Rossby Waves and Quasi-Geostrophic Potential Vorticity: Linear Equation Solutions ( part 2a )
#waves #linearequations #vorticity
Explore the intricate dynamics of Rossby waves and quasi-geostrophic potential vorticity (QGPV) with a focus on linear equation solutions.
Quasi Geostrophic (QG) Theory shows Rossby Waves should form in the atmosphere. QG Theory in Atmospheric Dynamics says that advection occurs only by the geostrophic flow with a small ageostrophic perturbation. Assume a beta plane in this case where the geostrophic flow is nondivergent so a stream function can be defined. Given the vertical stratification, this affects potential vorticity, as we will see.
When air parcels move poleward, their planetary vorticity increases, so their relative vorticity tends to decrease. When air parcels move equatorward, their planetary vorticity decreases, so their relative vorticity tends to increase.
We examine the conservation of Quasi-Geostrophic Potential Vorticity (QGPV), which is what leads to persistent troughs on the leeward side of mountain ranges.
We examine air parcel displacement perturbations on a beta plane with the Navier Stokes Equations. The mechanisms for Rossby wave oscillation and propagation are discussed. The wave dispersion relationship for Rossby waves in stratified flow is shown.
This video helps you to answer "What is the jet stream, where is it located, and how does it affect weather?
Rossby waves are also known as planetary waves, which are a type of inertial wave naturally occurring on the rotating earth in the atmosphere and ocean. Carl Gustaf Rossby first identified them.
Atmospheric Rossby waves result from the conservation of potential vorticity and are influenced by the Coriolis force and pressure gradient. Earth rotation causes air to turn to the right as it moves in the northern hemisphere and to the left as it moves in the southern hemisphere. FoThese deviations are caused by the Coriolis force and conservation of potential vorticity which leads to changes of relative vorticity. This is analogous to conservation of angular momentum in physics.
The terms "barotropic" and "baroclinic" are used to distinguish the vertical structure of Rossby waves. Barotropic Rossby waves do not vary in the vertical, and have the fastest propagation speeds. The baroclinic wave modes, on the other hand, do vary in the vertical. They are also slower, with speeds of only a few centimeters per second or less.
Most investigations of Rossby waves have been done on those in Earth's atmosphere. Rossby waves in the Earth's atmosphere are easy to observe as (usually 4-6) large-scale meanders of the jet stream. When these deviations become very pronounced, masses of cold or warm air detach, and become low-strength cyclones and anticyclones, respectively, and are responsible for day-to-day weather patterns at mid-latitudes. This is often described as the polar vortex.
Part 0 of Rossby Wave Quasi-Geostrophic Potential Vorticity (QGPV) Calculation Video:
• Understanding Rossby Waves and QGPV in a S...
Part 1 of Rossby Wave Quasi-Geostrophic Potential Vorticity (QGPV) Calculation Video:
• Rossby Waves & Quasi-Geostrophic Potential...
Chapters (Timestamps)
0:00 Intro: Rossby Waves using QGPV Conservation
0:18 Invoke Quasi Geostrophic Potential Vorticity
1:28 Linearize for psi streamfunction
3:01 Insert base state & perturbations
4:15 Expand and multiply out terms
5:06 Use base state or products of primes for zero terms
7:57 Find local time tendency of QGPV perturbation
8:18 Understand meridional (y) true advection
9:57 Calculate for Beta and psi prime streamfunction
11:19 Use Quasi Geostrophic Potential Vorticity perturbation definition (q')
12:27 d/dt of q', insert into QGPV conservation equation
12:57 Sigle predictive equation for perturbation streamfunction
14:41 Preview of Rossby Waveform Solutions
14:58 Summary of Linearization Steps
16:03 Part of Series of Videos
16:20 Take Action!
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Related Keywords :
Rossby wave dynamics,
Quasi-geostrophic theory,
Potential vorticity equation,
Linear wave solutions,
Atmospheric wave motion,
Planetary wave theory,
Geostrophic approximation,
Large-scale atmospheric dynamics,
Rossby wave propagation,
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#RossbyWaves #QuasiGeostrophicTheory
#PotentialVorticity #AtmosphericDynamics
#WaveMotion #LinearEquations
#GeostrophicApproximation #BetaEffect
#DispersionRelations #ClimateScience
#Meteorology #Oceanography
#WeatherPatterns #PlanetaryWaves
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