scholarly journals Piecewise potential vorticity inversion without far-field response?

2020 ◽  
Author(s):  
Joseph Egger ◽  
Klaus P. Hoinka
Keyword(s):  
Boundary Conditions ◽  
Potential Vorticity ◽  
Lower Layer ◽  
Far Field ◽  
Potential Vorticity Inversion ◽  
Field Response ◽  
Quasigeostrophic Model ◽  
Physical Impact ◽  
The Impact ◽  
Field Influence

AbstractGiven a flow domain D with subdomains D1 and D2, piecewise potential vorticity inversion (PPVI) inverts a potential vorticity (PV) anomaly in D2 and assumes vanishing PV in D1 where boundary conditions must be taken into account. It is a widely held view that the PV anomaly exerts a far-field influence on D1 which is revealed by PPVI. Tests of this assertion are conducted using a simple quasigeostrophic model where an upper layer D2 contains a PV anomaly and D1 is the layer underneath. This anomaly is inverted. Any downward physical impact of PV in D2 must also be represented in the results of a downward piecewise density inversion (PDI) based on the hydrostatic relation and the density in D2 as following from PPVI. There is no doubt about the impact of the mass in D2 on the flow in the lower layer D1. Thus results of PPVI and PDI have to agree closely. First, PPVI is applied to a locally confined PV-anomaly in D2. There is no far-field ’response’ in D1 if stationarity is imposed. Modifications of boundary conditions lead to “induced” flows in D1 but the results of PPVI and PDI differ widely. This leads to a simple proof that there is no physical far-field influence of PV-anomalies in D2. Wave patterns of the streamfunction restricted to D2 are prescribed in a second series of tests. The related PV-anomalies are obtained by differentiation and are also confined to D2 in this case. This approach illustrates the basic procedure to derive PV-fields from observations which excludes a far-field response.

scholarly journals On the Dynamics of Flows Induced by Topographic Ridges

2015 ◽  
Vol 45 (3) ◽  
pp. 927-940 ◽  
Author(s):  
Changheng Chen ◽  
Igor Kamenkovich ◽  
Pavel Berloff
Keyword(s):  
Potential Vorticity ◽  
Mesoscale Eddies ◽  
Dynamical Analysis ◽  
Far Field ◽  
Layer Potential ◽  
Zonal Jets ◽  
Vorticity Source ◽  
Quasigeostrophic Model ◽  
Stable Current

AbstractThis study describes a nonlocal mechanism for the generation of oceanic alternating jets by topographic ridges. The dynamics of these jets is examined using a baroclinic quasigeostrophic model configured with an isolated meridional ridge. The zonal topographic slopes of the ridge lead to the formation of a system of currents, consisting of mesoscale eddies, meridional currents over the ridge, and multiple zonal jets in the far field. Dynamical analysis shows that transient eddies are vital in sustaining the deep meridional currents over the ridge, which in turn play a key role in the upper-layer potential vorticity (PV) balance. The zonal jets in the rest of the domain owe their existence to the eddy forcing over the ridge but are maintained by the local Reynolds and form stress eddy forcing. The analysis further shows that a broad stable current that either becomes locally nonzonal or encounters a topographic ridge tends to become unstable. This instability provides a vorticity source and generates multiple zonal jets in the far field through a nonlocal mechanism.

scholarly journals Upgradient and Downgradient Potential Vorticity Fluxes Produced by Forced Rossby Waves. Part II: Parameter Sensitivity and Physical Interpretation

2018 ◽  
Vol 48 (5) ◽  
pp. 1211-1230 ◽  
Author(s):  
Genta Mizuta
Keyword(s):  
Potential Vorticity ◽  
Rossby Waves ◽  
Lower Layer ◽  
External Forcing ◽  
Direct Effects ◽  
Horizontal Scale ◽  
Wave Interactions ◽  
Weak Stratification ◽  
Quasigeostrophic Model ◽  
Basic Features

AbstractWe examine the potential vorticity (PV) flux produced by forced Rossby waves in a two-layer quasigeostrophic model, using a perturbation analysis. Rossby waves are excited by external forcing applied to the upper layer. The southward PV flux is produced in the lower layer by the higher-order Rossby waves that are excited by nonlinear wave–wave interactions, whereas the northward PV flux is produced in the upper layer. The direction of the PV flux is consistent with that obtained by an eddy-resolving model of the wind-driven circulation in previous studies. The southward PV flux is produced in a wide parameter range comparable to the eddy-resolving model. The basic features of the PV flux remain unchanged even in the limit of weak stratification. In this limit, stratification has nearly no effect on the flow, except that it isolates the lower layer from the direct effects of external forcing. The mechanism of the southward PV flux is explained using basic features of the barotropic Rossby waves and does not depend on details of the model. Furthermore, the resonant triad interaction of Rossby waves does not affect the PV flux. Stratification weakens or strengthens the PV flux depending on the horizontal scale of the external forcing.

scholarly journals On the Poleward Motion of Midlatitude Cyclones in a Baroclinic Meandering Jet

2013 ◽  
Vol 70 (8) ◽  
pp. 2629-2649 ◽  
Author(s):  
Ludivine Oruba ◽  
Guillaume Lapeyre ◽  
Gwendal Rivière
Keyword(s):  
Potential Vorticity ◽  
Statistical Study ◽  
Rossby Waves ◽  
Lower Layer ◽  
Finite Amplitude ◽  
Synoptic Scale ◽  
Beta Plane ◽  
The Cross ◽  
Quasigeostrophic Model ◽  
Pv Gradient

Abstract The motion of surface depressions evolving in a background meandering baroclinic jet is investigated using a two-layer quasigeostrophic model on a beta plane. Synoptic-scale finite-amplitude cyclones are initialized in the lower and upper layer to the south of the jet in a configuration favorable to their baroclinic interaction. The lower-layer cyclone is shown to move across the jet axis from its warm-air to cold-air side. It is the presence of a poleward-oriented barotropic potential vorticity (PV) gradient that makes possible the cross-jet motion through the beta-drift mechanism generalized to a baroclinic atmospheric context. The potential vorticity gradient associated with the jet is responsible for the dispersion of Rossby waves by the cyclones and the development of an anticyclonic anomaly in the upper layer. This anticyclone forms a PV dipole with the upper-layer cyclone that nonlinearly advects the lower-layer cyclone across the jet. In addition, the background deformation is shown to modulate the cross-jet advection. Cyclones evolving in a deformation-dominated environment (south of troughs) are strongly stretched while those evolving in a rotation-dominated environment (south of ridges) remain quasi isotropic. It is shown that the more stretched cyclones trigger a more efficient dispersion of energy, create a stronger upper-layer anticyclone, and move perpendicularly to the jet faster than the less stretched ones. Both the intensity and location of the upper-layer anticyclone explain the distinct cross-jet speeds. A statistical study consisting in initializing cyclones at different locations south of the jet core confirms that the cross-jet motion is faster for the more meridionally elongated cyclones evolving in areas of strongest barotropic PV gradient.

scholarly journals On Boundary-Value Problems for RANS Equations and Two-Equation Turbulence Models

2020 ◽  
Vol 85 (1) ◽  
Author(s):  
Stefan Langer ◽  
R. C. Swanson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Turbulence Modeling ◽  
Boundary Value ◽  
Transport Equations ◽  
Surface Boundary ◽  
Far Field ◽  
Rans Equations ◽  
Field Behavior ◽  
The Impact

Abstract Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier–Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In this article, we discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. In so doing, we defne the concept of a well-defined boundary-value problem. Additionally, a three-dimensional, rather than a simpler one-dimensional analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. This paper also addresses the impact of various transformations of two-equation models (e.g., the model of Wilcox) to remove the singular behavior of the dissipation rate ($$\omega $$ ω ) at the surface boundary. Finally, the issue of well-posedness regarding the governing equations is considered. A compelling argument (although not a proof) for ill-posedness is made for both direct and inverse problems.

scholarly journals Nonuniqueness of Attribution in Piecewise Potential Vorticity Inversion

2018 ◽  
Vol 75 (3) ◽  
pp. 875-883 ◽  
Author(s):  
Joseph Egger ◽  
Thomas Spengler
Keyword(s):  
Unique Solution ◽  
Vertical Velocity ◽  
Potential Vorticity ◽  
Superposition Principle ◽  
Balance Condition ◽  
Potential Vorticity Inversion ◽  
Inversion Procedure ◽  
Flow Domain ◽  
Ageostrophic Circulation ◽  
The Impact

Abstract Piecewise potential vorticity inversion (PPVI) seeks to determine the impact of observed potential vorticity (PV) anomalies on the surrounding flow. This widely used technique is based on dividing a flow domain D into subdomains D1 and D2 = D − D1. The influence of PV in D1 on the flow in D2 is assessed by removing all PV anomalies in D2 and then inverting the modified PV in D. The resulting flow with streamfunction ψ1 is attributed to the PV anomalies in D1. The relation of PV in D1 to ψ1 in D2 is not unique, because there are many PV distributions in D1 that induce the same ψ1. There is, however, a unique solution if the ageostrophic circulation is included in the inversion procedure. The superposition principle requires that the sum of inverted flows with PV = 0 in D2 and the complementary ones with PV = 0 in D1 equal the inverted flow for the complete observed PV in D. It is demonstrated, using two isolated PV balls as a paradigmatic example, that the superposition principle is violated if the ageostrophic circulation is included in PPVI, because the ageostrophic circulation cannot be associated with only one of the anomalies. Inversions of Ertel’s PV are carried out using Charney’s balance condition. PPVI is not unique in that case, because many different PV fields can be specified in D1, which all lead to the same inverted flow in D2. The balance condition assumes vanishing vertical velocity w so that uniqueness cannot be established by including w in the inversion, as was possible in the quasigeostrophic case.

A numerical investigation of the influence of yarn-level finite-element model on energy absorption by a flexible-fabric armour during ballistic impact

2008 ◽  
Vol 222 (4) ◽  
pp. 259-276 ◽  
Author(s):  
M Grujicic ◽  
G Arakere ◽  
T He ◽  
M Gogulapati ◽  
B A Cheeseman
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Element Model ◽  
Far Field ◽  
Field Boundary ◽  
Fem Model ◽  
Energy Absorbing ◽  
The Impact ◽  
Textile Fabric

A series of transient non-linear dynamic finite-element method (FEM) analyses pertaining to the interaction of a single-ply plain-woven balanced square textile-fabric armour with a spherical steel projectile is carried out in order to compare the corresponding results obtained for two different yarn models: (a) a solid FEM model in which the warp and weft yarns are represented using first-order three-dimensional solid elements and (b) a membrane model in which the same yarns are represented using second-order membrane elements. The analyses are carried out under different yarn—yarn and projectile—fabric frictional conditions and under different far-field boundary conditions applied to the edges of the fabric. The results obtained showed that the two sets of analyses yield comparable predictions regarding the temporal evolution and the spatial distribution of the deformation and damage fields within the fabric, regarding the ability of the fabric to absorb the projectile's kinetic energy and regarding the relative contributions of the main energy absorbing mechanisms. The work also confirmed the roles yarn—yarn and projectile—fabric friction play in the impact process as well as the effect of the far-field boundary conditions applied to the edges of the fabric.

Global far-field computational boundary conditions for C- and O-grid topologies

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 148-156
Author(s):  
A. Verhoff
Keyword(s):  
Boundary Conditions ◽  
Far Field

The impact of goal setting on unethical behavior: Boundary conditions and theoretical bases

2017 ◽  
Vol 25 (8) ◽  
pp. 1401
Author(s):  
Peng WEN ◽  
Xiaoya REN ◽  
Cheng CHEN
Keyword(s):  
Boundary Conditions ◽  
Goal Setting ◽  
Unethical Behavior ◽  
The Impact

Chemical Transport Facilitated by Multiphase Flow Systems1

1985 ◽  
Vol 17 (9) ◽  
pp. 1-12 ◽  
Author(s):  
Carl G. Enfield
Keyword(s):  
Organic Carbon ◽  
Boundary Conditions ◽  
Transport Equation ◽  
Fluid Phase ◽  
Chemical Transport ◽  
Facilitated Transport ◽  
Organic Fraction ◽  
Dispersive Transport ◽  
Transformation Of Variables ◽  
The Impact

Relatively immobile chemicals have been observed moving significantly faster than anticipated from hydrophobic theory. A theory is developed considering transport in three mobile fluid phases which can be used to describe this facilitated transport. The convective dispersive transport equation is solved utilizing a transformation of variables which permits utilizing existing solutions covering a wide variety of boundary conditions. The impact of the facilitated transport is demonstrated for one case where the soils organic carbon is 10%. If 2% of the fluid phase is an organic fraction, the theory developed projects that hydrophobic theory may underestimate mobility by more than 100 times. At concentrations of dissolved organic carbon normally observed in nature (5 - 10 mg/l), a measurable increased mobility is anticipated for the very immobile compounds like dioxins.

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