TY - JOUR

T1 - On the mechanism of self gravitating Rossby interfacial waves in proto-stellar accretion discs

AU - Yellin-Bergovoy, Ron

AU - Heifetz, Eyal

AU - Umurhan, Orkan M.

N1 - Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2016/5/3

Y1 - 2016/5/3

N2 - The dynamical response of edge waves under the influence of self-gravity is examined in an idealised two-dimensional model of a proto-stellar disc, characterised in steady state as a rotating vertically infinite cylinder of fluid with constant density except for a single density interface at some radius (Formula presented.). The fluid in basic state is prescribed to rotate with a Keplerian profile (Formula presented.) modified by some additional azimuthal sheared flow. A linear analysis shows that there are two azimuthally propagating edge waves, kin to the familiar Rossby waves and surface gravity waves in terrestrial studies, which move opposite to one another with respect to the local basic state rotation rate at the interface. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified) where self-gravity acts as a wave stabiliser irrespective of the stratification of the system. The propagation properties of the waves are discussed in detail in the language of vorticity edge waves. The roles of both Boussinesq and non-Boussinesq effects upon the stability and propagation of these waves with and without the inclusion of self-gravity are then quantified. The dynamics involved with self-gravity non-Boussinesq effect is shown to be a source of vorticity production where there is a jump in the basic state density In addition, self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect. Further applications of these mechanical insights are presented in the conclusion including the ways in which multiple density jumps or gaps may or may not be stable.

AB - The dynamical response of edge waves under the influence of self-gravity is examined in an idealised two-dimensional model of a proto-stellar disc, characterised in steady state as a rotating vertically infinite cylinder of fluid with constant density except for a single density interface at some radius (Formula presented.). The fluid in basic state is prescribed to rotate with a Keplerian profile (Formula presented.) modified by some additional azimuthal sheared flow. A linear analysis shows that there are two azimuthally propagating edge waves, kin to the familiar Rossby waves and surface gravity waves in terrestrial studies, which move opposite to one another with respect to the local basic state rotation rate at the interface. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified) where self-gravity acts as a wave stabiliser irrespective of the stratification of the system. The propagation properties of the waves are discussed in detail in the language of vorticity edge waves. The roles of both Boussinesq and non-Boussinesq effects upon the stability and propagation of these waves with and without the inclusion of self-gravity are then quantified. The dynamics involved with self-gravity non-Boussinesq effect is shown to be a source of vorticity production where there is a jump in the basic state density In addition, self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect. Further applications of these mechanical insights are presented in the conclusion including the ways in which multiple density jumps or gaps may or may not be stable.

KW - Protoplanetary accretion disc

KW - Rossby wave instability

KW - self gravity

KW - vorticity waves

UR - http://www.scopus.com/inward/record.url?scp=84962650005&partnerID=8YFLogxK

U2 - 10.1080/03091929.2016.1158816

DO - 10.1080/03091929.2016.1158816

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AN - SCOPUS:84962650005

SN - 0309-1929

VL - 110

SP - 274

EP - 294

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

IS - 3

ER -