##### Dynamics Test Study Guide
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#### Complete list of Terms and Definitions for Dynamics Test Study Guide

Terms Definitions
What is (ζ+f)(∂u/∂x+∂v/∂y)? Stretching term
When is vorticity positive? Cyclonic motions
When is vorticity negative? Anticyclonic motions
What is ∂ζ/∂t Local vorticity tendency
What is c? The phase speed
What does rising motion lead to? Cooling
What is the strongest curvature called? Vorticity
Where is vorticity minimum? In a ridge
What is ∂w/∂x ∂v/∂z-∂w/∂y ∂u/∂z? Tilting term
How many forces in the geopotential tendency and omega equations have physical processes that produce rising motions or height changes? 4
What chart shows the trough/ridge pattern? 500 mb
What is βv? Advection of planetary (earth's) vorticity
What is w ∂ζ/∂z? Vertical advection of vorticity
What order of magnitude is f? 10^-4 s^-1
What is the formula for relative vorticity? ζ=∂v/∂x-∂u/∂y
What is u ∂ζ/∂x+v ∂ζ/∂y? Horizontal advection of vorticity
What is the relationship between wave number and wavelength? k= 2π/L_x
What is 1/ρ^2 (∂ρ/∂x ∂p/∂y-∂ρ/∂y ∂p/∂x)? Solenoidal or baroclinic term
What is vorticity? Circulation per unit area, 2V/R=2ω, or 2Ωsinϕ
What processes lead to vertical motion on the synoptic scale? The omega equation
What quantity is held constant for the ridge/trough pattern to be true? Absolute vorticity
What is Rossby's dispersion relationship? Different wavelengths travel at different speeds. c=u ̅-(βL_x^2)/〖4π〗^2
What is the earth's vorticity? 2Ωsinϕ=f (the coriolis parameter). Varies from zero at the equator to 2Ω at the north pole. f is 10^-4 s^-1
What is the area if the body is circular? πR^2
What is the net radiative heating rate? -1.5 °C per day
What does the tilting term do? Helps explains how thunderstorms develop.
What causes the heights to change over time? The geopotential tendency equation
Relative to the storm, where are the winds? From south to north
What terms have a synoptic scale motion equal to 10^-11? Vertical advection of vorticity, tilting term, and baroclinic term.
What four equations make up the Quasi- Geostrophic Theory? Hydrostatic equation, mass continuity equation (incompressible form), vorticity equation, and thermodynamic energy equation (first law)
How is vorticity defined? A property of a fluid and is defined at every point in the fluid much the same as temperature and density for example.
What is a barotropic atmosphere? An atmosphere where there is no change in geostrophic wind with height. The temperature is constant on a constant pressure surface.
What is the e-folding time? The time taken for the vorticity to increase by a factor of e (or 2.7).
Why are Rossby waves dispersive waves? Because of the β effect. If β=0, then the earth is flat. If β is non zero, the earth is a sphere and makes the waves dispersive instead of going at the same phase speed.
Where is divergence located in the upper troposphere? The flow between the trough and downstream ridge.
What are the four assumptions made for the Quasi-Geostrophic Theory? 1. Vertical advection is small when compared to the horizontal advection. 2. f >> ζ in the stretching term 3. Advection by geostrophic wind 4. Stretching term f=fo, but not in advection term 5. The vorticity is geostrophic
Where is convergence located in the upper troposphere? The flow between the trough and the upstream ridge.
What two equations do we use to solve for ω and χ simultaneously? The first law of thermodynamics and the vorticity equation