Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model

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Condensation-Induced Winds a supplemental theorem to the traditional thermal wind model Deborah E. Ross University of Montana Department of Physics and Astronomy

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Deborah E. Ross University of Montana Department of Physics and Astronomy. Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model. Overview. Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds Derivation - PowerPoint PPT Presentation

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

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

Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds

DerivationExperimental Evidence

Greater Implications Future Research

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Weather vs Climate

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Basic Meteorological Assumptions: Hydrostatic Equilibrium

Ideal Gas Law

Adiabatic Expansion

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Hydrostatic Equilibrium

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Ideal Gas Law

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Adiabatic Expansion

Increase in volume without heat flow in or out of the volume

(mb)

apollo.lsc.vsc.edu

Height

Distance (m)

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Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds

DerivationExperimental Evidence

Greater Implications Future Research

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Traditional Wind Model

Solar Heating Causes Winds.

Wind is caused by differences in pressure resulting from differential heating of the earth’s surface.

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Pressure and Temperature

http://www.physicalgeography.net/fundamentals/7o.html

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Geostrophic Wind

ww2010.atmos.uiuc.edu

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Thermal Wind Equation

vg – Geostrophic windvT – Thermal windf – Coriolis parameterR – Ideal gas law constant

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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

Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds

DerivationExperimental Evidence

Greater Implications Future Research

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Equations of State for Moist AirMoist air as a whole

Water Vapor

Dry Air

P - pressureN – molar densityR – molar gas constantT – absolute temperature

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Relative Molar Density of Water Vapor The process of condensation in the rising air should be reflected through the changes in:

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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

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Coordinate System

w0,u0 is considered to be the isothermal plane whereasw,u is the horizontal plane.

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Stationary Continuity Equation

(2)

If we consider:

(3)

And the conservation of mass for dry air:

(4)

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We can conclude that:

If we assume an isothermal plane, molar density does not change.

(5)

(6)

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We can combine (1) and (5) with a substitution from (6) to obtain:

(7)

(1)

(5)

(6)

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Compact Form:

(9)

Using the definition for :

(8)

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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:

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Adiabatic Ascent

Parcel will not rise in a vertically isothermal atmosphere

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Adiabatic ascent with a temperature gradient applied in the vertical direction.

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Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds

DerivationExperimental Evidence

Greater Implications Future Research

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Cylindrical Transformation:Using change of coordinates:

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Cylindrical Coordinates

u(r) - radial velocityw(r) – vertical velocityv(r) – tangential velocity

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U - The velocity of hurricane movement as a whole also known as translation speed.

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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

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Theoretical Pressure profile vs Holland’s profile

Theoretical values for pressure vs Holland’s profile values (empirical).

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Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds

DerivationExperimental Evidence

Greater Implications Future Research

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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

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Overview Basic Meteorological Assumptions Traditional Wind Model Condensation Induced Winds

DerivationExperimental Evidence

Greater Implications Future Research

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Add a condensation component from the biotic pump theory to a climate model.

Future Research

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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