Abstract
Context. Rotational mixing transports angular momentum and chemical elements in stellar radiative zones. It is one of the key processes for modern stellar evolution. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. The weakest point of this hydrodynamical theory of rotational mixing is the assumption that anisotropic turbulent transport is stronger in horizontal directions than in the vertical one. Aims. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities that are obtained and discussed in the context of stellar radiative zones. Methods. The eigenvalue problem describing linear instabilities of a flow with a hyperbolictangent horizontal shear profile was solved numerically for a wide range of parameters. When possible, the Wentzel Kramers Brillouin Jeffreys (WKBJ) approximation was applied to provide analytical asymptotic dispersion relations in both the nondiffusive and highly diffusive limits. As a first step, we consider a polar f plane where the gravity and rotation vector are aligned. Results. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point (i.e., the zero second derivative of the shear flow) is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposedflow direction. While the maximum twodimensional growth rate is independent of the stratification, rotation rate, and thermal diffusivity, the threedimensional inflectional instability is destabilized by stable stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum value of p f (1 f ) in the inviscid limit as the vertical wavenumber goes to infinity, where f is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a selfsimilarity in both the inflectional and inertial instabilities based on the rescaled parameter PeN2 with the Pclet number Pe and the Brunt frequency N.
Original language  English 

Article number  A133 
Number of pages  13 
Journal  Astronomy and Astrophysics 
Volume  635 
Early online date  20 Mar 2020 
DOIs  
Publication status  Published  Mar 2020 
Externally published  Yes 
Bibliographical note
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Funder
European Research Council through ERC Grant SPIRE 647383 and from GOLF and PLATO CNES GrantsKeywords
 Hydrodynamics
 Stars: evolution
 Stars: rotation
 Turbulence
ASJC Scopus subject areas
 Astronomy and Astrophysics
 Space and Planetary Science
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Junho Park
 Research Centre for Fluid and Complex Systems  Assistant Professor Research
Person: Teaching and Research