Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid

2014 ◽  
Vol 743 ◽  
pp. 1-31 ◽  
Author(s):  
Bruno Ribstein ◽  
Riwal Plougonven ◽  
Vladimir Zeitlin
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Large Range ◽  
Baroclinic Instability ◽  
Forecast Model ◽  
Rotating Fluid ◽  
Nonlinear Saturation ◽  
Unstable Region ◽  
Long Wave ◽  
Inertial Instability

AbstractThe paper contains a detailed study of the inertial instability of a barotropic Bickley jet on the $f$-plane in the continuously stratified primitive equations model, and a comparison of this essentially ageostrophic instability with the classical baroclinic one. Analytical and numerical investigation of the linear stability of the jet in the long-wave sector is performed for a range of Rossby and Burger numbers. The major results are that: (1) the standard symmetric inertial instability, appearing at high enough Rossby numbers, turns out to be the infinite-wavelength limit of an asymmetric inertial instability, this latter having the highest growth rate for a large range of vertical wavenumbers; (2) inertial instability coexists with the standard baroclinic instability, which becomes dominant at small Rossby numbers. Nonlinear saturation of the inertial instability of the jet with a superimposed random small-amplitude perturbation is then studied, using the Weather Research and Forecast model. It is shown that at first stages the inertial instability dominates. It is localized near the maximum of the anticyclonic shear and is associated with the highest attainable value of the vertical wavenumber. The saturation of the inertial instability leads to the homogenization of the geostrophic momentum in the unstable region. At later stages, another baroclinic instability develops, characterized by lower values of the vertical wavenumber. This instability saturates by forming large-scale vortices downstream. It is identified as the leading instability of a marginally inertially stable jet resulting from the initial one through homogenization of the geostrophic momentum. The rough scenario of the evolution of essentially ageostrophic jets is, thus, as follows: the inertial instability rapidly saturates and baroclinic instability takes over. It is shown that reorganization of the flow due to developing instabilities is an efficient source of inertia-gravity waves.

Instabilities of Jets and Fronts and their Nonlinear Evolution

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Trapped Modes ◽  
Nonlinear Saturation ◽  
Parallel Flows ◽  
Inertial Instability ◽  
Shear Instabilities ◽  
Linear And Nonlinear ◽  
Flow Configurations ◽  
Characteristic Features

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

scholarly journals Influence of the Upstream Terrain on the Formation of a Cold Frontal Snowband in Northeast China

2021 ◽  
Author(s):  
Na Li ◽  
Baofeng Jiao ◽  
Lingkun Ran ◽  
Zongting Gao ◽  
Shouting Gao
Keyword(s):  
Gravity Waves ◽  
Northeast China ◽  
Large Scale ◽  
Control Experiment ◽  
Vertical Motion ◽  
Near Surface ◽  
Inertial Instability ◽  
Two Factors ◽  
Negative Effect ◽  
Conditional Instability

AbstractWe investigated the influence of upstream terrain on the formation of a cold frontal snowband in Northeast China. We conducted numerical sensitivity experiments that gradually removed the upstream terrain and compared the results with a control experiment. Our results indicate a clear negative effect of upstream terrain on the formation of snowbands, especially over large-scale terrain. By thoroughly examining the ingredients necessary for snowfall (instability, lifting and moisture), we found that the release of mid-level conditional instability, followed by the release of low-level or near surface instabilities (inertial instability, conditional instability or conditional symmetrical instability), contributed to formation of the snowband in both experiments. The lifting required for the release of these instabilities was mainly a result of frontogenetic forcing and upper gravity waves. However, the snowband in the control experiment developed later and was weaker than that in the experiment without upstream terrain. Two factors contributed to this negative topographic effect: (1) the mountain gravity waves over the upstream terrain, which perturbed the frontogenetic circulation by rapidly changing the vertical motion and therefore did not favor the release of instabilities in the absence of persistent ascending motion; and (2) the decrease in the supply of moisture as a result of blocking of the upstream terrain, which changed both the moisture and instability structures leeward of the mountains. A conceptual model is presented that shows the effects of the instabilities and lifting on the development of cold frontal snowbands in downstream mountains.

scholarly journals Synoptic Responses to Mountain Gravity Waves Encountering Directional Critical Levels

2007 ◽  
Vol 64 (3) ◽  
pp. 828-848 ◽  
Author(s):  
Armel Martin ◽  
François Lott
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Large Scale ◽  
Baroclinic Instability ◽  
General Circulation Models ◽  
Small Scale ◽  
Mountain Range ◽  
Critical Levels ◽  
Sensitivity Tests ◽  
Large Scale Flow

Abstract A heuristic model is used to study the synoptic response to mountain gravity waves (GWs) absorbed at directional critical levels. The model is a semigeostrophic version of the Eady model for baroclinic instability adapted by Smith to study lee cyclogenesis. The GWs exert a force on the large-scale flow where they encounter directional critical levels. This force is taken into account in the model herein and produces potential vorticity (PV) anomalies in the midtroposphere. First, the authors consider the case of an idealized mountain range such that the orographic variance is well separated between small- and large-scale contributions. In the absence of tropopause, the PV produced by the GW force has a surface impact that is significant compared to the surface response due to the large scales. For a cold front, the GW force produces a trough over the mountain and a larger-amplitude ridge immediately downstream. It opposes somehow to the response due to the large scales of the mountain range, which is anticyclonic aloft and cyclonic downstream. For a warm front, the GW force produces a ridge over the mountain and a trough downstream; hence it reinforces the response due to the large scales. Second, the robustness of the previous results is verified by a series of sensitivity tests. The authors change the specifications of the mountain range and of the background flow. They also repeat some experiments by including baroclinic instabilities, or by using the quasigeostrophic approximation. Finally, they consider the case of a small-scale orographic spectrum representative of the Alps. The significance of the results is discussed in the context of GW parameterization in the general circulation models. The results may also help to interpret the complex PV structures occurring when mountain gravity waves break in a baroclinic environment.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

Baroclinic Instability and Loss of Balance

2005 ◽  
Vol 35 (9) ◽  
pp. 1505-1517 ◽  
Author(s):  
M. Jeroen Molemaker ◽  
James C. McWilliams ◽  
Irad Yavneh
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Boussinesq Equations ◽  
Approximate Model ◽  
Slow Manifold ◽  
Energy Cascades ◽  
Centrifugal Instability ◽  
Forward Energy ◽  
Balanced Dynamics

Abstract Under the influences of stable density stratification and the earth’s rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics—sometimes called the slow manifold—in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear balance equations are a widely successful, approximate model for this regime, and mathematically explicit limits of their time integrability have been identified. It is hypothesized that these limits are indicative, at least approximately, of the transition from the larger-scale regime of inverse energy cascades by anisotropic flows to the smaller-scale regime of forward energy cascade to dissipation by more nearly isotropic flows and intermittently breaking inertia–gravity waves. This paper analyzes the particular example of an unbalanced instability of a balanced, horizontally uniform, vertically sheared current, as it occurs within the Boussinesq equations. This ageostrophic, anticyclonic, baroclinic instability is investigated with an emphasis on how it relates to the breakdown of balance in the neighborhood of loss of balanced integrability and on how its properties compare with other examples of ageostrophic anticyclonic instability of rotating, stratified, horizontally sheared currents. It is also compared with the more familiar types of instability for a vertically sheared current: balanced (geostrophic) baroclinic instability, centrifugal instability, and Kelvin–Helmholtz instability.

Ageostrophic instabilities of fronts in a channel in a stratified rotating fluid

2009 ◽  
Vol 627 ◽  
pp. 485-507 ◽  
Author(s):  
J. GULA ◽  
R. PLOUGONVEN ◽  
V. ZEITLIN
Keyword(s):  
Baroclinic Instability ◽  
Water Model ◽  
Small Scale ◽  
Rotating Fluid ◽  
Shallow Water Model ◽  
Mean Flow ◽  
Nonlinear Saturation ◽  
The Mean ◽  
Rotating Shallow Water ◽  
Stability Results

It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby–Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149–176) in a two-layer rotating shallow-water model. First, we benchmark our method by reproducing the linear stability results obtained by Sakai (1989) and extend them to more general configurations. Second, in order to determine the relevance of RK instability in more realistic flows, simulations of the evolution of a front in a continuously stratified fluid are carried out. They confirm the presence of RK instability with characteristics comparable to those found in the two-layer case. Finally, these simulations are used to study the nonlinear saturation of the RK modes. It is shown that saturation is achieved through the development of small-scale instabilities along the front which modify the mean flow so as to stabilize the RK mode. Remarkably, the developing instability leads to conversion of kinetic energy of the basic flow to potential energy, contrary to classical baroclinic instability.

scholarly journals Realizing Surface-Driven Flows in the Primitive Equations

2015 ◽  
Vol 45 (5) ◽  
pp. 1376-1392 ◽  
Author(s):  
Eric Bembenek ◽  
Francis J. Poulin ◽  
Michael L. Waite
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Primitive Equations ◽  
Rossby Number ◽  
Initial Flow ◽  
The Core ◽  
Gravitational Instabilities ◽  
Inertial Instability ◽  
Secondary Vortices ◽  
Surface Buoyancy

AbstractThe surface quasigeostrophic (SQG) model describes flows with surface buoyancy perturbations with no interior quasigeostrophic potential vorticity at small Rossby number Ro and O(1) Burger number, where quasigeostrophic dynamics are expected to hold. Numerical simulations of SQG dynamics have shown that vortices are frequently generated at small scales, which may have O(1) Rossby numbers and therefore may be beyond the limits of SQG. This paper examines the dynamics of an initially geostrophically balanced elliptical surface buoyancy perturbation in both the SQG model and the nonhydrostatic Boussinesq primitive equations (PE). In the case of very small Rossby number, it is confirmed that both models agree, as expected. For larger Ro, non-SQG effects emerge and as a result the solution of the PE deviates significantly from that of SQG. In particular, an increase in the Rossby number has the following effects: (i) the buoyancy filaments at the surface are stabilized in that they generate fewer secondary vortices; (ii) the core of the vortex experiences inertial instability, which results in a uniform buoyancy profile in its interior; (iii) the divergent part of the energy spectrum increases in magnitude; (iv) the PE model has significantly more gravity waves that are radiated from the vortex; (v) the magnitude of the vertical velocity increases; and (vi) in the mature stages of evolution, there are gravitational instabilities that develop because of the complicated dynamics inside the vortex. It is demonstrated that significant non-SQG effects are evident when the large-scale Rossby number of the initial flow is about 0.05 and the local Rossby number is O(1).

scholarly journals On the Dynamics, Thermodynamics, and Forecast Model Evaluation of Two Snow-Burst Events in Southern Alberta

2014 ◽  
Vol 29 (3) ◽  
pp. 725-749 ◽  
Author(s):  
Shawn M. Milrad ◽  
John R. Gyakum ◽  
Kelly Lombardo ◽  
Eyad H. Atallah
Keyword(s):  
North American ◽  
Large Scale ◽  
Forecast Model ◽  
Conveyor Belt ◽  
Synoptic Scale ◽  
Southern Alberta ◽  
Inertial Instability ◽  
Regional Reanalysis ◽  
Environmental Prediction ◽  
Fast Flow

Abstract Two high-impact convective snowband events (“snow bursts”) that affected Calgary, Alberta, Canada, are examined to better understand the dynamics and thermodynamics of heavy snowbands not associated with lake effects or the cold conveyor belt of synoptic-scale cyclones. Such events are typically characterized by brief, but heavy, periods of snow; low visibilities; and substantial hazards to automobile and aviation interests. Previous literature on these events has been limited to a few case studies across North America, including near the leeside foothills of the U.S. Rockies. The large-scale dynamics and thermodynamics are investigated using the National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR). Previously, high-resolution convection-explicit Weather Research and Forecasting Model (WRF) simulations have shown some ability to successfully reproduce the dynamics, thermodynamics, and appearance of convective snowbands, with small errors in location and timing. Therefore, WRF simulations are performed for both events, and are evaluated along with the NCEP North American Mesoscale (NAM) model forecasts. Both the NARR and WRF simulations show that while the two snow bursts are similar in appearance, they form as a result of different dynamic and thermodynamic mechanisms. The first event occurs downstream of an upper-tropospheric jet streak in a region of little synoptic-scale ascent, where ageostrophic frontogenesis helps to release conditional, dry symmetric, and inertial instability in an unsaturated environment. The inertial instability is determined to be related to fast flow over upstream high terrain. The second event occurs in a saturated environment in a region of Q-vector convergence (primarily geostrophic frontogenesis), which acts to release conditional, convective, and conditional symmetric instability (CSI).

Baroclinic instability of Kirchhoff's elliptic vortex

1994 ◽  
Vol 261 ◽  
pp. 253-271 ◽  
Author(s):  
Takeshi Miyazaki ◽  
Hideshi Hanazaki
Keyword(s):  
Baroclinic Instability ◽  
Deformation Mode ◽  
Short Wave ◽  
Linear Instability ◽  
The Other ◽  
Rotating Fluid ◽  
Long Wave ◽  
Bending Mode ◽  
Vortex Axis ◽  
Bending Wave

The linear instability of Kirchhoff's elliptic vortex in a vertically stratified rotating fluid is investigated using the quasi-geostrophic, f-plane approximation. Any elliptic vortex is shown to be unstable to baroclinic disturbances of azimuthal wavenumber m = 1 (bending mode) and m = 2 (elliptical deformation). The axial wavenumber of the unstable bending mode approaches Λc = 1.7046 in the limit of small ellipticity, indicating that it is a short-wave baroclinic instability. The instability occurs when the bending wave rotates around the vortex axis with angular velocity identical to the rotation rate of the undisturbed elliptic vortex. On the other hand, the wavenumber of the elliptical deformation mode approaches zero in the same limit, showing that it is a long-wave sideband instability.

scholarly journals A study of atmospheric gravity waves and travelling ionospheric disturbances at equatorial latitudes

1997 ◽  
Vol 15 (8) ◽  
pp. 1048-1056 ◽  
Author(s):  
R. L. Balthazor ◽  
R. J. Moffett
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Ionospheric Disturbance ◽  
Magnetic Equator ◽  
Ionospheric Disturbances ◽  
Atmospheric Gravity Waves ◽  
Opposite Hemisphere ◽  
Travelling Ionospheric Disturbances ◽  
F Region ◽  
Atmospheric Gravity

Abstract. A global coupled thermosphere-ionosphere-plasmasphere model is used to simulate a family of large-scale imperfectly ducted atmospheric gravity waves (AGWs) and associated travelling ionospheric disturbances (TIDs) originating at conjugate magnetic latitudes in the north and south auroral zones and subsequently propagating meridionally to equatorial latitudes. A 'fast' dominant mode and two slower modes are identified. We find that, at the magnetic equator, all the clearly identified modes of AGW interfere constructively and pass through to the opposite hemisphere with unchanged velocity. At F-region altitudes the 'fast' AGW has the largest amplitude, and when northward propagating and southward propagating modes interfere at the equator, the TID (as parameterised by the fractional change in the electron density at the F2 peak) increases in magnitude at the equator. The amplitude of the TID at the magnetic equator is increased compared to mid-latitudes in both upper and lower F-regions with a larger increase in the upper F-region. The ionospheric disturbance at the equator persists in the upper F-region for about 1 hour and in the lower F-region for 2.5 hours after the AGWs first interfere, and it is suggested that this is due to enhancements of the TID by slower AGW modes arriving later at the magnetic equator. The complex effects of the interplays of the TIDs generated in the equatorial plasmasphere are analysed by examining neutral and ion winds predicted by the model, and are demonstrated to be consequences of the forcing of the plasmasphere along the magnetic field lines by the neutral air pressure wave.

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