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\begin{document}

\title{Submarine Lava Morphology: A Review}



\author[1]{Eunseo Choi}%
\author[1]{Hao Lu}%
\affil[1]{University of Memphis}%


\vspace{-1em}



  
  \date{May 14, 2024}


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\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/pillow121/pillow121}
\caption{{Pillow lava \protect\hyperlink{gregg2000laboratory}{}\protect\citep*{gregg2000laboratory}
{\label{739997}}%
}}
\end{center}
\end{figure}



Pillow lavas have relatively slow travel speeds compared to cooling
speed. While fresh magma erupts out from a~vent, it moves rather slowly
and the~solidifying process on the outer layer is rapid. At the same
time, fresh hot lava inside the solidified shell continues to move and
crack the pillow and flow out to form a new pillow.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/pillow-lava-with-hammar3/pillow-lava-with-hammar3}
\caption{{Pillow lava ()
{\label{536396}}%
}}
\end{center}
\end{figure}

\textbf{It's important to notice what sheet flows have in common and
what separates them as a group from pillow lava.}The difference between
these sub-classes sheet flows is quite obvious. However~Sheet flows,
regardless their surface textures, are formed by relatively fast lava
flow and was able to travel further while cooling down and solidified.
This permits a generally sheet-like morphology. Sheet flows are the only
morphology that can form onshore and very commonly observed offshore as
well. They are the dominant form in most regions.

\par\null

\section*{Global Distribution of Lava Flows}

\textbf{Lava flow morphologies show a good correlation with spreading
rates.} From the data set collected from different regions,
\citet*{bonatti1988eruption}~created a plot showing the areal ratio of sheet flow
to pillow lava vs. spreading rate on axial zones of spreading ridges.
The plot shows a clear pattern of global distribution of sheet flow and
pillow lava: pillow lavas are much commonly seen at slow spreading
regions, and sheet lavas are predominate in fast spreading regions (Fig.
~{\ref{553712}}).

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Morphology-Ratio-vs-Spreading-Rate1/Morphology-Ratio-vs-Spreading-Rate1}
\caption{{Morphology ratio vs. spreading rate \protect\citep*{bonatti1988eruption}
{\label{553712}}%
}}
\end{center}
\end{figure}

\section*{}

\section*{Rheological Models For Lava
Flow}

{\label{589648}}

\textbf{Lava flow shows viscoplastic behaviors.} There is no
mathematical expression that can fully describe the behavior of lava
flows (REFS). Lava rheologies~are complex in thermodynamics and rheology
and therefore in mechanics (REFS). Its visco-plastic behavior is hard~to
describe mathematically and is different from case to case. Some
well-controlled laboratory experiments provide the most elementary
characteristics of the lava flow \citep{griffiths1992solidification,gregg2000laboratory}. However, the
results can only serve as the basic foundation for understanding more
complex models~\protect\hyperlink{griffiths2000dynamics}{(Griffiths
2000)}. Lava flows obey visco-plastic material behavior. A certain
threshold yield strength must be overcome before flow will move. A good
example to illustrate the visco-plastic material versus Newtonian Fluid
is as followed (Fig. ~{\ref{687278}}). From Fig.7, we
can see Newtonian Liquid can flow with any shear stress applied; Bingham
Fluid on the other hand, requires shear stress greater than yield stress
for flow to occur. A good example for Bingham fluid is toothpaste.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.56\columnwidth]{figures/Bingham1/Bingham1}
\caption{{Newtonian vs Bingham Fluid
\protect\hyperlink{wiki__colon__Bingham}{}\protect\cite{wiki:Bingham}
{\label{687278}}%
}}
\end{center}
\end{figure}

\par\null

\textbf{Yield strength and viscosity of lava increases as lava
crystallizes.}~The crystal fraction dependence of lava viscosity is the
reason why different flow rates can lead to significant changes in
morphology. What's more, as \citet*{hulme1974interpretation} proposed:

\(\begin{equation} \text{Thickness}(t) = \text{Yield Strength} / ( \rho g \tan a) \end{equation}\)

where \(a\) is the angle of flowing ~surface . It indicates
that with all else being equal, lava with high yield strength will
produce thicker flows; and lava will be thinner when flowing on steep
slopes \citep*{hulme1974interpretation}. Also, due to the temperature difference
between erupted lava and overlying ocean water, lava will lose its heat
energy once contact with water is made. Cooling induces very large
changes in rheology that eventually affects the flow regime.

\par\null

Lava cooling mechanisms depend on whether the flow is laminar or
turbulent and on the rate of cooling and rheological change compared
with the rate of spreading of the flow \citep*{griffiths2000dynamics}. Although
combining a set of thermal parameters such as P\selectlanguage{ngerman}éclet numbers (Pe),
global Nusselt number (Nu) and \(\Theta_{s}\) are sufficient to
describe a cooling process with small Reynolds number and given rheology
\protect\hyperlink{griffiths2000dynamics}{(Griffiths 2000)}, \textbf{a
dimensionless parameter} \(\Psi\) \textbf{} \citep*{griffiths1992solidification}
\textbf{was introduced to provide a more direct relationship between
time taken for material to solidify and time scale for horizontal
advection.} In the thin boundary layer regime, surface solidification
starts at distance \(d_{s} \approx u \, t_{s}\) from the origin vent, where
\(u\) is the surface velocity and \(t_{s}\) is the
time required for surface temperature \(T_{c}\) to cool down
from the vent temperature \(T_{e}\) to solidification
temperature \(T_{s}\). Scaling distance by \(H\)
and velocity by a suitable scale \(U\), the dimensionless
parameter is defined as:

\(\begin{equation} \Psi=\frac{U\,t_{s}}{H}=\frac{t_{S}}{t_{A}} \end{equation}\)The value ~\(t_{S}\) depends on
\(\Theta_{s}\) and the surface heat flux and should be obtained form
a heat transfer calculation, and it's on the order of 0.1 for submarine
lavas \citep*{griffiths1992solidification}. Basically, \(\Psi\) is the ratio of
time required for surface temperature to cool form the vent temperature
to solidification temperature and time required for flow through a
certain distance. As \(\Psi\) incorporates key physical
properties of both an extrusion and its environment, it includes effects
of thermo-physical properties (viscosity, heat capacity, thermal
diffusivity, density) \citep*{gregg1995quantification}. It can be seen as a global
perspective of description of the flow.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Correlation-Between-Laboratory-Derived-Ps-Values-and-Laboratory-and-Submarine-Flow-Morphologies1/Correlation-Between-Laboratory-Derived-Ps-Values-and-Laboratory-and-Submarine-Flow-Morphologies1}
\caption{{Correlation between laboratory-derived values and laboratory and
submarine flow morphologies \protect\citep*{gregg1995quantification}
{\label{148221}}%
}}
\end{center}
\end{figure}

\par\null

Figure {\ref{148221}} shows the relationship between
lava morphology and dimensionless parameter \(\Psi\) on a
gentle slope 6\selectlanguage{ngerman}° flowing slope. We can conclude that (nearly) without the
effect of slope, pillow lava form when \(\Psi\)\textless{}3,
and sheet flow form when it's greater than 3.

\section*{}

\section*{Effective Parameters}

{\label{614623}}

\textbf{How lava finally reaches its final shape~is governed by two
factors: the flow rate that decides how fast the lava is able to flow
and the solidify rate indicates how fast the lava is able to keep its
shape still and bring flow to a halt.} These two aspects affect the lava
morphology in an opposite way. With high flow rate and low solidify
rate, lava flow tends to form a sheet-like smooth texture shape; while
with low flow rate and high solidify rate, pillow-shaped lava is easy to
form. Note this relationship is general and on a relative mindset. And
it should all comes down to the parameters that contribute to each side.
To be more specific, the factors that affect lava morphology~can be
separated into following three aspects, which are characteristics of the
magma material, characteristics of volcano/eruption and characteristics
of the surrounding area.

\subsection*{}

\subsection*{Characteristics of The
Magma}

{\label{424467}}

\textbf{Characteristics of the magma include composition, viscosity, and
crystal content.} As for composition, 90 \% of lava are basaltic, with 8
\% andesitic and 2 \% dacite/rhyolite flow \citep*{blong2013volcanic}. From the
Figure. 9 above, we can observe there is a rapid increase in viscosity
of basaltic magma when crystals form (below 1200°C) and/or gas bubbles
ex-solve. In the submarine environment, crystallization at outer layer
of lava begins almost instantly when lava contact with sea water. With
increases in crystal content, a higher stress for yielding is required
for further movement. Basaltic lavas have a viscosity about 50
Pa\selectlanguage{english}[?]\textbackslash{}cdot\selectlanguage{english}[?]s at 1200degC. Also, as Basaltic lava mainly made
of mafic mineral including olivine, pyroxene, amphibole and biotite, it
has lower viscosity compared to lava that riches in felsic. The reason
is that mafic magma has lower content of silica, and silica tetrahedral
network must be ruptured for flowing to occur (Mallonee et al., 2017).

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.56\columnwidth]{figures/Basaltic-Lava-Viscosity-vs-Temperature-1/Basaltic-Lava-Viscosity-vs-Temperature-1}
\caption{{Basaltic lava viscosity vs temperature \protect\citep*{murase1973properties}
{\label{755655}}%
}}
\end{center}
\end{figure}

\par\null

\subsection*{}

\subsection*{Characteristics of the
Volcano}

{\label{151272}}

\textbf{Two characteristics of lava eruption, conduit and effusion rate,
affect the morphology.} With long and narrow conduit, pillow lavas are
more likely to form as fresh hot lavas have experienced a relatively
longer cooling time, extra loss in heat energy leads to easier
solidification, higher viscosity and lower flow rate; Also, its effusion
rate is lower because there is more friction effect between lava and
narrow conduit. In this case, pillow lava is more easily to form. With
short and wide conduits, ~lavas are relatively hotter with more
kinematic energy, and result in higher effusion rate with higher heat
energy to prevent immediate solidification. In this case, sheet lava is
more likely to form \citep*{bonatti1988eruption} (Fig.
{\ref{553201}}). Effusion rate is one of the most
important factors that affect the lava morphology. It directly affects
the lava material supply rate (or heat energy supply rate that affects
solidification rate) and flow rate. Recall the parameter
\selectlanguage{greek}Ψ\selectlanguage{english}\textbackslash{}Psi\selectlanguage{greek}Ψ \selectlanguage{english}we have already discussed, higher effusion rate
will lead to higher value of \selectlanguage{greek}Ψ\selectlanguage{english}\textbackslash{}Psi\selectlanguage{greek}Ψ \selectlanguage{english}with all the other
keeps the same. Thus, we can conclude that under high effusion rate,~
sheet lava is easier to form.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/conduidt1/conduidt1}
\caption{{Long narrow conduit vs short wide conduit
\protect\hyperlink{bonatti1988eruption}{}\protect\citep*{bonatti1988eruption}
{\label{553201}}%
}}
\end{center}
\end{figure}

\par\null\par\null

\subsection*{}

\subsection*{Characteristics of the Surrounding
Area}

{\label{423985}}

\textbf{Slope of the surrounding area affects lava morphology.} Slope
can affects the thickness of lava flow and with steeper slop, fraction
of gravitational force becomes greater and permit a higher flow rate
with narrower flow width. However, slope has limited effect if effusion
rate is low and/or solidification is rapid \cite{glancy}.

\par\null

Summry

A general list of factors that affect morphology is given in Figure
{\ref{357738}}.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Factors-Affect-Lava-Morphology1/Factors-Affect-Lava-Morphology1}
\caption{{Factors affect lava morphology \protect\cite{glancy}
{\label{357738}}%
}}
\end{center}
\end{figure}



\textbf{The parameter} \(\Psi\) \textbf{by} \citet*{gregg1995quantification}
\textbf{can be used to describe the relationship between flow rate and
time required for lava solidify.} This parameter skips over individual
consideration of each parameter and at the same time, shows their
interconnected relationship. As \(\Psi\) can be regarded as
relationship between flow extent and effect of solidification, it
generalized each single parameter in one variable. It means lava
morphology depends on a relative relationship between flow rate and
solidify rate.

\section*{}

\section*{Discussion}

{\label{889268}}

\textbf{Apart from our discussion of lava morphology, the global
distribution pattern of pillow lava and sheet flow suggests that the
genesis of the two types of submarine flows may be coupled to variations
in spreading rate processes.} Some possible explanations for this
pattern were raised by \citet{hekinian1985offset}. First, the upwelling of lava
material is reduced compared to those fast spreading ridges leads to
less material available for wide spreading sheet flow; and second,
pillow lavas are more likely be covered by the later eruption at fast
spreading regions.~ But, these proposed explanations have not been
proved yet. On geological aspect, the relationship between spreading
rate and conduit condition is not clear. It is possible that low
spreading rate leads to long and narrow conduits and high spreading rate
results in short wide conduits. Also, spreading rate may affect surface
topography vary with different rate and cause the difference in flowing
slope. Last but not the least, spreading rate may affect the effusion
rate directly and presents this unbalanced lava morphology distribution.

\par\null

\section*{}

\section*{Conclusion}

{\label{185726}}

Lava flow morphology is complex, and many factors can come into play.
Dimensionless parameter \(\Psi\) skips over individual
analysis of each parameter and reflects the core mechanism for each
surface morphology to form. Lava morphologies are unevenly distributed
in total number and area covered based on different spreading rate. And
the reason caused this distribution is not clear.

\section*{Acknowledgement}\label{acknowledgement}

This report follows the logic and layout of lecture slides by
\citet*{glancy}. Thanks for her comprehensive and nicely organized
class material.

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