3.7 Forces
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3.7 Forces
3.7.1 What Forces Do
A non-zero force operates to change the speed and/or the direction of motion of a
flui parcel. In geophysical flui dynamics, forces are conventionally expressed as
forces per unit mass, being directly proportional to acceleration or deceleration of
a flui parcel. So, whenever the term “force” appears in the following, this actually
should mean “force per unit mass”.
In component form, a temporal change of the velocity vector can be formally
written as:
du
dt
= F
x
dv
dt
= F
y
dw
dt
= F
z
where (F
x
,F
y
,F
z
) are the vector components of a force of certain magnitude and
direction. For example, (0, 0, −9.81 m/s
2
) is a force operating into the negative z-direction (downward). With two forces involved, the latter equations can be
written as:
du
dt
= F
x
1 + F
x
2
dv
dt
= F
y
1 + F
y
2
dw
dt
= F
z
1 + F
z
2
Acceleration or deceleration results if any component of the resultant net force is
different from zero. In the general case, the sum symbol “
” can be used to write:
du
dt
=
m
i=1
F
x
i
dv
dt
=
m
i=1
F
y
i ,
(3.5)
dw
dt
=
m
i=1
F
z
i
where m is the number of forces involved in a process, and the index i points to a
certain force.