Intertwined vorticity and elastodynamics in flapping wing propulsion

We performed numerical experiments on a one-dimensional elastic solid oscillating in a two-dimensional viscous incompressible fluid with the intent of discerning the interplay of vorticity and elastodynamics in flapping wing propulsion. Perhaps for the first time, we have established the role of foil deflection topology and its influence on vorticity generation, through spatially and temporally evolving foil slope and curvature. Though the frequency of oscillation of the foil has a definite role, it is the phase relation between foil slope and pressure that determines thrust or drag. Similarly, the phase difference between flapping velocity, and pressure and inertial forces, determine the power input to the foil, and in turn drives propulsive efficiency. At low frequencies of oscillation, the sympathetic slope and curvature of deformation of the foil allow generation of leading-edge vortices that do not separate; they cause substantial rise in pressure between the leading edge and mid-chord. The circulatory component of pressure is determined primarily by the leading-edge vortex and therefore thrust too is predominantly circulatory in origin at low frequencies. In the intermediate and high-frequency range, thrust and drag on the foil spatially alternate and non-circulatory forces dominate over circulatory and viscous forces. For the mass ratios we simulated, thrust due to flapping varies quadratically as a function of Strouhal number or trailing-edge flapping velocity; further, the trailing edge flapping velocities peak at the same set of frequencies where the thrust is also a maximum. Propulsive efficiency, on the other hand, is roughly a mirror image of the thrust variation with respect to Strouhal number. Given that most instances of flapping propulsion in nature are primarily through distributed muscular actuation that enables precise control of deformation shape, leading to high thrust and efficiency, the results presented here are pointers towards understanding some of the mechanisms that drive thrust and propulsive efficiency.

Prediction of Indian rainfall during the summer monsoon season on the basis of links with equatorial Pacific and Indian Ocean climate indices

Interannual variation of Indian summer monsoon rainfall (ISMR) is linked to El Nino-Southern oscillation (ENSO) as well as the Equatorial Indian Ocean oscillation (EQUINOO) with the link with the seasonal value of the ENSO index being stronger than that with the EQUINOO index. We show that the variation of a composite index determined through bivariate analysis, explains 54% of ISMR variance, suggesting a strong dependence of the skill of monsoon prediction on the skill of prediction of ENSO and EQUINOO. We explored the possibility of prediction of the Indian rainfall during the summer monsoon season on the basis of prior values of the indices. We find that such predictions are possible for July-September rainfall on the basis of June indices and for August-September rainfall based on the July indices. This will be a useful input for second and later stage forecasts made after the commencement of the monsoon season.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

Waxing and waning of observed extreme annual tropical rainfall

We begin by providing observational evidence that the probability of encountering very high and very low annual tropical rainfall has increased significantly in the most recent decade (1998-present) compared with the preceding warming era (1979-1997). These changes over land and ocean are spatially coherent and comprise a rearrangement of very wet regions and a systematic expansion of dry zones. While the increased likelihood of extremes is consistent with a higher average temperature during the pause (compared with 1979-1997), it is important to note that the periods considered are also characterized by a transition from a relatively warm to a cold phase of the El Nino Southern Oscillation (ENSO). To probe the relation between contrasting phases of ENSO and extremes in accumulation further, a similar comparison is performed between 1960 and 1978 (another extended cold phase of ENSO) and the aforementioned warming era. Though limited by land-only observations, in this cold-to-warm transition, remarkably, a near-exact reversal of extremes is noted both statistically and geographically. This is despite the average temperature being higher in 1979-1997 compared with 1960-1978. Taking this evidence together, we propose that there is a fundamental mode of natural variability, involving the waxing and waning of extremes in accumulation of global tropical rainfall with different phases of ENSO.

A hybrid finite element formulation for flexible multibody dynamics

This work deals with the transient analysis of flexible multibody systems within a hybrid finite element framework. Hybrid finite elements are based on a two-field variational formulation in which the displacements and stresses are interpolated separately yielding very good coarse mesh accuracy. Most of the literature on flexible multibody systems uses beam-theory-based formulations. In contrast, the use of hybrid finite elements uses continuum-based elements, thus avoiding the problems associated with rotational degrees of freedom. In particular, any given three-dimensional constitutive relations can be directly used within the framework of this formulation. Since the coarse mesh accuracy as compared to a conventional displacement-based formulation is very high, the scheme is cost effective as well. A general formulation is developed for the constrained motion of a given point on a line manifold, using a total Lagrangian method. The multipoint constraint equations are implemented using Lagrange multipliers. Various kinds of joints such as cylindrical, prismatic, and screw joints are implemented within this general framework. Hinge joints such as spherical, universal, and revolute joints are obtained simply by using shared nodes between the bodies. In addition to joints, the formulation and implementation details for a DC motor actuator and for prescribed relative rotation are also presented. Several example problems illustrate the efficacy of the developed formulation.