Rossby Wave Radiation from Nontranslating and Moving Vortices

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Rossby Wave Radiation from Non-translating and
Moving Vortices

• Kyle Krouse
• Adam Sobel, Lorenzo Polvani

Department of Applied Mathematics and Applied
Physics Columbia University
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Motivation Multiple Cyclone Events

• Dispersion from a Tropical Cyclone relevant to
  cyclogenesis
• (e.g. Frank, 1982 Davidson Hendon, 1989)
• TC movement emits Rossby wave radiation in its
  wake forming a wavetrain
• (e.g. Carr Elsberry, 1995)
• Simple mathematical explanation for this
  wavetrain? Particularly its wavelength?

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An Observed Multiple Cyclone Event
TC Jelawat exciting TC Ewiniar in WNP, Aug.,
2000. From Li et al, 2003
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Stationary Solutions

• Wavetrain is a stationary solution.
• Suspect that the wavetrain is due to Short
  Wavelength Rossby wave dispersion
• However, a non-translating vortex does not give
  you a strong signal (e.g. Carr Elsberry, 1995)

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Our Idea

• If the steering flows for the cyclone and the
  Rossby waves are the same ? expect no additional
  stationary states from dispersion relation
• BUT different steering flows ? a Doppler effect
  might admit new stationary states

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Numerical Model STSWMNonlinear SWEs on the
sphere

• (1)
• (2)
• (3)

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Numerical Model STSWMNonlinear forced SWEs on
the sphere

• (1)
• (2)
• (3)

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Numerical Model STSWMNonlinear forced SWEs on
the sphere

• (1)
• (2)
• (3)

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Numerical Model STSWMNonlinear forced SWEs on
the sphere

• (1)
• (2)
• (3)

Average depth of system set to get correct
gravity wave speed H 250 m
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Numerical Experiment

• Localized forcing
• Nonlinear response near vortex
• Linear response in far-field

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Linear Analysis

• In far-field, dispersion relation instructive
• Rossby wave mechanism
• Near the tropics
• ? analyzing linear SWEs with equatorial
  beta-plane approximation seems reasonable

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Dispersion Relation Non-translating Vortex
k zonal wavenumber n meridional wavenumber
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• No meaningful stationary points (? 0)

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Dispersion Relation Translating Vortex
Relative motion between the flow relevant to
the vortex and the flow relevant to the Rossby
waves
k zonal wavenumber n meridional wavenumber
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What is Ubar?

• Relative motion between different flows
• TC steering flow versus the flow that the waves
  live on
• The flows may be different
• TC-induced beta-gyres
• monsoon shears
• ubar 5 m/s reasonable
• imposed westward vortex motion ? the environment
  is moving eastward from the vortex frame

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Properties of the Solution

• Short-wavelength Rossby waves
• westward (absolute) phase propagation
• eastward energy propagation
• cyclonic anomaly is much stronger than in
  non-translating case grows in time
• catching phase that translates at ubar

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Conclusions

• A difference between the flows relevant to a
  vortex and to the SW Rossby waves that it
  radiates can result in a new stationary solution
  to the SWEs.
• These stationary SW Rossby wave solutions are of
  the observed length scale in a Multiple Cyclone
  event.
• These waves excite a strong cyclonic anomaly to
  the SE of the vortex, potentially important in
  the spinup of a second vortex in a Multiple
  Cyclone event.

My email address is kdk8_at_columbia.edu
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• Thank You!