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Lecture 10. Slice method Let’s pick out a sufficiently large layer of air

Lecture 10. Slice method

Let’s pick out a sufficiently large layer of

air
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Lecture 10. Slice method Slice method assumptions: all variations of the

Lecture 10. Slice method

Slice method assumptions:

all variations of the quantities within

the picked out layer come out adiabatically;
no advection (horizontal mass motion) is observed;
the mass of air above any layer remains unchanged.
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Lecture 10. Slice method The latter means that fluxes of air

Lecture 10. Slice method

The latter means that fluxes of air mass

through section S’ and S’’ are equal:
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Lecture 10. Slice method To derive the stability criterion:

Lecture 10. Slice method

To derive the stability criterion:

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Lecture 10. Slice method Suppose, particles come from lower level to upper one:

Lecture 10. Slice method

Suppose, particles come from lower level to upper

one:
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Lecture 10. Slice method From (10.10)-(10.13) we obtain:

Lecture 10. Slice method

From (10.10)-(10.13) we obtain:

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Lecture 10. Slice method Let’s use (10.9)

Lecture 10. Slice method

Let’s use (10.9)

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Lecture 10. Slice method Let’s consider 3 cases: Updraft and downdraft

Lecture 10. Slice method

Let’s consider 3 cases:
Updraft and downdraft air isn’t

saturated
Criteria of stability of both methods (parcel and slice ones) give the same result.
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Lecture 10. Slice method 2nd case: Updraft and downdraft air fluxes

Lecture 10. Slice method

2nd case:
Updraft and downdraft air fluxes are saturated
Criteria

of stability of both methods (parcel and slice ones) give the same result.
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Lecture 10. Slice method 3d case: Updraft air is saturated and

Lecture 10. Slice method

3d case:
Updraft air is saturated and
downdraft flux

is not.
Cu clouds development
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Lecture 10. Slice method From (10.18) and Stability criteria of both

Lecture 10. Slice method

From (10.18) and
Stability criteria of both methods are

coincide if the stratification is absolutely unstable and absolutely stable. However, often
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Lecture 10. Slice method Let’s introduce a critical lapse rate

Lecture 10. Slice method

Let’s introduce a critical lapse rate