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# Dynamics chapter 1

### Notes, Test, Homework

Order of Magnitude Reasoning quick approx answer to a problem.
Scale analysis how big are the terms in an equation? want to throw out the unimportant terms -estimating typical order of magnitude of terms in governing equations
Newtons 2nd Law F=Ma can use because earth's atmosphere has mass
contiuum mechanics object is a tiny infintesimal chunk of fluid(liquid or gas) or an elastic solid -dynamics os branch of this
What 2 forces act on blobs of air? body forces and surface forces
body force force on an object is proportinal to mass of object. Force due to action at a distance ex: gravity
surface force forces on an object is porportional to surface area of object. force due to contact of object with surroundings. force exerted on surface of fluid element by outside fluid ex: pressure force, friction
Pressure Gradient Force considering the net pressure forece acting on a blob of air force is proportional to gradient of p -acts in opposite direction of grad p
Gravitational Force applies to 2 forces w mass M and m.
Viscous force Friction force -force due to molecular friction
inertial reference frames non accelerating frames -stationary or moves at constant velocity F=Ma is with real forces(only true for intertial reference frames)
non-inertial reference frame speeds up or rotates -it accelerates -we use this one because fixed point on earth(earth rotates)
F=ma can be modified to use for non-inertial frame. Introduce what 2 apparent forces? apparent force=due to acceleration of the reference frame -centrifugal and Coriolis force
geopotential? work pum required to lift a mass from earth's surface to a height z
latitude rotation east and west for spherical coords
meridian rotation north and south for spherical coords
Exact way, almost exact way, quick-n-dirty way are used to find what? distances due to coriolis force. hockey puck
if atmosphere is at rest then... coriolis force=0 friction=0 acceleration=0 p isnt a function of x or y so have hydrostatic equation
density is bigger for ___ air colder
relation between definite integral and average average=have a dependent variable, independent variable and interval of independent variable.
independent variable time or space
dependent variable temp, pressure, u or v
hypsometric equation transform hydrostatic equation to treat z as dependent variable and p as independent variable
thickness is proportional to ___ in a layer temperature
when to use isobaric coords? when hydrostatic approx is available -uses pressure as the vertical coord(not z)
lagrangian describe how quantities change with time for an air parcel following the motion
dependent variables of lagrangian x(t), y(t), z(t)
independent variables of lagrangian t
Eularian describe how quantities change with time at a fixed point in space(not following blob)
independent variables of eularian x(t), y(t), z(t), t
degrees into radians multiply degree by 2 pi/360
typical radius for low pressure system 1000 km
typical horizontal length of tornado 100m-1000m
typical horizontal length of cumulonimbus 1 km-10 km
typical horizontal length of fronts (width) 10 km-100 km
typical horizontal length of H or L pressure systems 1000 km
starting point for dynamics is ___. translate this law into different equations to understand/predict air morion(weather) newtons 2nd law
F=ma means sum of forces acting on object=mass of object+acceleration of object
a=? Dv/Dt v= velocity
V=? Dr/Dt r=position vector
magnitude of grad p is big when there is close packing of isobars
newtons law of gravitation? Fg=(-GMm/r^2)(r vector/r) Fg= gravitational force on m due to M
r vector directed distance between 2 masses, points from big mass M to little mass m
rvector/r r hat (is of unit length)
Fg is ___ proportional to the square of the distance between 2 masses inversely
G universal gravitational constant 6.67*10^/-11 Nm^2/Kg^2
g* Fg/m gravitational force per unit mass
a 6370 km
in troposphere, z<__km so r=Z+_=_ 15, a,z
mass of earth M=4/3(pi)(a^3)(density of earth)
N kg*m/s^2
density of earth 5520 kg/m^3
no-slip condition molecular friction causes fluid to stick to solid objects/boundaries
steady state condition d( )/dt=0 stops changing in time
sheearing stress proportional to vertical derivative of x-comp velocity
newtons 3rd law fluid below box above it exerts equal and opposite force on bottom face
real forces gravitational, pgf, viscous force
earth rotates with angular velocity __ omega
if rotating, observers in that reference frame are ___ to be subject to a ___ force perceived, centrifugal
gravity force pum gravitational force pum + centrifugal force pum
centrifugal force= m*omega^2*R(vector)
u absolute= omega*R
magnitude of omega= 7.27*10^-5 1/s
coriolis force= m(-2omegaxu)
components of coriolis force Fx=m(2omegavsin(latitude)-2omegawcos(latitude)) Fy=m(-2omegausin(latitude)) Fz=m(2omegaucos(latitude))
if puck stays on flat ice z(t)=constant so w(t)=0
horizontal equations of motion(with w=0) du/dt=2omegavsin(latitude) dv/dt=-2omegausin(latitude)
f 2omegasin(latitude)
hydrostatic equation is an ___ equation for ___ atmosphere exact, resting
hydrostatic is a good approx for real moving atmosphere except when vertical accelerations are large (supercell, tornado)
integrating hydrostatic shows at any point in the resting atmosphere, pressure=weight(per unit area) of all air above it
p(H) (e^-1)Po
___ on constant z-surface carry same info as height contours on ____ isobars, isobaric surface
local derivative of T used for eularian
geosynchronous orbit hover over the same location on earth -angular velocity of object and eaerth are the same
absolute as observed in an inertial reference frame
Created by: leebee05