Downslope Wind Storms

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Downslope Wind Storms
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Flow Mountain Ridge

• Infinitely long mountain, no flow around ridge
• Consider first an airplane wing

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• Flow accelerates over the top of the wing in
  order to keep up with flow along shorter path
  under the wing
• Bernollui relationship tells us pressure must be
  lower at top of wing

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Small Ridge

• Similar to airplane wing

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Meso-Beta Scale Ridge

• Gravity response is involved, low pressure shifts
  down wind more and more as the scale of the ridge
  becomes larger

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Witch of Agnesi Ridge

• Lets consider a Witch of Agnesi, bell shaped
  mountain (normally used for analytical mountain
  wave studies) having the formula
• a is the half-width, h is the maximum height, and
  d is the distance from the ridge top

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More about Witch of Agnesi

• Easy for analytical solutions
• NOT a sine wave, is a bell shaped ridge that
  contains a spectrum of wave components
  representing many wavelengths
• Some parts of the ridge may be at super Rossby
  radius scale and some may be at sub-Rossby radius
  scale for instance

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Froude Number

• Important influences on atmosphere response to
  flow over an object
• (L) Length scale of the object
• (N) Brunt-Vasallai frequency, the vertical
  stability providing a restoring force for gravity
  waves
• (U) velocity of flow normal to the ridge

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Froude Number

• Define Froude Number

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Inertial Cutoff, ie Rossby Number

• The coriolis parameter is another important
  parameter. If the mountain is big enough, we get
  lee cyclogenesis, not gravity waves! So we must
  consider the Rossby Number, ie

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Flow Over a Ridge

• We consider flow over shallow (h ltlt depth of
  troposphere) ridges of several half-widths and
  look at the results of a linear analytical
  solution for the Witch of Agnesi mountain.
• The solution to the linear problem yields a wave
  equation of the form
• w- vertical velocity
• z- height above surface
• k vertical wave number
• l Scorer Parameter

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Vertical Wave Number

• Lz is the vertical wavelength of the gravity
  wave. This parameter is purely nonhydrostatic!

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Scorer Parameter

• This parameter is related to the transmissivity
  of the atmosphere to gravity waves considering
  only hydrostatic processes

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When Gravity Waves?

• Gravity wave solutions only exist when
• Therefore, there is a short wave cutoff scale,
  below which gravity waves cannot exist
• Lz is the vertical wavelength of the gravity wave
• Lz is the horizontal wavelength of the gravity
  wave

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Narrow Ridge Evanescent waves
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Medium Ridge Mountain (gravity) waves
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Broad Ridge Lee Cyclogenesis for larger modes,
GW for smaller modes
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Medium-Narrow ridge, but with Scorer Parameter
(l) varying with height. This traps shorter
waves of the Witch of Agnesi mountain, but
transmitts vertically the longer ones, leading to
lee waves. - This is mostly a nonhydrostatic
effect why? - The shorter waves have
solutions in low levels where l is large, but
do not above, so they reflect off