<commit_before>\section{Physics of Dust-Devils}
\label{sec:physics}
\begin{itemize}
\item phenomenological description
\item regions/frequency of occurance
\item review of sinclair, kanak and renno and other pertinent literature
\item known physics of dust devils and other cyclonic structures
\item dust-devil/tornado/hurricane genesis
\item scaling discussion as estimate of energy
\item Dust-Devil Generation Concept
\item Motivation of computational modeling
\item draw regions
\item eyewall
\end{itemize}

In order to motivate how best to \textit{engineer} a synthetic
dust-devil, we first address what is known about the naturally occuring
phenomena. We therefore begin this section with a qualitative discussion
of dust-devils, followed by a review of the known physics and pertinent 
literature review. 


\subsection{Phenomenological Character of Dust-Devils}
\begin{itemize}
 \item chart from sinclair of frequency (they are driven by delta t)
 \item turning direction independent
 \item characteristic velocities and sizes
 \item genesis diagram (thermal plume) -- mention ambient angular vorticity
 \item structure diagram and description
\end{itemize}


%
% good place to ref jacobson2005fundamentals
%

\subsection{Estimate of Energy Scaling}

In this subsection, we attempt to provide a rough estimate of the energy
available to a Dust-Devil. There are two objectives behind this
analysis. The first is to provide justification for the concept of
extracting energy from these phenomena, with the reasoning that should
sufficient energy be available, then attemping to extract it might be
worthwhile. The second objective is to provide a simple analysis that
can serve as a measure of the efficiency of the generation process,
e.g. ``What fraction of the available energy are we extracting?''.  

At present, we consider only the energy flowing into the entrainment
region due to the ambient conditions, in particular, the incoming wind
and heat through the front hemisphere of a cylindrical region. We
consider a medium-sized (3m radius) dust-devil with an incoming
freestream velocity of 5 m/s. The surface temperature is 343 Kelvin,
with a specified inflow boundary layer bridging the ground temperature
to the ambient air conditions of 313 Kelvin. 
% cite this?
These numbers were chosen
based on information provided by the Georgia Tech field team in Arizona
during the summer of 2014.  

There are two forms of energy to consider: kinetic and enthalpy. We
begin by considering the kinetic energy flux through the front of the
apparatus. From the first law of thermodynamics we can express the
kinetic energy flux as a surface integral over the upstream face of the device, 
\begin{equation*}
\text{KE} = \int_{CS} \frac{\vec V^2}{2} \rho \vec V \cdot \hat n dA.
\end{equation*}
%
% could cite fluid dynamics book here
% pg. 239
%
We assume our freestream velocity has no components in y and z.
We assume that the variation in z for the streamwise velocity is only on
account of the thin boundary layer near the ground. We functionally
approximate this behavior using the common 7th power function for a
turbulent boundary layer,  
\begin{equation*}
  u(z) = U \text{ min }\left(\left(\frac{z}{\delta}\right)^7,1\right)
\end{equation*}
where U is the constant freestream velocity and $\delta$ the assumed
boundary layer thickness. Our integral can be solved to show, 
\begin{align*}
\text{KE} & = -R \rho U^3 \left[ z_{\text{max}} - \frac{10}{11}\delta.
\right]
\end{align*}

%%  & = \frac{1}{2} R \rho u^3 z_\text{max}
%%  \int^{\frac{3\pi}{2}}_{\frac{\pi}{2}} \text{cos}\theta d\theta \\
%%  & = -R \rho u^3 z_\text{max}. 
%% \end{align*}

The negative sign here indicates that the kinetic energy is flowing into
the surface, in opposition to the outward facing unit normal, $\hat
n$. Characteristic values for this analysis are, $u = 5$ m/s, $\rho =
1.225$ Kg/$m^3$, $R = 3$ m, and $z_{\text{max}} = 2.5$ m. The boundary
layer thickness is $\approx 10$ cm. This provides
an estimate of 1144.26 Watts as the incoming kinetic energy flux. Or,
approximately 1.14 kW.  

Now we estimate the gravitational potential energy flux by integrating 
the boussinesq term by the height of the vanes, 
\begin{align*}
  \text{Potential Energy Flux} & = \int_{-h}^0 u(z) \Delta \rho g z dz. \\
  & = \int_{-h}^0 u(z) \rho' g z^2 dz. 
\end{align*}
Where the substitution, $\Delta \rho = \rho' z$ was made. At 
this point we again separate the integral into two components, 
for the boundary layer and the constant freestream velocity region. 
\begin{align*}
  & = \rho' g \left[ \int_{-\delta}^{0} U \left( \frac{z}{\delta} \right)^7 z^2 dz 
      + \int_{-h}^{-\delta} U z^2 dz \right] \\
  & = -\rho' g U \left[ \frac{h^3}{3} - \frac{7}{30} \delta^3 \right].
\end{align*}
Furthermore, we
note that $\rho' = -\beta \rho_0 \Delta T$, resulting in, 
%
% cite monin-yaglom page 59
%
\begin{equation}
 \text{Power } = U \beta \rho_0 \Delta T g \left[ \frac{h^3}{3} -
					    \frac{7}{30} \delta^3
					   \right]. 
\end{equation}

Using $\rho_0 = 1.225$ Kg/$m^3$, $T_{\text{ref}}=313$m Kelvin, $\beta_T = 0.003194$
(This is just 1/$T_{\text{ref}}$), $g=9.81$ m/$s^2$, and a freesteam
velocity of five meters per second results in an
estimate of 30 Watts for the gravitational potential energy. 

This interesting result implies that the majority of the available
energy is attributable to kinetic energy, not the gravitational
energy. This is consistent with the results of Renno, who demonstrated
that the thermal energy present was not sufficient to account 
thermodynamic energy 
%
% finish me!
%
While the gravitational potential energy is a small fraction of the
energy available, that does not imply it is without significant impact. 
<commit_msg>adding more intro text<commit_after>\section{Physics of Dust-Devils}
\label{sec:physics}
\begin{itemize}
\item phenomenological description
\item regions/frequency of occurance
\item review of sinclair, kanak and renno and other pertinent literature
\item known physics of dust devils and other cyclonic structures
\item \st{dust-devil/tornado/hurricane genesis}
\item scaling discussion as estimate of energy
\item Dust-Devil Generation Concept
\item Motivation of computational modeling
\item draw regions
\item eyewall
\end{itemize}

In order to motivate how best to \textit{engineer} a synthetic
dust-devil, we first address what is known about the naturally occuring
phenomena. We therefore begin this section with a qualitative discussion
of dust-devils, followed by a review of the known physics and pertinent 
literature review. We then briefly outline how we intend to leverage
these physical processess as a method of usable energy generation. 


\subsection{Phenomenological Character of Dust-Devils}
\begin{itemize}
 \item chart from sinclair of frequency (they are driven by delta t)
 \item turning direction independent
 \item characteristic velocities and sizes
 %\item genesis diagram (thermal plume) -- mention ambient angular vorticity
 \item structure diagram and description
\end{itemize}

No rigorous defintion of a Dust devil exists. This cannot be attributed
to the rarity of the processes. Rather, the phenomena of dust devils are
remarkably ubiquitous. These whirlwinds have been
observed across a wide variety of terrains, climates and even on several
other planets. While it is difficult to pin down a precise definition,
several features are characteristic of a dust devil. They are regions of
intense vorticity and rotation, coupled with strong upward motions. They
have a 

It is an almost self-sustaining vortex that maintains a funnel-like
chimney driven by hot air moving both upward and circularly. 


They typically exist for only a few minutes, but some have been observed
to exist for significantly longer, 

%
% solen from: http://glossary.ametsoc.org/wiki/Fujita_scale
%
Dust devils occasionally are strong enough to cause damage and injury,
with some reaching F1 on the Fujita Tornado intensity scale. 
%
% F1 (moderate damage): 33–49 m s-1
%
% ``F1 - Surface of roofs peeled off; mobile homes pushed off foundations
% or overturned; moving autos pushed off road. ``
Diameters range from about one meter to greater than thirty.  Their
average height is about thirty meters, but a few have been observed 
as high as 1 km or more. There appears to be no preferred direction, and
they are observed to rotate anticyclonically as well as
cyclonically. Although the vertical velocity 
is predominantly upward, the flow along the axis of large dust devils
may be downward. Large dust devils may also contain secondary vortices. 

%
% cite martian dust devils
%
 
Moreover, actual dust devils have been photographed from orbit, with
some of them as large as 1 to 2 kilometers across at their base and 10
km tall. 

Similarly visibly structured phenomena have been spotted over water, in
intense forest fires, 

%
% good place to ref jacobson2005fundamentals
%
This is to say nothing of other similar cyclonic phenomena, such as
tornados and hurricanes. 


Perhaps the most complete survey of the phenomena came from a series of
papers by Sinclair

\subsection{Estimate of Energy Scaling}

In this subsection, we attempt to provide a rough estimate of the energy
available to a Dust devil. There are two objectives behind this
analysis. The first is to provide justification for the concept of
extracting energy from these phenomena, with the reasoning that should
sufficient energy be available, then attemping to extract it might be
worthwhile. The second objective is to provide a simple analysis that
can serve as a measure of the efficiency of the generation process,
e.g. ``What fraction of the available energy are we extracting?''.  

At present, we consider only the energy flowing into the entrainment
region due to the ambient conditions, in particular, the incoming wind
and heat through the front hemisphere of a cylindrical region. We
consider a medium-sized (3m radius) dust devil with an incoming
freestream velocity of 5 m/s. The surface temperature is 343 Kelvin,
with a specified inflow boundary layer bridging the ground temperature
to the ambient air conditions of 313 Kelvin. 
% cite this?
These numbers were chosen
based on information provided by the Georgia Tech field team in Arizona
during the summer of 2014.  

There are two forms of energy to consider: kinetic and enthalpy. We
begin by considering the kinetic energy flux through the front of the
apparatus. From the first law of thermodynamics we can express the
kinetic energy flux as a surface integral over the upstream face of the device, 
\begin{equation*}
\text{KE} = \int_{CS} \frac{\vec V^2}{2} \rho \vec V \cdot \hat n dA.
\end{equation*}
%
% could cite fluid dynamics book here
% pg. 239
%
We assume our freestream velocity has no components in y and z.
We assume that the variation in z for the streamwise velocity is only on
account of the thin boundary layer near the ground. We functionally
approximate this behavior using the common 7th power function for a
turbulent boundary layer,  
\begin{equation*}
  u(z) = U \text{ min }\left(\left(\frac{z}{\delta}\right)^7,1\right)
\end{equation*}
where U is the constant freestream velocity and $\delta$ the assumed
boundary layer thickness. Our integral can be solved to show, 
\begin{align*}
\text{KE} & = -R \rho U^3 \left[ z_{\text{max}} - \frac{10}{11}\delta.
\right]
\end{align*}

%%  & = \frac{1}{2} R \rho u^3 z_\text{max}
%%  \int^{\frac{3\pi}{2}}_{\frac{\pi}{2}} \text{cos}\theta d\theta \\
%%  & = -R \rho u^3 z_\text{max}. 
%% \end{align*}

The negative sign here indicates that the kinetic energy is flowing into
the surface, in opposition to the outward facing unit normal, $\hat
n$. Characteristic values for this analysis are, $u = 5$ m/s, $\rho =
1.225$ Kg/$m^3$, $R = 3$ m, and $z_{\text{max}} = 2.5$ m. The boundary
layer thickness is $\approx 10$ cm. This provides
an estimate of 1144.26 Watts as the incoming kinetic energy flux. Or,
approximately 1.14 kW.  

We estimate the gravitational potential
energy flux by integrating the boussinesq term by the height of the vanes, 
\begin{align*}
  \text{Potential Energy Flux} & = \int_{-h}^0 u(z) \Delta \rho g z dz. \\
  & = \int_{-h}^0 u(z) \rho' g z^2 dz. 
\end{align*}
Where the substitution, $\Delta \rho = \rho' z$ was made. At 
this point we again separate the integral into two components, 
for the boundary layer and the constant freestream velocity region. 
\begin{align*}
  & = \rho' g \left[ \int_{-\delta}^{0} U \left( \frac{z}{\delta} \right)^7 z^2 dz 
      + \int_{-h}^{-\delta} U z^2 dz \right] \\
  & = -\rho' g U \left[ \frac{h^3}{3} - \frac{7}{30} \delta^3 \right].
\end{align*}
Furthermore, we
note that $\rho' = -\beta \rho_0 \Delta T$, resulting in, 
%
% cite monin-yaglom page 59
%
\begin{equation}
 \text{Power } = U \beta \rho_0 \Delta T g \left[ \frac{h^3}{3} -
					    \frac{7}{30} \delta^3
					   \right]. 
\end{equation}

Using $\rho_0 = 1.225$ Kg/$m^3$, $T_{\text{ref}}=313$m Kelvin, $\beta_T = 0.003194$
(This is just 1/$T_{\text{ref}}$), $g=9.81$ m/$s^2$, and a freesteam
velocity of five meters per second results in an
estimate of 30 Watts for the gravitational potential energy. 

This interesting result implies that the majority of the available
energy is attributable to kinetic energy, not the gravitational
energy. This is consistent with the results of Renno, who demonstrated
that the thermal energy present was not sufficient to account 
thermodynamic energy 
%
% TODO: finish me!
%
While the gravitational potential energy is a small fraction of the
energy available, that does not imply it is without significant impact. 

\subsection{Dust-Devil Generation Concept}

The preceeding discussion has provided justification for the idea of
using Dust-Devils as a method of extracting ambient kinetic and
gravitational potential energy 


Dust-Devils are a naturally occuring phenomena, which speaks to 

, possess
significant kinetic energy 

need an image of the two tiers

curved turning vanes?

turbine

cone

ALSO: Motivation of computational modeling


{'fraction_non_alphanumeric': 0.08144732174529976, 'fraction_numerical': 0.015395530329904221, 'mean_word_length': 4.142648668369208, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 3, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '6180567', 'n_tokens_mistral': 4273, 'n_tokens_neox': 3916, 'n_words': 1991}