Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional circulation with strong and weak reversals. The velocities are generated using a mean-field hydrodynamic and dynamo model—moving through the regimes with minimal parameter changes, counterrotation near the base of the tachocline is induced by sign inversion of the nondiffusive action of turbulent Reynolds stresses (Λ-effect) due to the radial inhomogeneity of the Coriolis number. By mimicking the stochastic excitation of resonant modes in the convective interior, we simulate realization noise present in solar observations. Using deep-focusing to analyze differences in travel-time signatures between the four regimes, as well as comparing to solar observations, we show that current helioseismology techniques may offer important insights about the location and strength of the return flow; however, it may not currently be possible to definitively distinguish between profiles of single-cell or double-cell meridional circulation.
We present a three-dimensional (3D) numerical solver of the linearized compressible Euler equations (Global Acoustic Linearized Euler), used to model acoustic oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh (0 ≤ ϕ ≤ 2π, 0 ≤ θ ≤ π, 0 ≤ r ≤ R ⊙) over a background state generated by the standard solar model S. We implement an efficient pseudospectral computational method to calculate the contribution of the compressible material derivative dyad to internal velocity perturbations, computing oscillations over arbitrary 3D background velocity fields. This model offers a foundation for a “forward-modeling” approach, using helioseismology techniques to explore various regimes of internal mass flows. We demonstrate the efficacy of the numerical method presented in this paper by reproducing observed solar power spectra, showing rotational splitting due to differential rotation, and applying local helioseismology techniques to measure travel times created by a simple model of single-cell meridional circulation.
We use data observed near the solar disk center by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) to mimic observations at high-latitude areas after applying geometric transform and projection. These data are then used to study how foreshortening affects the time-distance measurements of acoustic travel times. We find that foreshortening reduces the measured mean travel-times through altering the acousticpower weighting in different harmonic degrees, but the level of reduction and the latitude dependence are not as strong as those measured from the observation data at the same latitude. Foreshortening is not found to be accountable for the systematic center-to-limb effect in the measured acoustic travel-time differences, which is an essential factor for a reliable inference of the Sun's meridional-circulation profile. The differences in the acoustic power spectrum between the mimicked data and the observation data in high-latitude areas suggest that the optical spectrum-line formation height or convection cells in these areas may be the primary cause of the center-to-limb effect in helioseismic analyses.
Various models of solar subsurface stratification are tested in the global EULAG-MHD solver to simulate diverse regimes of near-surface convective transport. Sub-and superadiabacity are altered at the surface of the model (r > 0.95 R ) to either suppress or enhance convective flow speeds in an effort to investigate the impact of the near-surface layer on global dynamics. A major consequence of increasing surface convection rates appears to be a significant alteration of the distribution of angular momentum, especially below the tachocline where the rotational frequency predominantly increases at higher latitudes. These hydrodynamic changes correspond to large shifts in the development of the current helicity in this stable layer (r < 0.72R ), significantly altering its impact on the generation of poloidal and toroidal fields at the tachocline and below, acting as a major contributor towards transitions in the dynamo cycle. The enhanced near-surface flow speed manifests in a global shift of the toroidal field (B φ ) in the butterfly diagram -from a North-South symmetric pattern to a staggered anti-symmetric emergence.
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