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 - pressure

N – molar density

R – molar gas constant

T – 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