SME
Climatology · Problem type
Coriolis parameter and inertial circles
Use this for “At 45° N a current moves at 0.2 m/s with no force but the Coriolis effect. What are f, the radius of its inertial circle and its period?”
Diagram
velocity U: 1 at 0°, so velocity U = ⟨1, 0⟩.
Coriolis f × U: 1 at 270°, so Coriolis f × U = ⟨0, −1⟩.
This is an example. Type your own values to start a new problem.
f (s⁻¹)
=
2
×
7.292
×
10⁻⁵
×
sin(
φ
°)
φ is the latitude in degrees: 45 for 45° N.
U
Speed
example · m/s
r
Inertial radius
calculated
T
Inertial period
calculated
Formulas
f
=
2
×
7.292 ×
10
-5
×
sin(
φ
°)
1.0312 ×
10
-4
=
2
×
7.292 ×
10
-5
×
sin(45°)
r
=
U
f
1,939.4042
=
0.2
1.0312 ×
10
-4
T
=
2π
f
60,928.1807
=
2π
1.0312 ×
10
-4
Formulas are worked in s. The step-by-step shows the conversions.
Assumptions
•
Earth spins at Ω = 7.292 × 10⁻⁵ rad/s; the Coriolis acceleration f × U acts at 90° to the motion.
•
In the north it turns the motion right; in the south f is negative and the turn is left, with the same sizes.
•
No pressure gradient or friction: only the Coriolis effect turns the flow, so it runs in a circle.
Step-by-step
WE KNOW
φ = 45°, U = 0.2 m/s
FIND
Coriolis parameter (f), inertial radius (r), inertial period (T)
Step 1 · Find Coriolis parameter (f)
Use f = 2 × 7.292 × 10⁻⁵ × sin(φ°)
Only
the
part
of
Earth’s
spin
about
the
local
vertical
turns
level
motion:
Ω
sin
φ
,
doubled.
f
=
2
×
7.292 ×
10
-5
×
sin(45°)
f
=
2
×
(7.292
×
10
-5
)
×
0.70711
f
=
0.00014584
×
0.70711
f
=
1.0312445 ×
10
-4
s
-1
Step 2 · Find inertial radius (r)
Use r = U ÷ f
The
Coriolis
acceleration
f
×
U
is
the
centripetal
U
2
r
of
the
circle,
so
r
=
U
f
.
r
=
0.2
1.0312445 ×
10
-4
r
=
1,939.404
m
Step 3 · Find inertial period (T)
Use T = 2π ÷ f
The
flow
turns
at
f
radians
a
second,
so
one
full
turn
of
2π
takes
2π
f
.
T
=
2π
1.0312445 ×
10
-4
T
=
60,928.1807
s
Step 4 · Convert the answers
Change each answer back to the unit you chose.
T = 60,928.1807 s = 16.9245 h (1 h = 3600 s)
Check
Put the numbers back in. Both sides should match.
1.0312445 ×
10
-4
=
2
×
7.292 ×
10
-5
×
sin(45°)
✓
1,939.404
=
0.2
1.0312445 ×
10
-4
✓
60,928.18
=
2π
1.0312445 ×
10
-4
✓
Topic check
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