Hydromagnetic waves in Earth's core and their influence on ...

18 Chapter 2 — Space-time analysisFigure 2.1: Relation of latitude-longitude maps to time-longitude(TL) plots.Field values at all gridded longitudes at a chosen latitude (10 ◦ S here) are taken fromlatitude-longitude maps at each discrete time <strong>in</strong>terval to construct time-longitude plotsat the chosen latitude (the equator <strong>in</strong> this example).of non-axisymmetric field features.Hovmöller (1949) was the first to employ the technique of us<strong>in</strong>g TL plots to studywave motions <strong>in</strong> a planetary scale rotat<strong>in</strong>g fluid. He considered the height of the 500mb pressure level as a tracer field of atmospheric motions.The result<strong>in</strong>g TL plot isreproduced <strong>in</strong> figure 2.2a. He visually determ<strong>in</strong>ed the azimuthal phase speed of fieldmotions by follow<strong>in</strong>g the position of crests <strong>and</strong> troughs 1 (see, for example, the dashedl<strong>in</strong>es <strong>in</strong> figure 2.2a).He <strong>in</strong>ferred an azimuthal group speed by follow<strong>in</strong>g the path oftransmission of energy (proportional to squared field amplitude) by identify<strong>in</strong>g pathsalong which field maxima <strong>and</strong> m<strong>in</strong>ima are consistently observed (see the solid l<strong>in</strong>es <strong>in</strong>figure 2.2a).He used these observations to test whether the motions were consistentwith Rossby’s theory of planetary <strong>waves</strong> 2 <strong>in</strong> the atmosphere (Rossby, 1939), conclud<strong>in</strong>gthis was the case.1 A more sophisticated way to determ<strong>in</strong>e phase speeds, especially useful when energy is present over arange of frequencies <strong>and</strong> wavenumbers, is to filter so that only a s<strong>in</strong>gle frequency component or wavenumbercomponent rema<strong>in</strong>s. The azimuthal speed of these features is then the azimuthal phase speed associatedwith that frequency. By perform<strong>in</strong>g this procedure over a range of frequencies or wavenumbers,the dispersion (frequency versus wavenumber) characteristics of the field motion can be determ<strong>in</strong>ed.Azimuthal group speeds associated with the speed of transmission of energy are often determ<strong>in</strong>ed byfollow<strong>in</strong>g peaks of the square of the field amplitude.2 Planetary (or Rossby) <strong>waves</strong> are large scale, slowly propagat<strong>in</strong>g, <strong>waves</strong> found <strong>in</strong> rotat<strong>in</strong>g fluids.Their existence is a consequence of the restor<strong>in</strong>g force that arises due to the variation of the Coriolisforce with latitude. Readers unfamiliar with these <strong>waves</strong> should consult Andrews (2000) for an accessible<strong>in</strong>troductory account.