Context. The solar rotation profile is conical rather thancylindrical as it could be expected from classical rotating fluiddynamics (e.g. Taylor-Proudman theorem). Thermal coupling to thetachocline, baroclinic effects and latitudinal transport of heat havebeen suggested to explain this peculiar state of rotation. Aims. To test the validity of thermal wind balance in the solarconvection zone using helioseismic inversions for both the angularvelocity and fluctuations in entropy and temperature. Methods. Entropy and temperature fluctuations obtained from 3Dhydrodynamical numerical simulations of the solar convection zone arecompared with solar profiles obtained from helioseismic inversions. Results. The temperature and entropy fluctuations in 3Dnumerical simulations have smaller amplitude in the bulk of the solarconvection zone than those derived from seismic inversions. Seismicinversion provides variations of temperature from about 1K at thesurface to up to 100K at the base of the convection zone while in3D simulations they are of an order of 10K throughout theconvection zone up to 0.96.In 3D simulations, baroclinic effects are found to be important to tilt the isocontours of away from a cylindrical profile in most of the convection zone, helpedby Reynolds and viscous stresses at some locations. By contrast thebaroclinic effect inverted by helioseismology is much larger than whatis required to yield the observed angular velocity profile. Conclusions. The solar convection does not appear to be instrict thermal wind balance, Reynolds stresses must play a dominantrole in setting not only the equatorial acceleration but also theobserved conical angular velocity profile. Key words: Sun: interior - Sun: rotation - Sun: helioseismology - hydrodynamics - convection
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