Chapter 1: Analysis of Mid-lat syn systems using balance equations Flashcards Preview

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the two derived scalar quantities of the horizontal wind

Stream function

velocity potential

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stream function is represented by 

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velocity potential is represented by 

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The horizontal wind is then represented by these scalars as:

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the term means

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the term means

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psi represents

Stream function

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chi represents

velocity potential

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the following equation is the

The horizontal wind 

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the rotational (non-divergent) part of horizontal wind is represented by the term 

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the divergent (irrational) part of horizontal wind is represented by the term 

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Stream function, velocity potential are the

two derived scalar quantities of the horizontal wind

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The scalar equations for u and v can then be written in form of (stream function) and (velocity potential)as

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If one of the scalars (stream function) or (velocity potential) is set equal to zero, then the wind that remains can be one of the following

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Non-divergent or Rotational wind:

in non-divergent:

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Non-divergent or Rotational wind:

in scalar notation:

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irrotational or divergent wind:

the irrotational wind:

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irrotational or divergent wind:

in scalar notation:

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the following stands for

vorticity

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vorticity in terms of stream function

For horizontal motion that is rotational (non-divergent), the velocity components are given by

 

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Vorticity (ع ) in terms of streamfunction

substituting u and v for ع

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the velocity field and the vorticity can both be represented in terms of

the variation of the single scalar field, (psi)

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................................. and ........................... can both be represented in terms of the variation of the single scalar field, (psi)

the velocity field

the vorticity

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Obtain an expression for divergence of an irrotational wind

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The barotropic vorticity is written as

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the barotropic vorticity states that

the absolute vorticity is conserved following the hor. motion.

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The barotropic vorticity equation can be written as

prognostic eqn. for vorticity

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The barotropic vorticity equation can be written as a prognostic eqn. for vorticity in the form:

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the following term represents

local tendency of relative vorticity

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the following term represents

advection of absolute vorticity