scholarly journals The merger of geophysical vortices at finite Rossby and Froude number

2018 ◽  
Vol 848 ◽  
pp. 388-410 ◽  
Author(s):  
Jean N. Reinaud ◽  
David G. Dritschel
Keyword(s):  
Froude Number ◽  
Gravity Wave ◽  
Potential Vorticity ◽  
Initial Conditions ◽  
The Other ◽  
Vertical Shear ◽  
Wave Radiation ◽  
Rossby Number ◽  
Other Hand ◽  
Vorticity Anomaly

We investigate the merger of two co-rotating geophysical vortices at finite Rossby and Froude number. The initial conditions consist of two uniform potential vorticity vortices in near-equilibrium and in a nearly ‘balanced’ state (i.e. with negligible emission of inertia–gravity wave radiation). We determine the critical merger distance between the two vortices. This distance is found to increase with the magnitude of the Rossby number: intense cyclones or intense anticyclones are able to merge from further apart compared to weaker cyclones and anticyclones. Note that the Froude number is proportional to the Rossby number for the near-equilibrium initial conditions considered. The critical merging distance also depends on the sign of the potential vorticity anomaly, which is positive for ‘cyclones’ and negative for ‘anticyclones’. We show that ageostrophic motions occurring at finite Rossby number tend to draw cyclones together but draw anticyclones apart. On the other hand, we show that anticyclones tend to deform more, in particular when subject to vertical shear (as when the vortices are vertically offset). These two effects compete. Overall, nearly aligned cyclones tend to merge from further apart than their anticyclonic counterparts, while vertically offset anticyclones merge from further apart than cyclones.

Gravity wave radiation from vortex trains in rotating shallow water

1994 ◽  
Vol 281 ◽  
pp. 81-118 ◽  
Author(s):  
Rupert Ford
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Gravity Wave ◽  
Potential Vorticity ◽  
Strong Dependence ◽  
Cutoff Frequency ◽  
Wave Radiation ◽  
Aerodynamic Sound ◽  
Background Value ◽  
Parallel Flows

Gravity wave radiation by vortical flows in the f-plane shallow-water equations is investigated by direct nonlinear numerical simulation. The flows considered are initially parallel flows, consisting of a single strip in which the potential vorticity differs from the background value. The flows are unstable to the barotropic instability mechanism, and roll up into a train of vortices. During the subsequent evolution of the vortex train, gravity waves are radiated. In the limit of small Froude number, the gravity wave radiation is compared with that predicted by an appropriately modified version of the Lighthill theory of aerodynamic sound generation. It is found that the gravity wave field agrees well with that predicted by the theory, provided typical lengthscales of vortical motions are well within one deformation radius.It is found that the nutation time for vortices in the train increases rapidly with increasing Froude number in cases where the potential vorticity in the vortices is of the same sign as the background value, whereas the nutation time is almost independent of Froude number in cases where the potential vorticity in the vortices is zero or of opposite sign to the background. Consequently, in the former cases, the unsteadiness of the flow decreases with increasing Froude number, so the effect of the inertial cutoff frequency is increased, leading to an optimal Froude number for gravity wave radiation, above which the intensity of the radiated waves decreases as the Froude number is further increased. It is proposed that the existence of a finite range of interaction within the vortices, for flows with positive vortex potential vorticity, may account for the strong dependence of nutation time on Froude number in those cases. The interaction scale within the vortices becomes infinite in the limit of zero vortex potential vorticity, and so the arguments do not apply in those cases.

scholarly journals Effect of Spheroidization Annealing on Pearlite Banding

2019 ◽  
Vol 949 ◽  
pp. 40-47 ◽  
Author(s):  
Sergey Guk ◽  
Eva Augenstein ◽  
Maksim Zapara ◽  
Rudolf Kawalla ◽  
Ulrich Prahl
Keyword(s):  
Empirical Model ◽  
Initial Conditions ◽  
The Other ◽  
Experimental Investigations ◽  
Initial State ◽  
Ferritic Matrix ◽  
Other Hand ◽  
Initial States ◽  
Hot Rolled

The present paper deals with the influence of the duration of isothermal spheroidization annealing on the evolution of pearlite bands in various initial states. In this study, two initial conditions of the steel 16MnCrS5 are considered: a) industrially hot-rolled pearlite structures in their ferritic matrix and b) a specifically adjusted microstructure in the lab condition. Based on the experimental investigations and quantitative microstructural analyses, an empirical model for the prediction of pearlite banding within a broad range of annealing durations could be derived. Both, experiment and model, agree that pronounced pearlite bands in the initial state almost disappear after 25 h of spheroidization annealing. On the other hand, a marginal degree of pearlite banding in the initial state increases slightly during annealing. This fact could be explained by inhomogeneous cementite formation inside and outside the primary segregation regions of manganese.

scholarly journals Inertia–gravity-wave radiation by a sheared vortex

2008 ◽  
Vol 596 ◽  
pp. 169-189 ◽  
Author(s):  
E. I. ÓLAFSDÓTTIR ◽  
A. B. OLDE DAALHUIS ◽  
J. VANNESTE
Keyword(s):  
Gravity Wave ◽  
Couette Flow ◽  
Gravity Waves ◽  
Dimensional Structure ◽  
Analytic Description ◽  
Wave Radiation ◽  
Rossby Number ◽  
Spontaneous Radiation ◽  
Initial State ◽  
Inertia Gravity Waves

We consider the linear evolution of a localized vortex with Gaussian potential vorticity that is superposed on a horizontal Couette flow in a rapidly rotating strongly stratified fluid. The Rossby number, defined as the ratio of the shear of the Couette flow to the Coriolis frequency, is assumed small. Our focus is on the inertia–gravity waves that are generated spontaneously during the evolution of the vortex. These are exponentially small in the Rossby number and hence are neglected in balanced models such as the quasi-geostrophic model and its higher-order generalizations. We develop an exponential-asymptotic approach, based on an expansion in sheared modes, to give an analytic description of the three-dimensional structure of the inertia–gravity waves emitted by the vortex. This provides an explicit example of the spontaneous radiation of inertia–gravity waves by localized balanced motion in the small-Rossby-number regime.The inertia–gravity waves are emitted as a burst of four wavepackets propagating downstream of the vortex. The approach employed reduces the computation of inertia–gravity-wave fields to a single quadrature, carried out numerically, for each spatial location and each time. This makes it possible to unambiguously define an initial state that is entirely free of inertia–gravity waves, and circumvents the difficulties generally associated with the separation between balanced motion and inertia–gravity waves.

scholarly journals Lack of high-mass pre-stellar cores in the starless MDCs of NGC 6334

2019 ◽  
Vol 622 ◽  
pp. A99 ◽  
Author(s):  
F. Louvet ◽  
S. Neupane ◽  
G. Garay ◽  
D. Russeil ◽  
A. Zavagno ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Compact Objects ◽  
The Other ◽  
High Mass ◽  
Mass Star ◽  
Dense Cores ◽  
Other Hand ◽  
Static Models ◽  
Ngc 6334 ◽  
The One

Context. The formation of high-mass stars remains unknown in many aspects. There are two competing families of models to explain the formation of high-mass stars. On the one hand, quasi-static models predict the existence of high-mass pre-stellar cores sustained by a high degree of turbulence. On the other hand, competitive accretion models predict that high-mass proto-stellar cores evolve from low or intermediate mass proto-stellar cores in dynamic environments. Aims. The aim of the present work is to bring observational constraints at the scale of high-mass cores (~0.03 pc). Methods. We targeted with ALMA and MOPRA a sample of nine starless massive dense cores (MDCs) discovered in a recent Herschel/HOBYS study. Their mass and size (~110 M⊙ and r = 0.1 pc, respectively) are similar to the initial conditions used in the quasi-static family of models explaining for the formation of high-mass stars. We present ALMA 1.4 mm continuum observations that resolve the Jeans length (λJeans ~ 0.03 pc) and that are sensitive to the Jeans mass (MJeans ~ 0.65 M⊙) in the nine starless MDCs, together with ALMA-12CO(2–1) emission line observations. We also present HCO+(1–0), H13CO+(1–0) and N2H+(1–0) molecular lines from the MOPRA telescope for eight of the nine MDCs. Results. The nine starless MDCs have the mass reservoir to form high-mass stars according to the criteria by Baldeschi et al. (2017). Three of the starless MDCs are subvirialized with αvir ~ 0.35, and four MDCs show sign of collapse from their molecular emission lines. ALMA observations show very little fragmentation within the MDCs. Only two of the starless MDCs host compact continuum sources, whose fluxes correspond to <3 M⊙ fragments. Therefore, the mass reservoir of the MDCs has not yet been accreted onto compact objects, and most of the emission is filtered out by the interferometer. Conclusions. These observations do not support the quasi-static models for high-mass star formation since no high-mass pre-stellar core is found in NGC 6334. The competitive accretion models, on the other hand, predict a level of fragmentation much higher than what we observe.

scholarly journals The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

2008 ◽  
Vol 65 (8) ◽  
pp. 2498-2521 ◽  
Author(s):  
David A. Schecter
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Formal Theory ◽  
Resonant Absorption ◽  
Critical Layer ◽  
Wave Radiation ◽  
Rossby Number ◽  
Mean Flow ◽  
Surface Drag ◽  
Isentropic Coordinates

Abstract This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed. The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

scholarly journals Moist Static Potential Vorticity Budget in Tropical Motion Systems

2021 ◽  
Keyword(s):  
Potential Vorticity ◽  
Linear Regression Analysis ◽  
Potential Temperature ◽  
Wave Activity ◽  
The Other ◽  
Eastern Pacific ◽  
Synoptic Scale ◽  
Static Potential ◽  
Horizontal Advection ◽  
Other Hand

Abstract Analyses of simple models of moist tropical motion systems reveal that the column-mean moist static potential vorticity (MSPV) can explain their propagation and growth. The MSPV is akin to the equivalent PV except it uses moist static energy (MSE) instead of the equivalent potential temperature. Examination of an MSPV budget that is scaled for moist off-equatorial synoptic-scale systems reveals that α, the ratio between the vertical gradients of latent and dry static energies, describes the relative contribution of dry and moist advective processes to the evolution of MSPV. Horizontal advection of the moist component of MSPV, a process akin to horizontal MSE advection, governs the evolution of synoptic-scale systems in regions of high humidity. On the other hand, horizontal advection of dry PV predominates in a dry atmosphere. Derivation of a “moist static” wave activity density budget reveals that α also describes the relative importance of moist and dry processes to wave activity amplification and decay. Linear regression analysis of the MSPV budget in eastern Pacific easterly waves shows that the MSPV anomalies originate over the eastern Caribbean and propagate westward due to dry PV advection. They are amplified by the fluxes of the moist component of MSPV over the Caribbean sea and over the eastern Pacific from 105-130°W, underscoring the importance of moist processes in these waves. On the other hand, dry PV convergence amplifies the waves from 90-100°W, likely as a result of the barotropic energy conversions that occur in this region.

scholarly journals Exponential Smallness of Inertia–Gravity Wave Generation at Small Rossby Number

2008 ◽  
Vol 65 (5) ◽  
pp. 1622-1637 ◽  
Author(s):  
J. Vanneste
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Initial Conditions ◽  
Wave Generation ◽  
Rossby Number ◽  
Spontaneous Generation ◽  
Steady Flows ◽  
Generation Mechanisms ◽  
Inertia Gravity Waves ◽  
Exponentially Small

Abstract This paper discusses some of the mechanisms whereby fast inertia–gravity waves can be generated spontaneously by slow, balanced atmospheric and oceanic flows. In the small Rossby number regime relevant to midlatitude dynamics, high-accuracy balanced models, which filter out inertia–gravity waves completely, can in principle describe the evolution of suitably initialized flows up to terms that are exponentially small in the Rossby number ɛ, that is, of the form exp(−α/ɛ) for some α &gt; 0. This suggests that the mechanisms of inertia–gravity wave generation, which are not captured by these balanced models, are also exponentially weak. This has been confirmed by explicit analytical results obtained for a few highly simplified models. These results are reviewed, and some of the exponential-asymptotic techniques that have been used in their derivation are presented. Two types of mechanisms are examined: spontaneous-generation mechanisms, which generate exponentially small waves from perfectly balanced initial conditions, and unbalanced instability mechanisms, which amplify unbalanced initial perturbations of steady flows. The relevance of the results to realistic flows is discussed.

scholarly journals On the Relative Contribution of Inertia–Gravity Wave Radiation to Asymmetric Instabilities in Tropical Cyclone–like Vortices

2016 ◽  
Vol 73 (9) ◽  
pp. 3345-3370 ◽  
Author(s):  
Konstantinos Menelaou ◽  
David A. Schecter ◽  
M. K. Yau
Keyword(s):  
Tropical Cyclone ◽  
Gravity Wave ◽  
Tropical Cyclones ◽  
Potential Vorticity ◽  
Three Dimensional ◽  
Life Cycles ◽  
Wave Radiation ◽  
Ambient Conditions ◽  
Layer Potential ◽  
The Impact

Abstract Intense atmospheric vortices such as tropical cyclones experience various asymmetric instabilities during their life cycles. This study investigates how vortex properties and ambient conditions determine the relative importance of different mechanisms that can simultaneously influence the growth of an asymmetric perturbation. The focus is on three-dimensional disturbances of barotropic vortices with nonmonotonic radial distributions of potential vorticity. The primary modes of instability are examined for Rossby numbers between 10 and 100 and Froude numbers in the broad neighborhood of unity. This parameter regime is deemed appropriate for tropical cyclone perturbations with vertical length scales ranging from the depth of the vortex to moderately smaller scales. At relatively small Froude numbers, the main cause of instability inferred from analysis typically involves the interaction of vortex Rossby waves with each other and/or critical-layer potential vorticity perturbations. As the Froude number increases from its lower bound, the main cause of instability transitions to inertia–gravity wave radiation. In some cases, the transition occurs abruptly at a critical point where a mode whose growth is driven almost entirely by radiation suddenly becomes dominant. In other cases, the transition is gradual and less direct as the fastest-growing mode continuously changes its structure. Examination of the angular pseudomomentum budget helps quantify the impact of radiation. The radiation-driven instabilities examined herein are shown to be quite fast and potentially relevant to real-world tropical cyclones. Their sensitivities to parameterized moisture and outer vorticity skirts are briefly addressed.

scholarly journals Cold Collapse as a Way of Making Elliptical Galaxies

1987 ◽  
Vol 127 ◽  
pp. 519-520
Author(s):  
L.A. Aguilar ◽  
D. Merritt ◽  
M. Duncan
Keyword(s):  
Angular Momentum ◽  
Surface Density ◽  
Initial Conditions ◽  
Elliptical Galaxies ◽  
The Other ◽  
Dynamical Instability ◽  
Density Profiles ◽  
Axis Ratio ◽  
Other Hand ◽  
Radial Orbit

SummaryWe investigate whether dissipationless collapse starting from very cold, non-rotating initial conditions can produce objects resembling real elliptical galaxies. We also study the effect of various initial geometries on the shape of the final object. Collapses that are initially very cold (2T/W < 0.1) are different from warmer collapses, due to the presence of a dynamical instability associated with clumping of nearly-radial orbits (Polyachenko 1981). This instability can produce very elongated bars (1.6 to 2.1 axis ratio) from spherical initial conditions. the instability is also present in models evolved from oblate and triaxial initial conditions. Warm collapses tend to preserve their initial shapes. Cold initial conditions produce objects whose surface density profiles are well fit by a de-Vaucouleurs law; warm collapses, on the other hand, produce a core-halo profile. A large collapse factor seems necessary to produce objects resembling real galaxies; the same collapse factor guarantees the presence of the radial orbit instability. It thus appears that initial flattening is not crucial for producing prolate or nearly prolate galaxies. Oblate galaxies, on the contrary, seem very difficult to form, unless extremely flattened initial conditions are invoked. Preliminary experiments suggest that these results are not changed by realistic amounts of angular momentum.

Circular islands as resonators of long-wave energy

1972 ◽  
Vol 272 (1225) ◽  
pp. 361-402 ◽  
Keyword(s):  
Continental Shelf ◽  
Power Spectra ◽  
The Other ◽  
Wave Radiation ◽  
Other Hand ◽  
Water Region ◽  
Trapped Wave ◽  
Critical Circle ◽  
Island Shelf ◽  
Wave Modes

A study is made of the long gravity waves trapped around isolated, cylindrically symmetrical island-continental shelf topographies. Numerical evaluation of the discrete complex spectra of the trapped wave modes reveals that the oscillations are of two, essentially different kinds. The ‘ trapped-leaky ’ wave-modes are the analogue of the trapped (edge) wave-modes along straight shorelines and many of their properties, including the Coriolis split in frequency, are deducible from the simpler geometry. On the other hand, the ‘shelf-island’ modes have no counterpart in the motions trapped along extended shorelines; they are virtually generated in the ocean round a vertical-walled circular island of radius equal to that of the island-shelf system at the sea floor. It is shown that the trapped wave-modes do not necessarily have the ‘inner critical circle’ property elucidated by Longuet-Higgins (1967) for the similar modes of oscillations of the waters over a circular seamount. On the other hand, the modes do have ‘wave’ domains adjacent to the coast whenever the undisturbed depth of water at the island’s shoreline is zero; there may still be critical circles in the shallow water region over the continental shelf. For those islands where the water has non-zero depth at the shoreline, the computation verifies Longuet-Higgins’s hypothesis (Longuet-Higgins 1967, § 13) concerning the affect on the trapped wave-modes of the presence of an island in the middle of the sea-mount. It is also shown that the fundamental ‘ trapped-leaky’ modes dominate the disturbance observed at the coast when plane wave radiation from the ocean interacts with the island-shelf system. For the particular example where the excitation has the form of a rectilinear pulse, it is shown that power spectra of the resulting oscillations exhibit some of the features of the spectra of real wave records made at islands following the passage of tsunamis.

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