Irrotational Component Research Articles

Feasibility of Estimating Sea Surface Height Anomalies from Surface Ocean Currents and Winds

Abstract We propose a method to reconstruct sea surface height anomalies (SSHA) from vector surface currents and winds. This analysis is motivated by the proposed satellite ODYSEA, which is a Doppler scatterometer that measures coincident surface vector winds and currents. If it is feasible to estimate SSHA from these measurements, then ODYSEA could provide collocated fields of SSHA, currents, and winds over a projected wide swath of ∼1700 km. The reconstruction also yields estimates of the low-frequency surface geostrophic, Ekman, irrotational, and nondivergent current components and a framework for separation of balanced and unbalanced motions. The reconstruction is based on a steady-state surface momentum budget including the Ekman drift, Coriolis acceleration, and horizontal advection. The horizontal SSHA gradient is obtained as a residual of these terms, and the unknown SSHA is solved for using a Helmholtz–Hodge decomposition given an imposed SSHA boundary condition. We develop the reconstruction using surface currents, winds, and SSHA off the U.S. West Coast from a 43-day coupled ROMS–WRF simulation. We also consider how simulated ODYSEA measurement and sampling errors and boundary condition uncertainties impact reconstruction accuracy. We find that temporal smoothing of the currents for periods of 150 h is necessary to mitigate large reconstruction errors associated with unbalanced near-inertial motions. For the most realistic case of projected ODYSEA measurement noise and temporal sampling, the reconstructed SSHA fields have an RMS error of 2.1 cm and a model skill (squared correlation) of 0.958 with 150-h resolution. We conclude that an accurate SSHA reconstruction is feasible using information measured by ODYSEA and external SSHA boundary conditions.

A method to investigate mid and high-frequency vibration energy transfer paths using the irrotational intensity

Structural intensity fields provide a clear understanding of the noise, vibration and harshness (NVH) behavior of complex structures by showing the vibration energy flow between zones of excitation and dissipation. The use of models with fine meshes for automotive structures has allowed structural intensity calculations to be performed at high frequencies. However, fields are difficult to understand at medium and high frequencies: the intensity field has a vortical character that hides the vibration energy flow in these frequency ranges. In this work, a methodology is presented to filter out vortices in the structural intensity field. The approach uses the Hodge–Helmholtz decomposition: the structural intensity field is decomposed into rotational, irrotational, and harmonic components. Among them, only the irrotational component is needed to describe the path of energy flow from sources to sinks. The proposed methodology involves calculating the dynamic response and solving a diffusion equation similar to the thermal conduction equation to obtain the irrotational field of interest. Plate examples are used to illustrate the efficiency of the method, which provides a better understanding of the mid- and high-frequency energy transmission paths.

Design and analysis of an exactly divergence-free hybridised discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells

We generalise a hybridised discontinuous Galerkin method for incompressible flow problems to non-affine cells, showing that with a suitable element mapping the generalised method preserves a key invariance property that eludes most methods, namely that any irrotational component of the prescribed force is exactly balanced by the pressure gradient and does not affect the velocity field. This invariance property can be preserved in the discrete problem if the incompressibility constraint is satisfied in a sufficiently strong sense. We derive sufficient conditions to guarantee discretely divergence-free functions are exactly divergence-free and give examples of divergence-free finite elements on meshes with triangular, quadrilateral, tetrahedral, or hexahedral cells generated by a (possibly non-affine) map from their respective reference cells. In the case of quadrilateral cells, we prove an optimal error estimate for the velocity field that does not depend on the pressure approximation. Our analysis is supported by numerical results.

Decomposition of Displacement Field into the Irrotational and Solenoidal Component Using Fast Fourier Transform

Purpose: A new code based on Helmholtz decomposition is presented to separate longitudinal (pressure) and transverse (shear) components of a mixed wave field. This algorithm will help isolate shear or pressure components of an elastic wave to further concentrate on each specific wave and its physical characteristics, particularly in medical imaging instrument development and image processing techniques.
 Materials and Methods: Using the combination of Fourier transform and Helmholtz decomposition, first, the mathematical basis of the work is prepared. After reaching a usable formula, this basis is embedded in the Code written in MATLAB program. Then, various test data containing shear and pressure waves were created and fed to the Code to evaluate its ability to decompose the displacements into the shear and pressure waves.
 Results: This new algorithm successfully isolated the transverse and longitudinal wavefront of the mixed wavefield. The Code demonstrated 100% accuracy for separating the shear wave and more than 99% for the pressure wave. Moreover, the background noise was kept under 0.03% in every step.
 Conclusion: The results show that using Helmholtz decomposition in Fourier space on 3D data can help decompose a displacement field into its irrotational and solenoidal components with high accuracy. A weak dependency on wave thickness and contrast was observed, but the algorithm's accuracy never fell below 99%.

An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes.

Tensor fields are useful for modeling the structure of biological tissues. The challenge to measure tensor fields involves acquiring sufficient data of scalar measurements that are physically achievable and reconstructing tensors from as few projections as possible for efficient applications in medical imaging. In this paper, we present a filtered back-projection algorithm for the reconstruction of a symmetric second-rank tensor field from directional X-ray projections about three axes. The tensor field is decomposed into a solenoidal and irrotational component, each of three unknowns. Using the Fourier projection theorem, a filtered back-projection algorithm is derived to reconstruct the solenoidal and irrotational components from projections acquired around three axes. A simple illustrative phantom consisting of two spherical shells and a 3D digital cardiac diffusion image obtained from diffusion tensor MRI of an excised human heart are used to simulate directional X-ray projections. The simulations validate the mathematical derivations and demonstrate reasonable noise properties of the algorithm. The decomposition of the tensor field into solenoidal and irrotational components provides insight into the development of algorithms for reconstructing tensor fields with sufficient samples in terms of the type of directional projections and the necessary orbits for the acquisition of the projections of the tensor field.

Effects of different momentum control variables in radar data assimilation on the analysis and forecast of strong convective systems under the background of northeast cold vortex

Based on the WRF-3DVar system, different momentum control variables in radar data assimilation are investigated for their effects on the analysis and forecast of strong convective weather systems in the study. The single observation assimilation tests are performed besides three cycling data assimilation experiments based on U-wind/V-wind (UV) and stream-function and velocity potential (ψχ) that are scalar representations of flow fields for their irrotational and divergence components. The wind field increments for both control variables in single observation tests show that when UV are the control variables, the wind field increments have a smaller range of influence that it better reflects the characteristics of the observed information itself at the convective scale than ψχ. When ψχ are used as control variables, negative increments are generated in the analyzed wind field because ψχ have the property of maintaining the integrated value of the wind field. In addition, radar data from 5 Doppler radars in northeast China are assimilated. The cycling assimilation experiments show that CV_UV produces enhanced forecast than CV_ψχ in terms of radar reflectivity and precipitation. Another case also proves this conclusion. In particular, CV_UV improves the dynamics field and water vapor convergence, which lead to better intensity and structure prediction of the strong convection process. In contrast, CV_ψχ yields relative discontinuous wind field structure, which tends to reduce the organization of the forecast strong echoes. Another set of experiments are further designed with only radar reflectivity assimilated with CV_UV. The results show that assimilating radial velocity is helpful to improve the forecasting skill.

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid

In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain mathbb {T}times mathbb {R}. In the inviscid case there is a generic Lyapunov type instability for the density and the irrotational component of the velocity field. More precisely, we prove that their L^2 norm grows as t^{1/2} and this confirms previous observations in the physics literature. On the contrary, the solenoidal component of the velocity field experiences inviscid damping, namely it decays to zero even in the absence of viscosity. For a viscous compressible fluid, we show that the perturbations may have a transient growth of order nu ^{-1/6} (with nu ^{-1} being proportional to the Reynolds number) on a time-scale nu ^{-1/3}, after which it decays exponentially fast. This phenomenon is also called enhanced dissipation and our result appears to be the first to detect this mechanism for a compressible flow, where an exponential decay for the density is not a priori trivial given the absence of dissipation in the continuity equation.

Seismic wavefield reconstruction using a pre-conditioned wavelet–curvelet compressive sensing approach

SUMMARY The proliferation of large seismic arrays have opened many new avenues of geophysical research; however, most techniques still fundamentally treat regional and global scale seismic networks as a collection of individual time-series rather than as a single unified data product. Wavefield reconstruction allows us to turn a collection of individual records into a single structured form that treats the seismic wavefield as a coherent 3-D or 4-D entity. We propose a split processing scheme based on a wavelet transform in time and pre-conditioned curvelet-based compressive sensing in space to create a sparse representation of the continuous seismic wavefield with smooth second-order derivatives. Using this representation, we illustrate several applications, including surface wave gradiometry, Helmholtz–Hodge decomposition of the wavefield into irrotational and solenoidal components, and compression and denoising of seismic records.

Newton Optimization on Helmholtz Decomposition for Continuous Games

Many learning problems involve multiple agents optimizing different interactive functions. In these problems, the standard policy gradient algorithms fail due to the non-stationarity of the setting and the different interests of each agent. In fact, algorithms must take into account the complex dynamics of these systems to guarantee rapid convergence towards a (local) Nash equilibrium. In this paper, we propose NOHD (Newton Optimization on Helmholtz Decomposition), a Newton-like algorithm for multi-agent learning problems based on the decomposition of the dynamics of the system in its irrotational (Potential) and solenoidal (Hamiltonian) component. This method ensures quadratic convergence in purely irrotational systems and pure solenoidal systems. Furthermore, we show that NOHD is attracted to stable fixed points in general multi-agent systems and repelled by strict saddle ones. Finally, we empirically compare the NOHD's performance with that of state-of-the-art algorithms on some bimatrix games and continuous Gridworlds environment.

Kinematic processes contributing to the intensification of anomalously strong North Atlantic jets

AbstractAnomalously strong North Atlantic jets, defined in this study as jets with wind speeds exceeding 100 m·s−1, are notable due to their potential to induce high‐impact weather. This study examines the kinematic processes that contribute to the intensification of anomalously strong North Atlantic jets, as well as the variability in those processes across a large number of events. Anomalously strong jets are objectively identified during September–May 1979–2018 within the Climate Forecast System Reanalysis and composited to reveal the synoptic‐scale flow evolution associated with jet intensification. The analysis demonstrates that anomalously strong North Atlantic jets are most frequent during the winter compared with the fall and spring, and that their development is preceded by low‐level warm‐air advection, poleward moisture advection, and moist ascent within the warm conveyor belt of a surface cyclone beneath the equatorward jet‐entrance region. A diagnosis of the irrotational and nondivergent components of the ageostrophic wind within the near‐jet environment reveals that both wind components facilitate jet intensification via their nonnegligible contributions to negative potential vorticity (PV) advection and PV frontogenesis in the vicinity of the dynamic tropopause. Weather Research and Forecasting (WRF) model simulations of a jet event from December 2013 with and without latent heating further suggest that the ageostrophic wind field within the near‐jet environment is substantially modulated by latent heating. The foregoing results indicate that a diagnosis of jet intensification during anomalously strong jet events is dependent on an accurate representation of the cumulative effects of latent heating within the near‐jet environment.

Asymmetric Rainband Processes Leading to Secondary Eyewall Formation in a Model Simulation of Hurricane Matthew (2016)

Abstract The dynamics of an asymmetric rainband complex leading into secondary eyewall formation (SEF) are examined in a simulation of Hurricane Matthew (2016), with particular focus on the tangential wind field evolution. Prior to SEF, the storm experiences an axisymmetric broadening of the tangential wind field as a stationary rainband complex in the downshear quadrants intensifies. The axisymmetric acceleration pattern that causes this broadening is an inward-descending structure of positive acceleration nearly 100 km wide in radial extent and maximizes in the low levels near 50 km radius. Vertical advection from convective updrafts in the downshear-right quadrant largely contributes to the low-level acceleration maximum, while the broader inward-descending pattern is due to horizontal advection within stratiform precipitation in the downshear-left quadrant. This broad slantwise pattern of positive acceleration is due to a mesoscale descending inflow (MDI) that is driven by midlevel cooling within the stratiform regions and draws absolute angular momentum inward. The MDI is further revealed by examining the irrotational component of the radial velocity, which shows the MDI extending downwind into the upshear-left quadrant. Here, the MDI connects with the boundary layer, where new convective updrafts are triggered along its inner edge; these new upshear-left updrafts are found to be important to the subsequent axisymmetrization of the low-level tangential wind maximum within the incipient secondary eyewall.

Meshless Approximation and Helmholtz-Hodge Decomposition of Vector Fields.

The analysis of vector fields is crucial for the understanding of several physical phenomena, such as natural events (e.g., analysis of waves), diffusive processes, electric and electromagnetic fields. While previous work has been focused mainly on the analysis of 2D or 3D vector fields on volumes or surfaces, we address the meshless analysis of a vector field defined on an arbitrary domain, without assumptions on its dimension and discretisation. The meshless approximation of the Helmholtz-Hodge decomposition of a vector field is achieved by expressing the potential of its components as a linear combination of radial basis functions and by computing the corresponding conservative, irrotational, and harmonic components as solution to a least-squares or to a differential problem. To this end, we identify the conditions on the kernel of the radial basis functions that guarantee the existence of their derivatives. Finally, we demonstrate our approach on 2D and 3D vector fields measured by sensors or generated through simulation.

Modeling Transverse Coastal Bedforms at Anna Maria Island (Florida)

AbstractSea bedforms with crests perpendicular to the coastline are observed at Anna Maria Island, close to the Passage Key inlet where the local velocity field is mainly driven by tidal currents and episodic longshore currents generated by the passage of cold fronts. An idealized model able to predict the formation and the geometrical characteristics of these bedforms is described. The depth‐averaged oscillating flow generated around the inlet by the tide propagation and by the longshore currents is analyzed by assuming the flow Reynolds number large enough to determine the flow field as the superposition of an irrotational component plus a contribution due to the vorticity shed by the edges of the inlet. Qualitative comparisons of the dynamics of the vortices shed by the inlet edges with laboratory and field visualizations suggest that the approach can provide a reliable evaluation of the depth‐averaged velocity. Then, the geometrical characteristics of the bedforms generated by the interaction of the local flow with the sea bed are determined by means of a linear stability analysis of the flat bed configuration. It is shown that the model fairly predicts the orientation and the wavelength of the observed bedforms. A southward migration of the bedforms is predicted only when the southward episodic currents observed in the area are taken into account.

Explosive Higher-Order Kuramoto Dynamics on Simplicial Complexes.

The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we formulate the higher-order Kuramoto model which describes the interactions between oscillators placed not only on nodes but also on links, triangles, and so on. We show that higher-order Kuramoto dynamics can lead to an explosive synchronization transition by using an adaptive coupling dependent on the solenoidal and the irrotational component of the dynamics.

Theoretical analysis of filmwise condensation in inclined tubes with nondivergent and irrotational flow components

The present theoretical study investigates laminar film condensation of a saturated vapor in inclined circular tubes. Nusselt thin film assumptions are implemented to derive the governing differential equations for mass, momentum, and energy. The impact of both rotation and divergence of the nonconservative Nusselt velocity vector field on film growth and mass conservation are investigated and a new film thickness equation was introduced. A transformation for effective peripheral angle during stratification is derived based on the assumed linear liquid-vapor interface of Chato at the lower region of the tube. The optimal inclination angle for heat transfer is 28.2° from the horizontal for a tube of infinite length. For a finite tube the inclination angle decreases with length from 90° to 28.2° but for tubes of length L* > 2, optimal inclination angle is in the range of 28.2° and 46.6°. An expression for entrance length, Le* was introduced as a function of inclination angle. The results for heat transfer ratio have been compared with experimental data and an empirical correlation from literature and a good agreement is obtained and shown between them.

Characterising and predicting the movement of clouds using fractional‐order optical flow

Estimating cloud motion with complex background through the sequence of satellite images plays an important role in weather forecasting. This motion can be used for characterization of clouds and predicting storms. Optical flow is used here for motion estimation which gives horizontal and vertical velocity components. Velocity field vector alone is not sufficient to analyze the cloud behavior for predicting extreme weather conditions and there is a need to develop some visual features for enhancing the weather prediction strategies. In this paper, we utilize the optical flow to localize the high alert regions. To have a better localization and motion signatures, we develop a fractional order technique to compute optical flow. Also, the localization is characterized by brightness of image, magnitude, directions, vorticity and irrotational components of the optical flow. We did analysis on sequence of images for Mumbai, India heavy rain that happened during August 28–29, 2017, cyclonic data sets for May 16, 2018, September 19–20, 2018 and October 14, 2018. Visual features show different patterns for extreme and normal weather situations. A study on interpolation and extrapolation of the image sequence is also presented. Optical flow based interpolation and Advection-anisotropic-diffusion based extrapolation model give promising results.

Classical and extended electrodynamics

Classical electrodynamics is modeled by Maxwell’s equations, as a system of eight scalar equations in six unknowns, thus appearing to be overdetermined. The no-magnetic- monopoles equation can be derived from the divergence of Faraday’s law, thus reducing the number of independent equations to seven. Derivation of Gauss’ law requires an assumption beyond Maxwell’s equations, which are then overdetermined as seven equations in six unknowns. This overdetermination causes well-known inconsistencies. Namely, the interface matching condition between two different media is inconsistent for a surface charge and surface current. Also, the irrotational component of the vector potential is gauged away, contrary to experimental measurements. These inconsistencies are resolved by extended electrodynamics (EED), as a provably unique system of 7 equations in 7 unknowns. This paper provides new physical insights into EED, along with preliminary experimental results that support the theory.

Helmholtz decomposition of the neuronal current for the ellipsoidal head model

In earlier work, the neuronal primary current was expressed via the Helmholtz decomposition in terms of its irrotational part characterised by a scalar function and its solenoidal part characterised by a vectorial function. Furthermore, it was shown that EEG data is affected only by the irrotational part of the current, whereas MEG data is affected by two scalar functions, namely the irrotational component and the radial part of the solenoidal vectorial function. Here, we focus on the numerical implementation of this approach on the three-layer ellipsoidal model. The parametrization of the unknown functions in terms of ellipsoidal harmonics implicitly regularizes the highly ill-posed associated inverse problems. However, despite the above parametrization of these two unknown functions in terms of ellipsoidal harmonics, the inversion matrices are highly ill-conditioned for both EEG and MEG. In order to bypass this problem, we propose an alternative approach to the inversion problem. This involves revisiting the general inversion formulas presented earlier by one of the authors and expressing them as surface integrals. By choosing a suitable parametrization for the relevant unknown functions, these surface integrals can be evaluated using a method for numerical quadrature over smooth, closed surfaces. The method uses local radial basis function interpolation for generating quadrature weights for any given node set. This gives rise to a stable linear system of equations suitable for inversion and reconstruction purposes. We illustrate the effectiveness of our approach by presenting simple reconstructions for both EEG and MEG in a setting where data are contaminated with Gaussian white noise of signal to noise ratio (SNR) of 20 dB.

Importance of irrotational components of swimming flows on the stability of a suspension of weakly-squirming microorganisms

Importance of irrotational components of swimming flows on the stability of a suspension of weakly-squirming microorganisms

Vector Aeroacoustics for Uniform Mean Flow: Acoustic Velocity and Vortical Velocity

Acoustic and vortical disturbances in uniform mean flow bounded with solid surfaces are investigated in this paper. A convective vector wave equation and a convection equation that describe the acoustic velocity and vortical velocity in uniform mean flow, respectively, are deduced by combining the Helmholtz–Hodge decomposition method with the method of Mao et al. Analytical acoustic velocity integral formulations for the monopole and dipole sources in uniform mean flow are deduced from the developed vector wave equation and are also verified through numerical test cases. Moreover, this paper clarifies that aerodynamic sound is radiated from the monopole source as well as the irrotational components of the dipole and quadrupole sources. The solenoidal parts of the dipole and quadrupole sources are acoustically nonradiating, but they induce vortical disturbances in uniform mean flow.