scholarly journals Three-Dimensional Ageostrophic Motion in Mesoscale Vortex Dipoles

2007 ◽  
Vol 37 (1) ◽  
pp. 84-105 ◽  
Author(s):  
Enric Pallàs-Sanz ◽  
Álvaro Viúdez
Keyword(s):  
Vertical Velocity ◽  
Potential Vorticity ◽  
Extreme Values ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Shear Velocity ◽  
Horizontal Shear ◽  
Dipole Axis ◽  
Centripetal Acceleration ◽  
Vortex Dipoles

Abstract The three-dimensional motion of mesoscale baroclinic dipoles is simulated using a nonhydrostatic Boussinesq numerical model. The initial conditions are two ellipsoidal vortices of positive and negative potential vorticity anomalies. The flow is moderately ageostrophic with a maximum absolute Rossby number equal to 0.71. The trajectory of the dipole is related to the maximum potential vorticity anomaly and size of the vortices. Three cases are considered depending on the curvature of the dipole trajectory: negative, close to zero, and positive. The ageostrophic flow strongly depends on the distance between the ellipsoidal vortices d0. For small d0 the vortices move steadily as a compact dipole, and the vertical velocity w has an octupolar three-dimensional pattern. The horizontal ageostrophic velocity is due to the advective acceleration of the flow, particularly the centripetal acceleration. The speed acceleration is only relatively important at the rear and front parts of the dipole axis, where the flow curvature is small but where the flow confluence and diffluence are, respectively, large. The geostrophy is maximal at the dipole center, on the dipole axis, where both curvature and speed acceleration are minimal. As d0 increases, the dipole self-propagating velocity and the extreme values of |w| decrease, and vortex oscillations highly distort the octupolar pattern of w. In all cases, as is typical of balanced mesoscale geophysical flows, the vertical velocity is related to the advection of vertical vorticity by the horizontal shear velocity uhz · ∇hζ.

The origin of the stationary frontal wave packet spontaneously generated in rotating stratified vortex dipoles

2007 ◽  
Vol 593 ◽  
pp. 359-383 ◽  
Author(s):  
ÁLVARO VIÚDEZ
Keyword(s):  
Wave Packet ◽  
Vertical Velocity ◽  
Large Scale ◽  
Three Dimensional ◽  
Rate Of Change ◽  
Vertical Shear ◽  
Dipole Axis ◽  
Frontal Wave ◽  
Vortex Dipoles ◽  
Vorticity Vector

The origin of the stationary frontal wave packet spontaneously generated in rotating and stably stratified vortex dipoles is investigated through high-resolution three-dimensional numerical simulations of non-hydrostatic volume-preserving flow under the f-plane and Boussinesq approximations. The wave packet is rendered better at mid-depths using ageostrophic quantities like the vertical velocity or the vertical shear of the ageostrophic vertical vorticity. The analysis of the origin of vertical velocity anomalies in shallow layers using the generalized omega-equation reveals that these anomalies are related to the material rate of change of the ageostrophic differential vorticity, which in shallow layers are themselves related to the large-scale ageostrophic flow along the dipole axis, and in particular, to the advective acceleration. It is found that on the anticyclonic side of the dipole axis the combined effect of the speed and centripetal accelerations causes an anticyclonic rotation of the horizontal ageostrophic vorticity vector in a time scale of about one inertial period. These facts support the hypothesis that the origin of the stationary and spontaneously generated frontal wave packet at mid-depths is the large acceleration of the fluid particles as they move along the anticyclonic side of the dipole axis in shallow layers.

scholarly journals Elliptic and hyperbolic interior solutions of piecewise-constant potential vorticity geophysical vortices

2012 ◽  
Vol 696 ◽  
pp. 301-318 ◽  
Author(s):  
Álvaro Viúdez
Keyword(s):  
Aspect Ratio ◽  
Potential Vorticity ◽  
Three Dimensional ◽  
Homogeneous Distribution ◽  
Gradient Term ◽  
Centripetal Acceleration ◽  
Piecewise Constant ◽  
Geostrophic Balance ◽  
Constant Potential ◽  
Pressure Anomaly

AbstractElliptic and hyperbolic geopotential solutions, for a homogeneous distribution of potential vorticity (PV), are obtained via PV inversion in geophysical vortices. The flow in the axisymmetrical three-dimensional vortices is steady and horizontal, where the centripetal acceleration plus the Coriolis acceleration equals the pressure anomaly gradient term (gradient wind or cyclo-geostrophic balance). It is found that the family of geopotential solutions in the vortex interior is completely parameterized by the PV density in the vortex and the squared aspect ratio between the horizontal and vertical semi-axes of the ellipsoidal or hyperbolic geopotential surfaces. Thus, the PV inversion task consists of obtaining, via solution of algebraic cubic equations, the absolute vertical vorticity and vertical stratification as a function of PV and aspect ratio. It is found that there is always a critical aspect ratio, which depends on PV, beyond which the PV inversion solutions are multi-valued. The complete vorticity and stratification solutions for the different regions in the PV and aspect ratio space are obtained and analysed with emphasis on the inertial and static instability of the vortex flow.

scholarly journals Three-Dimensional Mesoscale Dipole Frontal Collisions

2007 ◽  
Vol 37 (9) ◽  
pp. 2331-2344 ◽  
Author(s):  
Sara Dubosq ◽  
Álvaro Viúdez
Keyword(s):  
Numerical Model ◽  
Potential Vorticity ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Vortex Interactions ◽  
Diffusion Effects ◽  
Two Dimensional Flow ◽  
Frontal Collisions ◽  
Bounce Back

Abstract Frontal collisions of mesoscale baroclinic dipoles are numerically investigated using a three-dimensional, Boussinesq, and f-plane numerical model that explicitly conserves potential vorticity on isopycnals. The initial conditions, obtained using the potential vorticity initialization approach, consist of twin baroclinic dipoles, balanced (void of waves) and static and inertially stable, moving in opposite directions. The dipoles may collide in a close-to-axial way (cyclone–anticyclone collisions) or nonaxially (cyclone–cyclone or anticyclone–anticyclone collisions). The results show that the interacting vortices may bounce back and interchange partners, may merge reaching a tripole state, or may squeeze between the outer vortices. The formation of a stable tripole from two colliding dipoles is possible but is dependent on diffusion effects. It is found that the nonaxial dipole collisions can be characterized by the interchange between the domain-averaged potential and kinetic energy. Dipole collisions in two-dimensional flow display also a variety of vortex interactions, qualitatively similar to the three-dimensional cases.

scholarly journals Diagnosing Mesoscale Vertical Motion from Horizontal Velocity and Density Data

2005 ◽  
Vol 35 (10) ◽  
pp. 1744-1762 ◽  
Author(s):  
Enric Pallàs Sanz ◽  
Álvaro Viúdez
Keyword(s):  
Vertical Velocity ◽  
Extreme Values ◽  
Vertical Motion ◽  
Shear Velocity ◽  
Horizontal Velocity ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Vertical Vorticity ◽  
Omega Equation ◽  
Q Vector

Abstract The mesoscale vertical velocity is obtained by solving a generalized omega equation (ω equation) using density and horizontal velocity data from three consecutive quasi-synoptic high-resolution surveys in the Alboran Sea. The Atlantic Jet (AJ) and the northern part of the Western Alboran Gyre (WAG) were observed as a large density anticyclonic front extending down to 200–230 m. The horizontal velocity uh in the AJ reached maxima of 1.2 m s−1 for the three surveys, with extreme Rossby numbers of ζ/f ≈ −0.9 in the WAG and +0.9 in the AJ (where ζ is the vertical vorticity and f is the Coriolis parameter). The generalized ω equation includes the ageostrophic horizontal flow. It is found that the most important “forcing” term in this equation is ( fζph + ∇hϱ) · ∇2huh, where ζph is the horizontal (pseudo) vorticity and ϱ is the buoyancy. This term is related to the horizontal advection of vertical vorticity by the vertical shear velocity, uhz · ∇hζ. Extreme values of the diagnosed vertical velocity w were located at 80–100 m with max{w} ⊂ [34, 45] and min{w} ⊂ [−64, −34] m day−1. Comparison with the quasigeostrophic (QG) ω equation shows that, because of the large Rossby numbers, non-QG terms are important. The differences between w and the QG vertical velocity are mainly related to the divergence of the ageostrophic part of the total Q vector (Qh ≡ ∇huh · ∇hϱ) in the ω equation.

scholarly journals Dynamics of Cloud-Top Generating Cells in Winter Cyclones. Part I: Idealized Simulations in the Context of Field Observations

2016 ◽  
Vol 73 (4) ◽  
pp. 1507-1527 ◽  
Author(s):  
Jason M. Keeler ◽  
Brian F. Jewett ◽  
Robert M. Rauber ◽  
Greg M. McFarquhar ◽  
Roy M. Rasmussen ◽  
...  
Keyword(s):  
Vertical Velocity ◽  
Radiative Forcing ◽  
Initial Conditions ◽  
Vertical Wind Shear ◽  
Weather Research And Forecasting ◽  
Velocity Spectrum ◽  
Latent Heating ◽  
Heating Rates ◽  
Winter Storms ◽  
Radiation Parameterizations

Abstract This paper assesses the influence of radiative forcing and latent heating on the development and maintenance of cloud-top generating cells (GCs) in high-resolution idealized Weather Research and Forecasting Model simulations with initial conditions representative of the vertical structure of a cyclone observed during the Profiling of Winter Storms campaign. Simulated GC kinematics, structure, and ice mass are shown to compare well quantitatively with Wyoming Cloud Radar, cloud probe, and other observations. Sensitivity to radiative forcing was assessed in simulations with longwave-only (nighttime), longwave-and-shortwave (daytime), and no-radiation parameterizations. The domain-averaged longwave cooling rate exceeded 0.50 K h−1 near cloud top, with maxima greater than 2.00 K h−1 atop GCs. Shortwave warming was weaker by comparison, with domain-averaged values of 0.10–0.20 K h−1 and maxima of 0.50 K h−1 atop GCs. The stabilizing influence of cloud-top shortwave warming was evident in the daytime simulation’s vertical velocity spectrum, with 1% of the updrafts in the 6.0–8.0-km layer exceeding 1.20 m s−1, compared to 1.80 m s−1 for the nighttime simulation. GCs regenerate in simulations with radiative forcing after the initial instability is released but do not persist when radiation is not parameterized, demonstrating that radiative forcing is critical to GC maintenance under the thermodynamic and vertical wind shear conditions in this cyclone. GCs are characterized by high ice supersaturation (RHice > 150%) and latent heating rates frequently in excess of 2.00 K h−1 collocated with vertical velocity maxima. Ice precipitation mixing ratio maxima of greater than 0.15 g kg−1 were common within GCs in the daytime and nighttime simulations.

Internal-inertia waves in a fluid of variable depth

1973 ◽  
Vol 73 (1) ◽  
pp. 205-213 ◽  
Author(s):  
W. D. McKee
Keyword(s):  
Exact Solutions ◽  
Surface Waves ◽  
Internal Waves ◽  
Vertical Velocity ◽  
General Problem ◽  
Three Dimensional ◽  
Variable Depth ◽  
Internal Inertia ◽  
Perturbation Pressure ◽  
Rotating Stratified Fluid

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

scholarly journals Dynamical and Physical Processes Leading to Tropical Cyclone Intensification under Upper-Level Trough Forcing

2013 ◽  
Vol 70 (8) ◽  
pp. 2547-2565 ◽  
Author(s):  
Marie-Dominique Leroux ◽  
Matthieu Plu ◽  
David Barbary ◽  
Frank Roux ◽  
Philippe Arbogast
Keyword(s):  
Angular Momentum ◽  
Tropical Cyclone ◽  
Potential Vorticity ◽  
Weather Prediction ◽  
Three Dimensional ◽  
Vertical Wind Shear ◽  
Thick Layer ◽  
Limited Area ◽  
Southwest Indian Ocean ◽  
Upper Level

Abstract The rapid intensification of Tropical Cyclone (TC) Dora (2007, southwest Indian Ocean) under upper-level trough forcing is investigated. TC–trough interaction is simulated using a limited-area operational numerical weather prediction model. The interaction between the storm and the trough involves a coupled evolution of vertical wind shear and binary vortex interaction in the horizontal and vertical dimensions. The three-dimensional potential vorticity structure associated with the trough undergoes strong deformation as it approaches the storm. Potential vorticity (PV) is advected toward the tropical cyclone core over a thick layer from 200 to 500 hPa while the TC upper-level flow turns cyclonic from the continuous import of angular momentum. It is found that vortex intensification first occurs inside the eyewall and results from PV superposition in the thick aforementioned layer. The main pathway to further storm intensification is associated with secondary eyewall formation triggered by external forcing. Eddy angular momentum convergence and eddy PV fluxes are responsible for spinning up an outer eyewall over the entire troposphere, while spindown is observed within the primary eyewall. The 8-km-resolution model is able to reproduce the main features of the eyewall replacement cycle observed for TC Dora. The outer eyewall intensifies further through mean vertical advection under dynamically forced upward motion. The processes are illustrated and quantified using various diagnostics.

A Quasi-three-dimensional Finite-volume Shallow Water Model for Green Water on Deck

2013 ◽  
Vol 57 (03) ◽  
pp. 125-140
Author(s):  
Daniel A. Liut ◽  
Kenneth M. Weems ◽  
Tin-Guen Yen
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Green Water ◽  
Water Model ◽  
Ship Motions ◽  
Shallow Water Model

A quasi-three-dimensional hydrodynamic model is presented to simulate shallow water phenomena. The method is based on a finite-volume approach designed to solve shallow water equations in the time domain. The nonlinearities of the governing equations are considered. The methodology can be used to compute green water effects on a variety of platforms with six-degrees-of-freedom motions. Different boundary and initial conditions can be applied for multiple types of moving platforms, like a ship's deck, tanks, etc. Comparisons with experimental data are discussed. The shallow water model has been integrated with the Large Amplitude Motions Program to compute the effects of green water flow over decks within a time-domain simulation of ship motions in waves. Results associated to this implementation are presented.

A Combined Eulerian and Lagrangian Method for Prediction of Evaporating Sprays

2002 ◽  
Vol 124 (3) ◽  
pp. 481-488 ◽  
Author(s):  
M. Burger ◽  
G. Klose ◽  
G. Rottenkolber ◽  
R. Schmehl ◽  
D. Giebert ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Lagrangian Method ◽  
Phase Flow ◽  
Two Phase Flows ◽  
Two Phase ◽  
Lagrangian Methods ◽  
Eulerian Method ◽  
Lagrangian Modeling

Polydisperse sprays in complex three-dimensional flow systems are important in many technical applications. Numerical descriptions of sprays are used to achieve a fast and accurate prediction of complex two-phase flows. The Eulerian and Lagrangian methods are two essentially different approaches for the modeling of disperse two-phase flows. Both methods have been implemented into the same computational fluid dynamics package which is based on a three-dimensional body-fitted finite volume method. Considering sprays represented by a small number of droplet starting conditions, the Eulerian method is clearly superior in terms of computational efficiency. However, with respect to complex polydisperse sprays, the Lagrangian technique gives a higher accuracy. In addition, Lagrangian modeling of secondary effects such as spray-wall interaction enhances the physical description of the two-phase flow. Therefore, in the present approach the Eulerian and the Lagrangian methods have been combined in a hybrid method. The Eulerian method is used to determine a preliminary solution of the two-phase flow field. Subsequently, the Lagrangian method is employed to improve the accuracy of the first solution using detailed sets of initial conditions. Consequently, this combined approach improves the overall convergence behavior of the simulation. In the final section, the advantages of each method are discussed when predicting an evaporating spray in an intake manifold of an internal combustion engine.

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