On the Stability of Magnetohydrodynamic Shear Flows: Characterization of Critical Pressure-Velocity-Magnetic-Field Interactions

Plasma shear flows are abundant in nature and frequently encountered in engineering applications. The stability characteristics of plasma shear flows are of much fundamental interest. Shear flows are susceptible to various algebraic and modal instabilities, i.e., velocity perturbations grow as a polynomial or an exponential function of time. It is well known in literature that background magnetic field applied along the flow direction and compressibility have a stabilizing influence on these shear instabilities. In this dissertation, a systematic investigation of the stabilization mechanisms is performed. This dissertation consists of three studies, each addressing a different type of free shear layer: Study 1 - homogeneously sheared flows in the incompressible regime; Study 2 - inhomogeneously sheared mixing layers in the incompressible regime; Study 3 - inhomogeneously sheared planar jets in the compressible regime. The common theme of all the studies investigate the nature of pressure-velocity-magnetic-field interactions that influence stabilizing mechanisms. For the case of homogeneous shear investigated in the first study, velocity perturbations in the absence of the magnetic field are susceptible to algebraic instability, i.e., kinetic energy contained in the perturbations (k) grows as, k ~ O(t^n). The stabilizing influence of magnetic field strength and perturbation orientation (β) on the instability is characterized using linear analysis and direct numerical simulations. Linear analysis indicates that the perturbation growth is dependent on the parameter, RvA ≡ VvAk/S, where, VvA, k and S are the Alfvén wave speed, initial wavenumber and mean flow shear, respectively. Analytical solutions for various perturbation energies at extreme RvA regimes – RvA» 1 and RvA « 1 – are derived and compared to numerical simulations. The behavior of perturbations at different RvA regimes and β values is also explicated using numerical simulations. In the second study, a tangent hyperbolic profile is chosen for the mean velocity field. Owing to the presence of an inflection point in the profile, the flow field is subjected to Kelvin-Helmholtz (KH) instability leading to exponential growth of perturbations, i.e., k ~ O(e^t). In the absence of any magnetic field (hydrodynamic limit), the precursor vortices form and roll up into a primary vortex. The primary vortex further entrains fluid leading to the onset of nonlinear asymptotic stage and formation of secondary vortex bands. We investigate the linear and nonlinear effects of magnetic field on this three-stage evolution of KH instability. Flow field features such as circulation, gauge pressure and perturbation energies are utilized to delineate the parameter space into strong, weak and intermediate magnetic-field stabilization regimes. The mechanisms of magnetic field stabilization in each of the three regimes is investigated using direct numerical simulations. In the third study, the evolution of pressure-, kinetic- and magnetic-perturbation energies for the case of compressible magnetohydrodynamic (MHD) planar jets is investigated. A streamwise background magnetic field is again applied. The change in the nature of interactions between velocity and magnetic fields due to compressibility is established using linear analysis. Numerical simulations of single mode and random, isotropic initial perturbations are performed to examine these new agencies of exchange and their subsequent effect on the overall stability of the flow field. The findings of this dissertation are expected to further our understanding of various compressible and magnetic field mechanisms and their roles in perturbation evolution. This will aid in the development of closure models for MHD shear flows which could be used for designing efficient plasma propulsion engines and flow control devices

ICON-Sapphire: simulating the components of the Earth system and their interactions at kilometer and subkilometer scales

International audienceState-of-the-art Earth system models typically employ grid spacings of O(100 km), which is too coarse to explicitly resolve main drivers of the flow of energy and matter across the Earth system. In this paper, we present the new ICON-Sapphire model configuration, which targets a representation of the components of the Earth system and their interactions with a grid spacing of 10 km and finer. Through the use of selected simulation examples, we demonstrate that ICON-Sapphire can (i) be run coupled globally on seasonal timescales with a grid spacing of 5 km, on monthly timescales with a grid spacing of 2.5 km, and on daily timescales with a grid spacing of 1.25 km; (ii) resolve large eddies in the atmosphere using hectometer grid spacings on limited-area domains in atmosphere-only simulations; (iii) resolve submesoscale ocean eddies by using a global uniform grid of 1.25 km or a telescoping grid with the finest grid spacing at 530 m, the latter coupled to a uniform atmosphere; and (iv) simulate biogeochemistry in an ocean-only simulation integrated for 4 years at 10 km. Comparison of basic features of the climate system to observations reveals no obvious pitfalls, even though some observed aspects remain difficult to capture. The throughput of the coupled 5 km global simulation is 126 simulated days per day employing 21 % of the latest machine of the German Climate Computing Center. Extrapolating from these results, multi-decadal global simulations including interactive carbon are now possible, and short global simulations resolving large eddies in the atmosphere and submesoscale eddies in the ocean are within reach

ICON-Sapphire: simulating the components of the Earth system and their interactions at kilometer and subkilometer scales

International audienceState-of-the-art Earth system models typically employ grid spacings of O(100 km), which is too coarse to explicitly resolve main drivers of the flow of energy and matter across the Earth system. In this paper, we present the new ICON-Sapphire model configuration, which targets a representation of the components of the Earth system and their interactions with a grid spacing of 10 km and finer. Through the use of selected simulation examples, we demonstrate that ICON-Sapphire can (i) be run coupled globally on seasonal timescales with a grid spacing of 5 km, on monthly timescales with a grid spacing of 2.5 km, and on daily timescales with a grid spacing of 1.25 km; (ii) resolve large eddies in the atmosphere using hectometer grid spacings on limited-area domains in atmosphere-only simulations; (iii) resolve submesoscale ocean eddies by using a global uniform grid of 1.25 km or a telescoping grid with the finest grid spacing at 530 m, the latter coupled to a uniform atmosphere; and (iv) simulate biogeochemistry in an ocean-only simulation integrated for 4 years at 10 km. Comparison of basic features of the climate system to observations reveals no obvious pitfalls, even though some observed aspects remain difficult to capture. The throughput of the coupled 5 km global simulation is 126 simulated days per day employing 21 % of the latest machine of the German Climate Computing Center. Extrapolating from these results, multi-decadal global simulations including interactive carbon are now possible, and short global simulations resolving large eddies in the atmosphere and submesoscale eddies in the ocean are within reach

ICON-Sapphire: simulating the components of the Earth system and their interactions at kilometer and subkilometer scales

International audienceState-of-the-art Earth system models typically employ grid spacings of O(100 km), which is too coarse to explicitly resolve main drivers of the flow of energy and matter across the Earth system. In this paper, we present the new ICON-Sapphire model configuration, which targets a representation of the components of the Earth system and their interactions with a grid spacing of 10 km and finer. Through the use of selected simulation examples, we demonstrate that ICON-Sapphire can (i) be run coupled globally on seasonal timescales with a grid spacing of 5 km, on monthly timescales with a grid spacing of 2.5 km, and on daily timescales with a grid spacing of 1.25 km; (ii) resolve large eddies in the atmosphere using hectometer grid spacings on limited-area domains in atmosphere-only simulations; (iii) resolve submesoscale ocean eddies by using a global uniform grid of 1.25 km or a telescoping grid with the finest grid spacing at 530 m, the latter coupled to a uniform atmosphere; and (iv) simulate biogeochemistry in an ocean-only simulation integrated for 4 years at 10 km. Comparison of basic features of the climate system to observations reveals no obvious pitfalls, even though some observed aspects remain difficult to capture. The throughput of the coupled 5 km global simulation is 126 simulated days per day employing 21 % of the latest machine of the German Climate Computing Center. Extrapolating from these results, multi-decadal global simulations including interactive carbon are now possible, and short global simulations resolving large eddies in the atmosphere and submesoscale eddies in the ocean are within reach