View in EDS

The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres

Saved in:
Bibliographic Details
Title: The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres
Authors: Warneford, Emma S.
Committee Members: Dellar, Paul J.
Summary: Observations of Jupiter show a super-rotating (prograde) equatorial jet that has persisted for decades. Shallow water simulations run in the Jovian parameter regime reproduce the mixture of robust vortices and alternating zonal jets observed on Jupiter, but the equatorial jet is invariably sub-rotating (retrograde). Recent work has obtained super-rotating equatorial jets by extending the standard shallow water equations to relax the height field towards its mean value. This Newtonian cooling-like term is intended to model radiative cooling to space, but its addition breaks key conservation properties for mass and momentum. In this thesis the radiatively damped thermal shallow water equations are proposed as an alternative model for Jovian atmospheres. They extend standard shallow water theory by permitting horizontal variations of the thermodynamic properties of the fluid. The additional temperature equation allows a Newtonian cooling term to be included while conserving mass and momentum. Simulations reproduce equatorial jets in the correct directions for both Jupiter and Neptune (which sub-rotates). Quasi-geostrophic theory filters out rapidly moving inertia-gravity waves. A local quasi-geostrophic theory of the radiatively damped thermal shallow water equations is derived, and then extended to cover whole planets. Simulations of this global thermal quasi-geostrophic theory show the same transition, from sub- to super-rotating equatorial jets, seen in simulations of the original thermal shallow water model as the radiative time scale is decreased. Thus the mechanism responsible for setting the direction of the equatorial jet must exist within quasi-geostrophic theory. Such a mechanism is developed by calculating the competing effects of Newtonian cooling and Rayleigh friction upon the zonal mean zonal acceleration induced by equatorially trapped Rossby waves. These waves transport no momentum in the absence of dissipation. Dissipation by Newtonian cooling creates an eastward zonal mean zonal acceleration, consistent with the formation of super-rotating equatorial jets in simulations, while the corresponding acceleration is westward for dissipation by Rayleigh friction.
URL: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532
Database: OpenDissertations
FullText Text:
  Availability: 0
Header DbId: ddu
DbLabel: OpenDissertations
An: ddu.oai.ethos.bl.uk.618532
AccessLevel: 6
PubType: Dissertation/ Thesis
PubTypeId: dissertation
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Warneford%2C+Emma+S%2E%22">Warneford, Emma S.</searchLink>
– Name: Author
  Label: Committee Members
  Group: Au
  Data: <searchLink fieldCode="CO" term="%22Dellar%2C+Paul+J%2E%22">Dellar, Paul J.</searchLink>
– Name: Abstract
  Label: Summary
  Group: Ab
  Data: Observations of Jupiter show a super-rotating (prograde) equatorial jet that has persisted for decades. Shallow water simulations run in the Jovian parameter regime reproduce the mixture of robust vortices and alternating zonal jets observed on Jupiter, but the equatorial jet is invariably sub-rotating (retrograde). Recent work has obtained super-rotating equatorial jets by extending the standard shallow water equations to relax the height field towards its mean value. This Newtonian cooling-like term is intended to model radiative cooling to space, but its addition breaks key conservation properties for mass and momentum. In this thesis the radiatively damped thermal shallow water equations are proposed as an alternative model for Jovian atmospheres. They extend standard shallow water theory by permitting horizontal variations of the thermodynamic properties of the fluid. The additional temperature equation allows a Newtonian cooling term to be included while conserving mass and momentum. Simulations reproduce equatorial jets in the correct directions for both Jupiter and Neptune (which sub-rotates). Quasi-geostrophic theory filters out rapidly moving inertia-gravity waves. A local quasi-geostrophic theory of the radiatively damped thermal shallow water equations is derived, and then extended to cover whole planets. Simulations of this global thermal quasi-geostrophic theory show the same transition, from sub- to super-rotating equatorial jets, seen in simulations of the original thermal shallow water model as the radiative time scale is decreased. Thus the mechanism responsible for setting the direction of the equatorial jet must exist within quasi-geostrophic theory. Such a mechanism is developed by calculating the competing effects of Newtonian cooling and Rayleigh friction upon the zonal mean zonal acceleration induced by equatorially trapped Rossby waves. These waves transport no momentum in the absence of dissipation. Dissipation by Newtonian cooling creates an eastward zonal mean zonal acceleration, consistent with the formation of super-rotating equatorial jets in simulations, while the corresponding acceleration is westward for dissipation by Rayleigh friction.
– Name: URL
  Label: URL
  Group: URL
  Data: <link linkTarget="URL" linkTerm="https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532" linkWindow="_blank">https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618532</link>
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ddu&AN=ddu.oai.ethos.bl.uk.618532
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: 532
        Type: general
      – SubjectFull: Mathematics ; Fluid mechanics (mathematics) ; Geophysics (mathematics) ; geophysical fluid dynamics ; computational applied mathematics ; Hamiltonian mechanics ; asymptotic analysis ; thermal shallow water equations ; Jupiter ; zonal jets
        Type: general
    Titles:
      – TitleFull: The thermal shallow water equations, their quasi-geostrophic limit, and equatorial super-rotation in Jovian atmospheres
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Warneford, Emma S.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2014
ResultId 1