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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 333
/
1
/
ii
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 333
1
ii
2026-09-28
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Differentiate the
second
momentum
equation
in
x
, the
first
in
y
, subtract, and use continuity:
(
v
x
−
u
y
)
t
=
−
f
(
u
x
+
v
y
)
=
c
2
f
ϕ
t
.
(1)
Hence the linear
shallow-water potential vorticity
P
=
v
x
−
u
y
−
c
2
f
ϕ
(2)
satisfies
P
t
=
0
.
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ii
1
Paper 333
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
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