Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model
description
Transcript of Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model
![Page 1: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/1.jpg)
Condensation-Induced Winds
a supplemental theorem to the traditional thermal wind model
Deborah E. Ross University of Montana
Department of Physics and Astronomy
![Page 2: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/2.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 3: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/3.jpg)
Weather vs Climate
![Page 4: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/4.jpg)
Basic Meteorological Assumptions: Hydrostatic Equilibrium
Ideal Gas Law
Adiabatic Expansion
![Page 5: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/5.jpg)
Hydrostatic Equilibrium
![Page 6: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/6.jpg)
Ideal Gas Law
![Page 7: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/7.jpg)
Adiabatic Expansion
Increase in volume without heat flow in or out of the volume
(mb)
apollo.lsc.vsc.edu
Height
Distance (m)
![Page 8: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/8.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 9: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/9.jpg)
Traditional Wind Model
Solar Heating Causes Winds.
Wind is caused by differences in pressure resulting from differential heating of the earth’s surface.
![Page 10: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/10.jpg)
Pressure and Temperature
http://www.physicalgeography.net/fundamentals/7o.html
![Page 11: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/11.jpg)
Geostrophic Wind
ww2010.atmos.uiuc.edu
![Page 12: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/12.jpg)
Thermal Wind Equation
vg – Geostrophic windvT – Thermal windf – Coriolis parameterR – Ideal gas law constant
![Page 13: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/13.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 14: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/14.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 15: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/15.jpg)
Equations of State for Moist AirMoist air as a whole
Water Vapor
Dry Air
P - pressureN – molar densityR – molar gas constantT – absolute temperature
![Page 16: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/16.jpg)
Relative Molar Density of Water Vapor The process of condensation in the rising air should be reflected through the changes in:
![Page 17: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/17.jpg)
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
![Page 18: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/18.jpg)
Coordinate System
w0,u0 is considered to be the isothermal plane whereasw,u is the horizontal plane.
![Page 19: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/19.jpg)
Stationary Continuity Equation
(2)
If we consider:
(3)
And the conservation of mass for dry air:
(4)
![Page 20: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/20.jpg)
We can conclude that:
If we assume an isothermal plane, molar density does not change.
(5)
(6)
![Page 21: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/21.jpg)
We can combine (1) and (5) with a substitution from (6) to obtain:
(7)
(1)
(5)
(6)
![Page 22: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/22.jpg)
Compact Form:
(9)
Using the definition for :
(8)
![Page 23: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/23.jpg)
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:
![Page 24: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/24.jpg)
Adiabatic Ascent
Parcel will not rise in a vertically isothermal atmosphere
![Page 25: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/25.jpg)
Adiabatic ascent with a temperature gradient applied in the vertical direction.
![Page 26: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/26.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 27: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/27.jpg)
Cylindrical Transformation:Using change of coordinates:
![Page 28: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/28.jpg)
Cylindrical Coordinates
u(r) - radial velocityw(r) – vertical velocityv(r) – tangential velocity
![Page 29: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/29.jpg)
U - The velocity of hurricane movement as a whole also known as translation speed.
![Page 30: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/30.jpg)
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
![Page 31: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/31.jpg)
Theoretical Pressure profile vs Holland’s profile
Theoretical values for pressure vs Holland’s profile values (empirical).
![Page 32: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/32.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 33: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/33.jpg)
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
![Page 34: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/34.jpg)
Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds
DerivationExperimental Evidence
Greater Implications Future Research
![Page 35: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/35.jpg)
Add a condensation component from the biotic pump theory to a climate model.
Future Research
![Page 36: Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model](https://reader036.fdocuments.in/reader036/viewer/2022070423/5681674a550346895ddbf97e/html5/thumbnails/36.jpg)
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