Geodynamics
Plate-driving forces
Lecture 10.6 - Ridge push and the drag force
Lecturer: David Whipp
david.whipp@helsinki.fi
Geodynamics
www.helsinki.fi/yliopisto
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Goals of this lecture
•
Calculate the ridge push and drag forces acting on a
lithospheric plate
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Ridge push
FRP
Forsyth and Uyeda, 1975
•
Ridge push results from the elevation of oceanic ridges relative to the
seafloor
•
The difference in elevation results in a pressure head that drives the plate away
from the ridge
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
•
This motion may also be viewed as gravitational sliding
To calculate the ridge push force 𝐹𝑅𝑃 we must consider the forces acting on
the top (𝐹1), bottom (𝐹2) and side (𝐹3) of the oceanic lithospheric plate:
FRP = F1
F2
F3
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Ridge push
FRP
6.22 The Forces that Drive
Plate
Tectonics
Forsyth
and Uyeda,
1975
With this force balance in mind, we
can see
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
Fig. 6.44, Turcotte and Schubert, 2014
1. The horizontal force on the base
of the plate must be equal to the
integrated lithostatic pressure in
the mantle along RD
2. The horizontal force on the top of
the plate must be equal to the integrated hydrostatic pressure along AB
Figure 6.44 Horizontal forces acting on a section of the ocean, li
and mantle at an ocean ridge.
3. The horizontal force acting on the lithospheric section BC is equal to the
integrated pressure in the lithosphere
•
The integrated pressure force on the upper surface of the lith
Note that this pressure
that resulting
frombecause
the overlying
equal toshould
F4 , theinclude
net pressure
force on AB,
the section o
oceanic water must be in equilibrium. Thus we can integrate the hydrostat
4
the water to obtain
!
Ridge push
FRP
6.22 The Forces that Drive
Plate
Tectonics
Forsyth
and Uyeda,
1975
Fig. 6.44, Turcotte and Schubert, 2014
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
At a constant depth 𝑦
P = ⇢gy
assuming constant density of the overlying material
•
Figure 6.44 Horizontal forces acting on a section of the ocean, li
depthand
range
𝑦1 to
mantle
at 𝑦
an2
ocean ridge.
Integrated over a
Z y2
Pint =
⇢gy
Thedyintegrated pressure force on the upper surface of the lith
y1
equal to F4 , the net pressure force on AB, because the section o
must be in equilibrium. Thus we can integrate the hydrostat
5
the water to obtain
!
Ridge push
FRP
6.22 The Forces that Drive
Plate
Tectonics
Forsyth
and Uyeda,
1975
•
•
FRP = F1
F2
Fig. 6.44, Turcotte and Schubert, 2014
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
Going back to the original force
balance equation for ridge push,
we see
F3
After some mathematical substitutions
and integrations we find
FRP

2 ⇢m ↵v (T1 T0 )
= g⇢m ↵v (TFigure
T06.44
) 1Horizontal
+
t
1
forces
acting
on
a section of the ocean, li
⇡ (⇢m ⇢w )
and mantle at an ocean ridge.
𝜌𝑚 Mantle density
𝜌𝑤
𝑇1
surface
0 Temperature
The integrated𝑇pressure
force onat
theplate
upper
surface of the lith
force onplate
AB, because the section o
Water density equal to F4 , the net
Age of oceanic
𝑡 pressure
must be in equilibrium. Thus we can integrate the hydrostat
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Mantle temperature
the water to obtain
!
Ridge push
FRP
6.22 The Forces that Drive
Plate
Tectonics
Forsyth
and Uyeda,
1975
Fig. 6.44, Turcotte and Schubert, 2014
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
Using typical values, we find the ridge
push force is
𝐹𝑅𝑃 = ~4×1012 N m-1
•
Note that this is about an order
Figure 6.44 Horizontal forces acting on a section of the ocean, li
of magnitude smaller than
the slab
and mantle at an ocean ridge.
pull force
The integrated pressure force on the upper surface of the lith
equal to F4 , the net pressure force on AB, because the section o
must be in equilibrium. Thus we can integrate the hydrostat
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the water to obtain
!
Drag force
FDF
416
Fluid
Mechanics
Forsyth
and Uyeda, 1975
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The drag force on the base of the oceanic
lithosphere can both drive and resist plate
tectonics, depending on the relative motion
between the plate and the underlying mantle
•
If we assume that the underlying mantle
Fig. 6.2, Turcotte and Schubert, 2014
resists or drives plate motion by viscous
flow across a fixed-thickness layer, the drag force on the plate is simply
FDF = ⌘as
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
u
L
h
𝜂𝑎𝑠 Viscosity of asthenosphere
ℎ Thickness of viscous layer
𝛥𝑢 Velocity difference
𝐿
Length of the plate
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Figure 6.2 One-dimensional channel flows of a constan
Drag force
FDF
416
Fluid
Mechanics
Forsyth
and Uyeda, 1975
Downloaded from http://gji.oxfordjournals.org/ at Dalhousie University on September 1, 2013
•
Again using typical values, we find the drag
force is
𝐹𝐷𝐹 = ~1×1013 N m-1
•
Fig. 6.2, Turcotte and Schubert, 2014
Note that this value is similar in magnitude to the slab pull force
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Figure 6.2 One-dimensional channel flows of a constan
Let’s see what you’ve learned…
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If you’re watching this lecture in Moodle, you will now be
automatically directed to the quiz!
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Reference(s):
Forsyth, D., & Uyeda, S. (1975). On the Relative Importance of the Driving Forces of Plate Motion*.
Geophysical Journal International, 43(1), 163–200. doi:10.1111/j.1365-246X.1975.tb00631.x
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