# MU ESCI 343 - Atmospheric Dynamics (2 pages)

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# Atmospheric Dynamics

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## Atmospheric Dynamics

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2
School:
Millersville University
Course:
Esci 343 - Atmospheric Dynamics II
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ESCI 343 Atmospheric Dynamics II Answers to Selected Exercises for Lesson 12 4 Use equations 1 2 4 and 6 to show the following phase relations between u v and w for a wave propagating in the x z plane l 0 d If w cos kx mz t what are u and v Answer Let kx mz t Then w cos which is the same as Re e i u m k w m k cos m k cos kx mz t v ifm k w ifm k Re e i Re ifm k e i fm k sin fm k sin kx mz t 5 a Use 4 a to determine whether the horizontal velocity vector will rotate cyclonically or anticyclonically with time Will this change if the wave is propagating upward versus downward Answer From 4 a if v cos then u sin Therefore graphs of u and v versus phase look like which shows that as gets larger the velocity vector rotates counterclockwise Since kx mz t then as time gets bigger gets smaller Therefore the velocity vector rotates clockwise anticyclonically with time b Use the results from 4 a to determine whether the horizontal velocity vector will rotate cyclonically or anticyclonically with height Will this change if the wave is propagating upward versus downward Answer As in part a as gets larger the velocity vector rotates counterclockwise For an upward propagating wave gets larger as z increases Therefore the velocity vector rotates counter clockwise cyclonically with height for upward propagation For a downward propagating wave gets smaller as z increases because m 0 Therefore the velocity vector rotates clockwise anticyclonically with height 6 Show that V 0 is the same as equation 4 Answer V ku lv mw kA lB mC e i kx ly mz t 0 which is the same as kA lB mC 0 2

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