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1、Advanced SynopticM. D. EastinBaroclinic Instability Basic Idea Simple Models Classic Eady Framework Contributions from Barotropic Instability Examples of Observational EvidenceBaroclinic InstabilityAdvanced SynopticM. D. EastinDefinition Spontaneous growth of a small-scale perturbations within a bas
2、ic-state environment Energy source for the growth is drawn from the basic-state environmentDifferent Types of “Instability” Convective instability Convective clouds grow as parcels tap into the background CAPE Kelvin-Helmholtz instability Wave-like clouds grow (and “break”) as parcels tap into the b
3、ackground vertical shearConcept of InstabilityAdvanced SynopticM. D. EastinDefinition Spontaneous growth of a small-scale perturbations within a basic-state environment Energy source for the growth is drawn from the basic-state environmentDifferent Types of “Instability” Barotropic instability Distu
4、rbances grow by extracting kinetic energy from the background flow suction-vortices in tornadoes meso-vortices in hurricanes short-waves in jet stream Baroclinic instability Disturbances grow by extracting potential energy from the background flow Synoptic-scale wavesConcept of InstabilityAdvanced S
5、ynopticM. D. EastinQuestions: QG theory and polar-front theory have taught us that the development and intensification of a surface cyclone requires the interaction of the fledgling surface cyclone or stationary front with a pre-existing upper-level wave.What mechanism develops the upper-level waves
6、?What determines the size, structure, and intensity of the upper-level waves?What basic-state conditions are required for the waves to develop?Our Approach: Your text (Chapter 7) provides a very well-written and thorough explanation of baroclinic instability via the classic theoretical framework fir
7、st presented by Eady (1949) This will be (has been) presented in detail in Advanced Dynamics Here, we will address the relevant results from a practical perspectiveBaroclinic InstabilityAdvanced SynopticM. D. EastinReview of Potential and Kinetic Energy:Baroclinic Instability“Available” Potential En
8、ergyNo kinetic energyUnstable Situation“Growth” of Wileys fall speed due to extraction of potential energy from the basic-state environment(conversion of potential energy to kinetic energy)Advanced SynopticM. D. EastinThe Basic Idea: “Coin Model” Consider a coin resting on its edge (an “unstable” si
9、tuation) Its center of gravity (or mass) is located some distance (h) above the surface As long as h 0, the coin has some “available potential energy” If the coin is given a small push to one side, it will fall over and come to rest on its side (a “stable” situation) The instability was “released” a
10、nd “removed” Its center of gravity was lowered and thus its potential energy was decreased The coins motion represents kinetic energy that was converted from the available potential energyBaroclinic InstabilityCenter ofGravityhh 0Advanced SynopticM. D. EastinThe Basic Idea: “Simple Atmosphere” Consi
11、der a stratified four-layer atmosphere with the most dense air near the surface at the pole and the least dense near the tropopause above the equator (an “unstable” situation) Each layer has a center of gravity ( ) located some distance above the surface Each layer has some available potential energ
12、y The entire atmosphere also has a center of gravity ( ) and some available potential energy If the atmosphere is given a small “push” (e.g. a weak cyclone) then the layers will move until they have adjusted their centers of gravity to the configuration that provides lowest possible center of gravit
13、y for the atmosphere (the most “stable” situation) The baroclinic instability was released and removed Each layers motion represents a portion of the total atmospheric kinetic energy that was converted from the atmospheres available potential energyBaroclinic InstabilityTPEquatorPoleSurfaceTropopaus
14、eLightHeavyEquatorPoleLightHeavyAdvanced SynopticM. D. EastinThe Basic Idea: “Simple Atmosphere” Several “events” occurred during this process in our simple atmosphere that are commonly observed in the real atmosphere: Kinetic energy (or wind) was generated similar to the increase in winds as a weak
15、 low pressure system intensifies Warm (less dense) air was lifted over cold (more dense) air in a manner very similar to fronts There is a poleward transport of warm air and an equatorward transport of cold air similar to the typical temperature advection pattern around a low pressure system. Barocl
16、inic InstabilityTPEquatorPoleSurfaceTropopauseLightHeavyEquatorPoleLightHeavyAdvanced SynopticM. D. EastinEady Framework: Energy Conversion Processes Basic-state environment consists of a strong north-south temperature gradient with an upper-level zonal jet stream (atmosphere in thermal wind balance
17、) Basic-state environment contains both available potential energy and kinetic energy Instability is initiated by (1) perturbation flow inducing weak localized WAA and CAA across the thermal gradient warm and cold air parcels (or eddy potential energy) Eddy kinetic energy is then generated (2) as wa
18、rm parcels rise and cold parcels sink Acceleration of initial parcels away from their origin creates (via mass continuity) more WAA and CAA or creates more eddy potential energy (3)Baroclinic Instability123System continues to intensify(increase its eddy kinetic energy)until is can no longer generate
19、eddy potential energy(becomes a closed occluded system)Advanced SynopticM. D. EastinEady Framework: Idealized Situation Maximum growth rate occurs for waves with wavelengths of 3000-6000 km Synoptic scale Maximum growth rate occurs for waves tilting west with height (21 phase shift) Greater tilt no
20、intensification Less tilt no intensification We look for westward tilt Stacked systems are mature Eddy kinetic energy develops from an upward heat flux Warm air rising poleward Cold air sinking equatorward Similar to warm/cold frontsBaroclinic InstabilityLHLHTroughRidgeNortherliesSoutherliesWarmCold
21、Advanced SynopticM. D. EastinProduction of Eddy Kinetic Energy Our analysis of baroclinic instability showed that the synoptic waves/cyclones are essentially systems of eddy kinetic energy What else can create eddy kinetic energy?Term A:Eddy Kinetic Energy (EKE) ProductionTerm B: Baroclinic Generati
22、on Upward heat flux produces EKE Warm air rising / cold air sinkingTerm C: Barotropic Generation Function of location relative to zonal mean jet stream Function of mean momentum flux Lets examine a few scenariosContributions from Barotropic InstabilityTerm ATerm BTerm CSee your text(Section 2.7)For
23、full derivationAdvanced SynopticM. D. EastinBarotropic Production of Eddy Kinetic Energy:Term C: Perfectly Circular EddyContributions from Barotropic InstabilityTerm ATerm BTerm CAverage of ugvg over entire eddyis zeroCircular systemsdo NOT intensifyfrom barotropicprocesses(but they can from) (baroc
24、linic processes)Advanced SynopticM. D. EastinBarotropic Production of Eddy Kinetic Energy:Term C: Asymmetric Eddy with Negative TiltContributions from Barotropic InstabilityTerm ATerm BTerm CAverage of ugvg over entire eddyis negative“Negatively tilted” systemsCAN intensifyfrom barotropicprocesses I
25、F located south of the u maximumAdvanced SynopticM. D. EastinBarotropic Production of Eddy Kinetic Energy:Contributions from Barotropic Instabilityt = 0t = 0t = 0t = +6 hrsAdvanced SynopticM. D. EastinObservational Evidence for Possible Cyclogenesis?Answer #1: When a jet core is upstream of a trough
26、 axis that is above and west of a weak surface low Upstream jet streaks have large positive vorticity on their poleward flank with PVA downstream near the trough axis and over the weak surface low PVA ascent Psfc decreases P increases EKE increases enhances WAA / CAA maintains any ongoing baroclinic
27、 instability processBaroclinic/Barotropic InstabilityExample of a Trough with an Upstream Jet StreakL+Advanced SynopticM. D. EastinObservational Evidence for Possible Cyclogenesis?Answer #2: When a diffluent trough is above and west of a weak surface low Diffluent upper-level troughs induce deep-lay
28、er ascent Ascent Psfc decreases P increases EKE increases enhances WAA / CAA maintains any ongoing baroclinic instability processBaroclinic/Barotropic InstabilityNote how the distancebetween the 6 heightcontours increasesdownstream of thetrough axis Example of a Diffluent TroughLAdvanced SynopticM.
29、D. EastinObservational Evidence for Possible Cyclogenesis?Answer #3: When a negatively-tilted trough is above and west of a weak surface low and south of the zonal mean jet core Negative tilts permit barotropic processes to generate a net increase in eddy kinetic energy EKE enhances WAA / CAA mainta
30、ins any ongoing baroclinic instability processBaroclinic/Barotropic InstabilityExample of a Negatively-tilted TroughLNote how the slopeof the trough axisis negative in theX-Y coordinatesystemXYAdvanced SynopticM. D. EastinObservational Analysis Tips: Not all negatively-tilted troughs intensify Not a
31、ll diffluent troughs intensify Not all troughs with upstream jet cores intensify Must evaluate the vertical tilt of the system Westward may intensify (21 optimal) Stacked should not intensify much Eastward should not intensify Must evaluate the latitude of the zonal mean jet core Negatively-tilted s
32、ystems south of the jet core may intensify Positively-tilted systems north of the jet core may intensify Negatively-tilted systems north of the jet core should not intensify Positively-tilted systems south of the jet core should not intensify Should evaluate all forcing terms in modified QG Omega eq
33、uation Should evaluate all forcing terms in modified QG Height Tendency equation Baroclinic/Barotropic InstabilityAdvanced SynopticM. D. EastinReferencesBluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of WeatherSystems. Oxford University Press,
34、 New York, 594 pp.Bretherton, F. P., 1966: Critical layer instability in baroclinic flows, Quart. J. Roy. Meteor. Soc., 92, 325-334.Charney, J. G., 1947: the dynamics of long waves in a baroclinic westerly current. J. Meteor., 6, 56-60.Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 33-5
35、2.Lackmann, G., 2019: Mid-latitude Synoptic Meteorology Dynamics, Analysis and Forecasting, AMS, 343 pp.Orlanski, I., 1968; Instability of frontal waves. J. Atmos. Sci., 25, 178-200.谢谢你的阅读v知识就是财富v丰富你的人生供娄浪颓蓝辣袄驹靴锯澜互慌仲写绎衰斡染圾明将呆则孰盆瘸砒腥悉漠堑脊髓灰质炎(讲课2019)脊髓灰质炎(讲课2019)供娄浪颓蓝辣袄驹靴锯澜互慌仲写绎衰斡染圾明将呆则孰盆瘸砒腥悉漠堑脊髓灰质炎(讲课2019)脊髓灰质炎(讲课2019)
