Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model
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Transcript of Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model
Condensation-Induced Winds
a supplemental theorem to the traditional thermal wind model
Deborah E. Ross University of Montana
Department of Physics and Astronomy
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Weather vs Climate
Basic Meteorological Assumptions: Hydrostatic Equilibrium
Ideal Gas Law
Adiabatic Expansion
Hydrostatic Equilibrium
Ideal Gas Law
Adiabatic Expansion
Increase in volume without heat flow in or out of the volume
(mb)
apollo.lsc.vsc.edu
Height
Distance (m)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Traditional Wind Model
Solar Heating Causes Winds.
Wind is caused by differences in pressure resulting from differential heating of the earth’s surface.
Pressure and Temperature
http://www.physicalgeography.net/fundamentals/7o.html
Geostrophic Wind
ww2010.atmos.uiuc.edu
Thermal Wind Equation
vg – Geostrophic windvT – Thermal windf – Coriolis parameterR – Ideal gas law constant
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Equations of State for Moist AirMoist air as a whole
Water Vapor
Dry Air
P - pressureN – molar densityR – molar gas constantT – absolute temperature
Relative Molar Density of Water Vapor The process of condensation in the rising air should be reflected through the changes in:
Molar rate of condensation per unit volume:
(1)
- velocity vector directed along the temperature gradient toward the lower temperature - vertical velocity - horizontal velocity
vertical condensation
rate
Gravitational expansion
Horizontal expansion
Coordinate System
w0,u0 is considered to be the isothermal plane whereasw,u is the horizontal plane.
Stationary Continuity Equation
(2)
If we consider:
(3)
And the conservation of mass for dry air:
(4)
We can conclude that:
If we assume an isothermal plane, molar density does not change.
(5)
(6)
We can combine (1) and (5) with a substitution from (6) to obtain:
(7)
(1)
(5)
(6)
Compact Form:
(9)
Using the definition for :
(8)
Hydrostatic Equilibrium
Adiabatic ascent of moist saturated air
The only phase transition will be condensation in the vertical direction.
Looking strictly at isothermal horizontal plane:
Adiabatic Ascent
Parcel will not rise in a vertically isothermal atmosphere
Adiabatic ascent with a temperature gradient applied in the vertical direction.
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Cylindrical Transformation:Using change of coordinates:
Cylindrical Coordinates
u(r) - radial velocityw(r) – vertical velocityv(r) – tangential velocity
U - The velocity of hurricane movement as a whole also known as translation speed.
Theoretical radial and tangential velocity vs category 5 data set
o – Data at different levels from twelve observed category 5 hurricanes. - Median values of data sets.
Data Analysis from Makarieva and Gorshkov
Theoretical Pressure profile vs Holland’s profile
Theoretical values for pressure vs Holland’s profile values (empirical).
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Forestry and Precipitation “The biotic pump is a mechanism in
which natural forests create and control ocean-to-land winds, bringing moisture to all terrestrial life.”
- -Gorshkov and Makarieva 2012
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
Add a condensation component from the biotic pump theory to a climate model.
Future Research
Acknowledgements Jennifer Fowler – Mentor and all around
awesome lady. Makarieva and Gorshkov – Theory
Authors. Alex Bulmahn MSGC (Montana Space Grant
Consortium) University of Montana Physics and
Astronomy Department