Vorticity Model Research Articles

Vortex theory approach to stochastic hydrodynamics

The objective of the paper is to study a jump-diffusion type vorticity model, describing evolution of an incompressible homogeneous viscous fluid in R 2 in terms of its rotation. The model arises from a particle systems perspective, adopted in the point vortex theory, and represents a measure-valued stochastic partial differential equation (SPDE) whose solution, under certain conditions, is an empirical process generated by a finite system of randomly moving vortices, which interact via a (regularized) logarithmic potential and are driven by suitable independent space-time Wiener processes and compensated Poisson random measure. A continuous diffusion approximation to the above vorticity model is also presented.

Variability of the Kuroshio Extension Jet, Recirculation Gyre, and Mesoscale Eddies on Decadal Time Scales

Abstract Twelve years of sea surface height (SSH) data from multiple satellite altimeters are used to investigate the low-frequency changes and the interconnections of the Kuroshio Extension (KE) jet, its southern recirculation gyre, and their mesoscale eddy field. The dominant signal is characterized by the steady weakening of the KE jet/recirculation gyre from 1993 to 1996, followed by a gradual strengthening after 1997. During the weakening period of 1993–96, the KE path migrated southward in general, and this path migration reversed in direction during the strengthening period of the KE jet and recirculation gyre after 1997. By hindcasting the SSH signals using linear vorticity dynamics, it was found that weakening (strengthening) in the KE jet and recirculation gyre is consistent with westward propagation of negative (positive) SSH anomalies generating in the eastern North Pacific and strengthening during their westward propagation. When the KE jet and recirculation gyre were in a weak mode during 1996–2001, the regional eddy kinetic energy level was observed to be higher than when the jet and recirculation gyre were in a strong mode. This negative correlation between the mean flow intensity and the level of regional eddy kinetic energy is found in both the SSH data and the linear vorticity model to result from the migration of the KE jet inflow over the Izu–Ogasawara Ridge. When it is forced southward by the impinging negative SSH anomalies, the KE jet inflow rides over the ridge through a shallow segment, leading to large-amplitude downstream meanders. Impinging of positive SSH anomalies, on the other hand, strengthens the recirculation gyre and forces the inflow northward where it passes through a deep channel, minimizing the path perturbations in the downstream region.

On the Separation of a Barotropic Western Boundary Current from a Cape

AbstractThe problem of western boundary current separation is investigated using a barotropic vorticity model. Specifically, a boundary current flowing poleward along a boundary containing a cape is considered. The meridional gradient of the Coriolis parameter (the β effect), the strength of dissipation, and the geometry of the cape are varied. It is found that 1) all instances of flow separation are coincident with the presence of a flow deceleration, 2) an increase in the strength of the β effect is able to suppress flow separation, and 3) increasing coastline curvature can overcome the suppressive β effect and induce separation. These results are supported by integrated vorticity budgets, which attribute the acceleration of the boundary current to the β effect and changes in flow curvature. The transition to unsteady final model states is found to have no effect upon the qualitative nature of these conclusions.

Francis Lodwick's Creation: Theology and Natural Philosophy in the Early Royal Society

This paper examines the cosmological theories of Francis Lodwick (1619-94), the Fellow of the Royal Society, language theorist and close associate of Robert Hooke, concentrating on some unnoticed manuscripts he wrote on this issue. It is demonstrated that Lodwick's account of creation acts as a commentary on the opening chapters of Genesis, influenced in equal measures by the new corpuscular philosophy, and by the heretical, messianic ideas of the Frenchman Isaac La Peyrere, whose Prae-Adamitae (1655) so shocked European scholars. Such a conclusion emphasizes that in the case of Lodwick no clear distinction between biblical criticism and natural philosophy can be maintained, and that the theological ideas he brought to his vortical model of creation were strongly heretical. Such a situation contradicts the proposition insisted upon by early apologists for the Royal Society that the institutionalizing of scientific work would promote orthodox Christianity.

Numerical Analysis of Stochastic Schemes in Geophysics

We present and study the stability, convergence, and order of convergence of a numerical scheme used in geophysics, namely, the stochastic version of a deterministic implicit leapfrog scheme which has been developed for the approximation of the so-called barotropic vorticity model. Two other schemes which might be useful in the context of geophysical applications are also introduced and discussed.

An Investigation of the Influence of Latent Heat Release on Cold-Frontal Motion

Abstract The effects of condensational heating on cold-frontal translation speed are explored through the use of potential vorticity (PV) diagnostics and model sensitivity experiments. It is hypothesized that condensational heating can lead to faster frontal translation speeds in the presence of vertical shear because of the horizontal propagation of the positive PV anomaly associated with the front. A case study of a cold front with an evolving precipitation structure is presented. A positive correlation existed between the position of condensational heating relative to the frontal zone and frontal translation speed, with faster frontal movement occurring when condensational heating was present in the prefrontal zone. This front was numerically simulated to see if the hypothesized mechanism for frontal movement was active. Through the use of a PV budget, it was confirmed that condensational heating did contribute to the forward propagation of the cold-frontal PV band. Numerical experiments were performed...

Potential and Viscous Interactions for a Multi-Blade-Row Compressor

A computationally efficient time-accurate vortex method for unsteady incompressible flows through multiple blade row systems is presented. The method represents the boundary surfaces using vortex systems. A local coordinate system is assigned to each independently moving blade row. Blade shed vorticity is determined from two generating mechanisms and convected using the Euler equation. The first mechanism of vorticity generation is a potential mechanism from a nonlinear unsteady pressure-type Kutta condition applied at the blade trailing edges. The second mechanism is a viscous mechanism from a viscous wake vorticity (VWV) model implemented to simulate the viscous shear layers on the blade pressure and suction sides. Two different two-blade-row compressor systems, a rotor/stator (R/S) system and a stator/rotor (S/R) system, were used to investigate the interaction forces on each blade row. Computational results of the potential and viscous interaction forces are presented and compared to measurements. The comparison suggests that the viscous wake interaction accounts for 25–30% of the peak loading for an axial spacing of 10% chord length between the blade rows. The efficient computational method is particularly attractive for blade indexing study. Therefore a three-blade-row rotor/stator/rotor (R1/S/R2) compressor system is used to demonstrate the indexing calculations between the two rotor positions. Resultant forces on each blade row are presented for ten rotor indexing positions and three axial gap sizes for the gaps between R1 and S and between S and R2. The unsteady peak-to-peak force can reach 10–15% of inflow dynamic head for the gap spacing investigated. The minimum-to-maximum variation of the unsteady force can account for 40–50% of averaged unsteady force.

Analytic Solution for Diffusional Filtration across Granular Beds in Low Knudsen Number Regime

AbstractThe collection efficiency of aerosols in the low Knudsen number region was studied using a system of multiple spheres. Kuwabara's free vorticity model was expanded to include the effects of gas slip at the collector surface, with the collection efficiency due to diffusion obtained analytically and compared with existing experimental results. The results showed that the diffusional collection efficiency increases as the Knudsen number increases due to gas slippage at the collector surface. The obtained analytical solution converged to the existing collection efficiency of a solid sphere system with a Knudsen number of zero, and that of a bubble with an infinite Knudsen number. The comparison of the experimental results with analytic solution in this study shows that the trends agree well. Therefore, this study is a subsequent expansion of the collection efficiency in the finite Knudsen number region, and can be used for a broad range of collector sizes, pressures and temperatures.

Analysis of stochastic numerical schemes for the evolution equations of geophysics

We present and study the stability and convergence, and order of convergence of a numerical scheme used in geophysics, namely, the stochastic version of a deterministic “implicit leapfrog” scheme which has been developed for the approximation of the so-called barotropic vorticity model. Two other schemes which might be useful in the context of geophysical applications are also introduced and discussed.

Patterns of Local Circulation in the Itaipu Lake Area: Numerical Simulations of Lake Breeze

Abstract The lake-breeze circulation in the Itaipu region was investigated numerically using a nonhydrostatic version of the Topographic Vorticity Model. The area of study corresponds to a 100 km × 180 km rectangle, located on the Brazil–Paraguay border, with Itaipu Lake in its center. The characteristics of the lake breeze generated by the numerical experiments were consistent with the observations available in the area. The numerical experiments have shown that the land use effect is important in the spatial distribution of the lake-breeze circulation and that the topography contributes to modulating the breeze intensity, with the daytime valley–mountain circulation intensifying the lake breeze. However, the circulation pattern observed during daytime over the region is mainly due to the Itaipu Lake presence. The numerical results indicated that Itaipu Lake is able to generate and sustain a lake breeze, with 3.5 m s−1 of maximum intensity and 1500-m depth, that propagates inland at 5.1 km h−1 under typi...

Can Pacific Ocean Thermocline Depth Anomalies Be Simulated by a Simple Linear Vorticity Model?

Abstract This study attempts to reproduce the salient features of the variability in the depth of the thermocline in the marginally eddy-resolving Parallel Ocean Climate Model (POCM) of Semtner and Chervin, using a simple linear vorticity model that only permits local Ekman pumping and the propagation of long Rossby waves. The dynamic upper-ocean variability in the POCM is examined in response to changes in daily European Centre for Medium-Range Weather Forecasts wind stresses across the tropical and subtropical Pacific Ocean (31°S–31°N) between 1983 and 1989. The POCM provides a complete and physically consistent representation of the state of the Pacific Ocean, with the phase of the thermocline depth anomalies being consistent with the observed El Nino/La Nina variations in the near-equatorial zone and southwest Pacific during the decade. A series of vorticity model sensitivity experiments, incorporating scaled Rossby wave speeds based on recent observations from the TOPEX/Poseidon satellite altimeter, ...

Some Effects Of An Ekman Boundary-Layer Parameterization On Various Models Of Atmospheric Flow

The traditional Ekman boundary-layer parameterization is introduced into the quasigeostrophic Eady baroclinic instability model and into the deformation flow model, to couple the planetary boundary layer with the inviscid interior flow aloft. An explicit time-dependent version of this parameterization is then introduced into an unbalanced zero potential vorticity model to evaluate the initial transient response. It is noted that the adaptation of the geostrophic flow to the same parameterization is different in each of the balanced models. The characteristic flow response reflects thedifferent constraints imposed by each model. Further, the zero potential vorticity condition constrains the evolution of the baroclinic geostrophic part of the flow, which leads to an unphysical flow response when the Ekman boundary-layer parameterization is employed with this unbalanced model. The barotropic part of the flow does, however, evolve in a physically consistent manner spinning down to reflect the introduction of low momentum air pumped into the interior from the boundary layer. Moreover, the transient spin-up processis shown to have an insignificant effect on this spin-down process.

Flow structure and seasonalityin the Hebridean slope current

The intensity, structure and variability of the slope current have been determined from 16 months of observations with Acoustic Doppler Current Profilers (ADCP) and conventional current meters on a cross-slope section at the Hebridean shelf edge during the Shelf Edge Study (SES) programme. After removal of the tidal signals, the mean flow over the upper slope is found to be closely parallel to the topography with speeds of ≈ 20 cm·s –1. The flow extends down to a depth of 500 m and is predominantly barotropic, especially in winter when the flow is practically uniform between 350 m and the surface. In summer, there is a significant baroclinic component with a pronounced maximum in current at a depth of about 200 m but more than 80% of the kinetic energy is in the barotropic component. Flow in the core of the current is highly persistent with the Neumann’s steadiness St > 0.8 in summer. In winter the flow is generally more energetic and variable and extends onto the adjacent shelf. The cross-slope profile of sea surface elevation, computed from the mean barotropic currents, shows a consistent relation to seabed topography through the seasonal cycle. Long-term averages of the cross-slope components are generally small (≈ 2 cm·s –1) with some indication of persistent down-slope flow in the bottom Ekman layer. Measurements with shipboard ADCP on sections at intervals along the slope show a high degree of continuity in the structure of the flow. The core of the flow appears to be related to a weak positive salinity anomaly and a depression of the 9.5 °C isotherm near the shelf, but there is no strong correlation between the core of the slope-current and the core of the salinity anomaly. It is proposed that this may be due to differences in the cross-stream diffusion of salt and momentum which have different boundary conditions at the slope. The observed cross-stream structure of the current supports the hypothesis that JEBAR is the principal forcing mechanism but the result cannot be regarded as conclusive since a uniform potential vorticity model of the flow produces a similar cross-sectional structure of the current.

Relations between SGS Dissipation and GS Enstrophy of a Wake of a Rectangular Cylinder. Investigation by Numerical Analysis Using LES.

Among the various methods of turbulent flow computation, Large Eddy Simulation (LES) with Dynamic Mixed Subgrid-Scale (SGS) model proposed by Vreman et al, in 1994 is expected to be the most effective method to evaluate the inverse transfer of turbulent energy from unresolved small size eddies to resolved large ones (the backscatter). In this paper, we discuss mainly on the results of a numerical analysis for the turbulent flow around a rectangular cylinder in order to show instantaneous turbulent properties. By phase-averaging these properties, the principal features of periodic phenomena can be made clear. Especially we focus on the relation between SGS dissipation and Grid-Scale (GS) enstrophy. As a result, it is shown that the Vorticity model that has been said to have less physical meaning has, however, possibility to be one of a useful SGS models by reason of positive correlation between SGS dissipation and GS enstrophy.

Formulation and Evaluation of a Nonhydrostatic Mesoscale Vorticity Model (TVM)

This paper describes the formulation and the application of the nonhydrostatic anelastic vorticity model (TVM). This model is constructed using a method involving two horizontal streamfunctions and two horizontal vorticity components. The evaluation of this formulation is performed by simulating various bidimensional hydrostatic and nonhydrostatic mountain wave cases. Results are compared with analytical solutions and in particular with those developed by Laprise and Peltier for nonlinear forcings. The anelastic formulation is also validated with respect to the highly nonlinear 1972 Boulder windstorm. TVM is shown to accurately reproduce these mountain wave test cases in both its incompressible and anelastic formulations. In the second part of this paper, the adequacy of the hydrostatic and anelastic assumptions in simulating thermally induced circulations is investigated and compared to previous works. For a moderate surface thermal forcing, typical geographical setups are used and show slight differences between hydrostatic and nonhydrostatic horizontal wind speeds. For vertical wind speeds, differences are shown to be much larger and more sensitive to changes in grid resolution. For more stringent thermal surface forcing, differences remain low for horizontal wind speeds but increase considerably for the vertical wind component. The comparison between anelastic and incompressible solutions for the same cases shows the adequacy of the incompressible assumption when circulations are forced by the surface and are characterized by a relatively shallow vertical extent. In such conditions, virtually no differences are observed between the two formulations.

Optimal initialization of manipulation dynamics by vorticity model of robot hand preshaping. Part I: Vorticity model

The manipulation phase of a multifingered robot hand is initialized, upon contact, by the impact force patterns imparted to the object at contact points, in the final state of a preshaped hand closure. The object then inherits from contacts different helix motion tendencies (translation, rotation) as the initial conditions of manipulation. These motion tendencies are caused by the forces/torques imparted to the object upon impact, and are generated by changes of momenta of the closing hand preshape at the contact locations. The generalized impact force patterns vary for different hand preshapes, since each preshape closes upon an object with different momenta types. Consequently, the purposive closing of a preshaped hand should be kinematically modeled in such a way that impact force patterns can be naturally deduced from the model and compared to the desired ones so that this preshaped closing can be optimized according to the impact force pattern it applies to the object at contact. This would generate the optimal initial conditions of manipulation. Our work in this two part article focuses on developing methods of determining, optimally, the preshape of a robot hand closing onto an object, in order to achieve at contact a certain stability and manipulability degree based on kinematic considerations. Toward this objective, in Part I of the manuscript we define the stability and manipulability criteria of a robot hand preshape based on vortex theory, dealing with the analysis of vorticities in the robot hand workspace. © 2000 John Wiley & Sons, Inc.

Optimal initialization of manipulation dynamics by vorticity model of robot hand preshaping. Part II: Analyses of grasp initialization and its vorticity based optimization

Our work focuses on developing methods of determining the optimal preshape of a robot hand closing onto an object in order to achieve at contact a certain stability and manipulability degree based on kinematic considerations. This purposive closing of a preshaped hand should then be kinematically modelled in such a way that impact force patterns on the object can naturally be deduced from the model and be optimized such that upon contacting the object the desired optimum initial conditions of manipulation are generated. We define in Part I of this two part article the stability and manipulability criteria of a robot hand preshape based on vertex theory dealing with the analysis of vorticities in the robot hand workspace. The grasp initialization patterns are generated as a forward stress problem using the finite element method. There, in Part II of the article they are further related to the concept of manipulability so that a robot hand grasping problem is formulated that maximizes manipulability and stability upon landing of fingertips onto the object. This problem is solved in Part II by finding the proper contact locations of fingertips for optimally impacting the object and properly initializing the manipulation phase. © 2000 John Wiley & Sons, Inc.

On the influence of bottom topography and the Deep Western Boundary Current on Gulf Stream separation

The Gulf Stream separates abruptly from the North American coastline at Cape Hatteras. The absence of significant seasonal and interannual variability in the separation point, compared with that of other separating boundary currents, suggests that Gulf Stream separation is locally controlled. In this paper we consider the possible influence of bottom topography and the Deep Western Boundary Current (DWBC), which descends underneath the Gulf Stream at Cape Hatteras. The path of the DWBC is strongly constrained by bottom topography. At Cape Hatteras, the continental shelf widens and the DWBC is forced to swing offshore and pass beneath the Gulf Stream. Three possible mechanisms by which bottom topography and the DWBC can affect the separation of the Gulf Stream are proposed and investigated: (i) topography modifies the background potential vorticity contours; (ii) the DWBC advects the Gulf Stream separation point southward; (iii) intense downwelling as the DWBC passes beneath the Gulf Stream induces an adverse pressure gradient in the Gulf Stream, leading to its separation. Results from a series of idealized numerical experiments with a geostrophic vorticity model are presented to investigate these mechanisms. Topography alone does have an impact on the separation point, broadly consistent with modification of the background potential vorticity. We also show that the presence of a DWBC does, indeed, push the time average separation of the Gulf Stream farther southward, consistent with both the advection and adverse pressure gradient mechanisms. However, the time-dependent boundary current separation is more nonlinear than suggested by each of the above mechanisms, undergoing a series of abrupt transitions between northern and southern separation states. As the DWBC transport is increased, the southern separation state is occupied more and more frequently.

Inertial Oscillations and Frontogenesis in a Zero Potential Vorticity Model

Abstract Geostrophic adjustment and frontogenesis are examined by means of a two-dimensional, inviscid, rotating and nonlinear fluid model that satisfies the condition of zero potential vorticity. The fluid is bounded top and bottom by level, rigid lids. The initial state is one of no motion, but an unbalanced horizontal temperature gradient is prescribed. The subsequent motion is represented as the sum of an inertial oscillation, with the frequency of the local Coriolis frequency f, and an evolving geostrophic flow. When a nondimensional parameter a, a Rossby number, satisfies a < 1, the gradient of the evolving geostrophic flow increases (frontogenesis) during the period 0 < t ⩽ π/f; the gradient decreases during the period π/f < t ⩽ 2π/f (frontolysis). When a ≥ 1, the relative vorticity of the evolving geostrophic flow becomes infinite: a discontinuity forms at the top and bottom boundaries during the period 0 < t ⩽ π/f. There is an equipartition of energy between the inertial oscillation and the geost...

Linear Baroclinic Instability in Extended Regime Geostrophic Models

The linear wave and baroclinic instability properties of various geostrophic models valid when the Rossby number is small are investigated. The models are the ‘‘L1’’ dynamics, the ‘‘geostrophic potential vorticity’’ equations, and the more familiar quasigeostrophic and planetary geostrophic equations. Multilayer shallow water equations are used as a control. The goal is to determine whether these models accurately portray linear baroclinic instability properties in various geophysically relevant parameter regimes, in a highly idealized and limited set of cases. The L1 and geostrophic potential vorticity models are properly balanced (devoid of inertio-gravity waves, except possibly at solid boundaries), valid on the b plane, and contain both quasigeostrophy and planetary geostrophy as limits in different parameter regimes; hence, they are appropriate models for phenomena that span the deformation and planetary scales of motion. The L1 model also includes the ‘‘frontal geostrophic’’ equations as a third limit. In fact, the choice to investigate such relatively unfamiliar models is motivated precisely by their applicability to multiple scales of motion. The models are cast in multilayer form, and the dispersion properties and eigenfunctions of wave modes and baroclinic instabilities produced are found numerically. It is found that both the L1 and geostrophic potential vorticity models have sensible linear stability properties with no artifactual instabilities or divergences. Their growth rates are very close to those of the shallow water equations in both quasigeostrophic and planetary geostrophic parameter regimes. The growth rate of baroclinic instability in the planetary geostrophic equations is shown to be generally less than the growth rate of the other models near the deformation radius. The growth rate of the planetary geostrophic equations diverges at high wavenumbers, but it is shown how this is ameliorated by the presence of the relative vorticity term in the geostrophic potential vorticity equations.