plate Damage

Injuries to the growth plate of the humerus can occur in children during motor vehicle accidents. These injuries can then lead to growth abnormalities and musculoskeletal issues as the child develops. This research was conducted to analyze and develop a solution to musculoskeletal strain caused by uneven weight distribution inherent in a case of upper limb length discrepancy. The issue is an imbalance due to the growth of a shorter humerus in the individual’s right upper limb (RUL) as the result of a prior surgery on the individual’s right humeral growth plate. This shortened RUL weighs less than the left upper limb (LUL). This effectively lowers the mass moment of inertia of the RUL, thus lowering the balancing moment on the torso. When the individual sprints during physical exercise, there is an imbalance in rotational momentum that is created between the two arms. This imbalance in momentum requires that the opposing lower limb of the shorter RUL, the individual’s left lower limb, drives harder, leading to eventual failure in the hip flexor. In order to solve this biomechanical problem, kinematic equations were developed to model the motion of a sprinter. These equations model the motions of the hands, torso, and legs. In particular, the model defines the influence of the imbalance of the upper limbs’ motion on the lower limbs’ motion, which results in a forward rotation of the torso while sprinting. To balance the rotational momentum of the upper limbs, a counter-acting weight was attached to the wrist of the RUL, minimizing the effects on the lower limb musculature. Hence, the left lower limb would not have to overcompensate for the shorter RUL’s lack of momentum. The equations were then reconfigured to account for the counterweight, and the effect was observed and analyzed. A simulation predicted an angle of tilt of up to 5.7° in the sagittal plane from the vertical. The force required to rotate the body to the normal position was 18N. This force was determined to cause a twist of 10.0° in the transverse plane from the frontal plane. While this study was conducted on an individual with a shortened right upper limb secondary to a surgical procedure, study results can readily be generalized to individuals with shortening of either upper limb secondary to other traumatic events, such as motor vehicle accidents.

Theoretical study of product polarization of O(1D) + HCl(v = 0; j = 0) → ClO + H and its isotope exchange reaction

O(1D) + HCl(v = 0; j = 0) → ClO + H and its isotope exchange reaction O(1D) + DCl(v = 0; j = 0) → ClO + D are studied in the collision energy range 14.0–20.0 kcal/mol based on the potential energy surface 1[Formula: see text] state. Reaction probabilities, integral cross sections, the two angular distribution functions (concerning the initial/final velocity vector, and the product rotational momentum vector), and the product rotational alignment parameters are calculated as a function of the collision energy for the two reactions. The four generalized polarization dependent differential cross sections are presented to manifest the polarization characters. Also, the effect of the collision energy and the kinetic isotope effect are studied.

Momentum Balance of the Wind-Driven and Meridional Overturning Circulation

When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces that are confined to the basin boundaries and drive the overturning circulation. Potential applications of the approach to diagnosing the output of ocean circulation models, alternative and more accurate formulations of numerical ocean models, the dynamics of boundary layer separation, and eddy forcing of the large-scale ocean circulation are discussed.

A NEW 3D ROLLER APPROACH FOR FACING ROTATIONAL SURF ZONE HYDRODYNAMICS

A 2DH highly nonlinear Boussinesq-type of model for breaking waves has been developed in order to investigate surf zone hydrodynamics, also in the presence of complex bathymetries. The set of equations includes continuity and rotational momentum equations, coupled with the vorticity transport equation. An appropriate spatial definition of the 3D roller concept, along with an algorithm for accurately tracking the roller position, have been on purposely developed. Several numerical simulations have been carried out for the case of a submerged elliptic shoal. The results have been compared with both experimental data and with the results of other numerical models available in the literature. Finally, the vorticity dynamics under a breaking wave has been analyzed both in time and space, showing that a fairly correct interpretation of the wake effect in the rear part of the wave crest is obtained.

Using Global Characteristics of a Centrifuge Outflow Experiment to Determine Unsaturated Soil Parameters

Several centrifugation scenarios enabling the determination of soil parameters for saturated-unsaturated flow in porous media are presented, investigated, and discussed. Only global characteristics of the infiltration process in a sample are used, so that only simple, noninvasive measurements are performed. The characteristics can be transient measurements of the rotational momentum, or of the gravitational center, or of the water amount injected and expelled from the sample. No information about the saturation or the head distribution in the sample is required. This setup is different from the common multioutflow experiments. We give numerical proof that this method allows for fast determination of soil parameters in comparison to traditional measurements based on equilibrium conditions. The mathematical model of infiltration is represented by Richards' strongly nonlinear and degenerate equation expressed in terms of soil parameters in the van Genuchten-Mualem ansatz. The parameter identification process is realized in an iterative way applying the Levenberg-Marquardt method. Numerical experiments support the efficiency of the analyzed method and allow one to identify the optimal centrifugation scenario for imbibition and drainage to be applied when using global characteristics.