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Examining the Impact of Prandtl Number and Heat Transport Models on Convective Amplitudes Bridget O’Mara*, Kyle Augustson, Nicholas Featherstone, Mark Miesch Regis University* 3333 Regis Blvd. Denver, CO 80221 HAO, Boulder, CO Abstract Methods Turbulent motions within the solar convection zone play a central role in the generation and maintenance of the Sun's magnetic field. This magnetic field reverses its polarity every 11 years and serves as the source of powerful space weather events, such as solar flares and coronal mass ejections, which can directly affect artificial satellites and power grids. The structure and inductive properties are linked to the amplitude (i.e speed) of convective motion. Using the NASA Pleiades supercomputer, a 3D fluids code simulates these processes by evolving the Navier-Stokes equations in time and under an anelastic constraint. This code imitates the fluxes describing heat transport in the sun. The theories behind the radiative, entropy, and kinetic energy flux have been well established, yet past models simulating the conductive and granulation fluxes have not produced results matching observations from the sun. New models implement a revised granulation flux at the sun’s surface. Results comparing the behavior of convection with and without the new model will be presented, as well as the behavior of convection with a varying prandtl number. • • Using the NASA’s Pleiades supercomputer, we solve the Navier Stokes equations in time under an anelastic constraint to model the small scale convection (๐น๐๐๐๐ for old model, ๐น๐ + ๐น๐๐๐๐ for new model) Anelastic constraint: • • Based on the conservation of mass, momentum, and energy equations • Spectra graphs for both models show similar trends ๐ป โ ๐๐ฃ = 0 The output is used to analyze the convective amplitude and structure and the heat transport by convection Motivation • Convection is a fundamental process that occurs often and regularly in everyday life • The convection in the sun contributes to the generation of magnetic fields, which cause space weather events such as CMEs and Solar Flares • Recent observational and modeling results suggest that an overestimation of the convective amplitude Background • • • Not expected… Previous models of surface convection use the following conservation of energy equation: ๐๐ธ = −๐ป โ ๐น๐๐๐ + ๐น๐ + ๐น๐ + ๐น๐๐๐๐ ๐๐ก In this model, ๐น๐๐๐๐ ∝ −๐ ๐๐ , ๐๐ • ๐ฃ๐๐๐ and convective structure show similar behavior with decreasing ๐ in both models • As ๐ decreases, ๐ฃ๐๐๐ increases, and no longer matches observations of the sun Prandtl Number Tests • A new model replaces ๐น๐๐๐๐ with ๐น๐ + ๐น๐๐๐๐ as flux representing the small scale surface convection on the sun (where ๐น๐ = ๐๐๐๐๐ข๐๐๐ก๐๐๐ ๐๐๐ข๐ฅ) • To understand the decrease in KE we look at the Prandtl number • The Prandtl number equals the ratio between viscous and thermal diffusivity • We run tests with a decreasing ๐ for both models and observe the differences • Generally, we expect to see increasing ๐ฃ๐๐๐ and kinetic energy (KE) with decreasing ๐ ๐๐ = We run tests to see the differences between a changing and constant ๐๐ • For changing values, ๐ is constant as ๐ changes • For constant values, ๐ = ๐ (so ๐๐ = 1) Next Steps • Where ๐น๐ ∝ ๐ฃ๐๐๐ ๐ ′ ≈ ๐นโ • If true, explains decreasing ๐ฃ๐๐๐ with increasing Prandtl number ๐ (๐ฃ๐๐ ๐๐๐ข๐ ) ๐ (๐กโ๐๐๐๐๐) • The Prandtl number makes a big difference on the convective amplitude! • As ๐ is decreased, holding ๐๐ constant, ๐ฃ๐๐๐ increases • As ๐ is decreased, holding ๐ constant (increasing ๐๐ ), ๐ฃ๐๐๐ decreases! (surprise!) • The second situation (increasing ๐๐ ) is very promising because ๐ฃ๐๐๐ in current convection simulations might be too big and the real ๐ of the Sun is very small • ๐ ′ ๐๐ ๐กโ๐ ๐๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐๐ฃ๐๐๐ก๐๐๐ ๐ง๐๐๐, ๐๐๐๐๐๐๐ ๐๐ ๐๐ ๐ฆ๐๐ข ๐๐๐๐๐๐๐ ๐ ๐ . ๐๐ Advantage: ๐น๐ ๐๐ ๐๐๐ก ๐๐๐๐๐๐๐ก๐๐๐๐๐ ๐ก๐ − ๐ , so we ๐๐ can decrease ๐ without raising ๐ฃ๐๐๐ • Testing the following Hypothesis: where ๐ = ๐กโ๐๐๐๐๐ ๐๐๐๐๐ข๐ ๐๐ฃ๐๐ก๐ฆ , (๐ ๐ ๐ข๐ ~107 , ๐ ๐๐๐๐๐ ~1012 ) • Initial Results • KE decreases with decreasing ๐ Conclusion • The structure and amplitude of deep convection is similar for both models of surface convection considered (conduction and fixed-flux) • Suggests that deep convection is not very sensitive to the details of the surface convection Navier Stokes equations: • • Results Acknowledgements • KE and ๐ฃ๐๐๐ increase with constant ๐๐ • KE and ๐ฃ๐๐๐ decrease with changing ๐๐ Thanks to the NSF REU program, LASP and HAO, and a special thanks to Erin Wood and Marty Snow