Mark Petersen | Los Alamos National Laboratory (original) (raw)

Papers by Mark Petersen

Applied Mathematics and Computation, 2002

We develop a one-dimensional, nonlinear, nonlocal model that governs the advection and dispersion... more We develop a one-dimensional, nonlinear, nonlocal model that governs the advection and dispersion of a chemical solute that reacts with a porous, mineral fabric to produce a change in porosity and a change in mineralogy. The flow is either driven by a pressure gradient, consistent with Darcy's law, or an imposed boundary velocity. Constitutive equations based on geometric considerations relate volume changes to the replacement reactions that occur. Numerical methods are used to analyze the behavior of the system. Ó

The Astrophysical Journal, 2007

The factors affecting vortex growth in convectively stable protoplanetary disks are explored usin... more The factors affecting vortex growth in convectively stable protoplanetary disks are explored using numerical simulations of a two-dimensional anelastic-gas model that includes baroclinic vorticity production and radiative cooling. The baroclinic feedback, in which anomalous temperature gradients produce vorticity through the baroclinic term and vortices then reinforce these temperature gradients, is found to be an important process in the rate of growth of vortices in the disk. Factors that strengthen the baroclinic feedback include fast radiative cooling, high thermal diffusion, and large radial temperature gradients in the background temperature. When the baroclinic feedback is sufficiently strong, anticyclonic vortices form from initial random perturbations and maintain their strength for the duration of the simulation, for over 600 orbital periods. Based on both simulations and a simple vortex model, we find that the local angular momentum transport due to a single vortex may be inward or outward, depending on its orientation. The global angular momentum transport is highly variable in time and is sometimes negative and sometimes positive. This result is for an anelastic-gas model and does not include shocks that could affect angular momentum transport in a compressible-gas disk.

Physics of Fluids, 2006

We investigate the interaction of two ellipsoidal vortices in the three-dimensional quasigeostrop... more We investigate the interaction of two ellipsoidal vortices in the three-dimensional quasigeostrophic fluid equations by first studying a reduced model of vortex interaction, the ellipsoidal moment model, and second by comparing the results to corresponding numerical simulations. The ellipsoidal moment model approximates the interaction of two ellipsoidal lumps of potential vorticity by a finite-degree-of-freedom Hamiltonian system. This approximation is derived explicitly in the natural moment coordinate system to first order in the ratio of the size of the vortices to their separation. Using this Hamiltonian system for the case of initially spheroidal identical vortices, the linear stability of vertically aligned vortices is analyzed. A new dynamical criterion for vortex merger and alignment is proposed and shown to give a clear and reasonable boundary for vortex merger. A similar boundary is shown to exist in the size of the largest Lyapunov exponent, although not in the chaotic region as measured by the 0-1 test of Gottwald and Melbourne ͓Proc. R. Soc. London, Ser. A 460, 603 ͑2004͔͒. There is no such sharp boundary for vortex alignment in this reduced model. A series of numerical experiments confirms the accuracy of the merger criterion used in the ellipsoidal moment model. The numerical simulations also suggest a mechanism for understanding the process of vortex alignment in terms of vortex Rossby waves.

Physics of Fluids, 2006

We present numerical simulations of decaying two-dimensional ͑2D͒ and three-dimensional quasigeos... more We present numerical simulations of decaying two-dimensional ͑2D͒ and three-dimensional quasigeostrophic ͑3D QG͒ turbulence. The resulting vorticity fields are decomposed into three components: the vortex cores, the strain cells, and the background. In 2D, the vortex cores induce five times the energy as the background, while in 3D QG the background plays a more dominant role and induces the same amount of energy as the vortex cores, quantifying previous observations that 3D QG has a more active filamentary background. The probability density function of the total velocity field is nearly Gaussian in 3D QG but significantly less so in 2D. In both 2D and 3D QG, the velocities induced by the vortex cores and the strain cells are non-Gaussian. In both 2D and 3D QG turbulence, the enstrophy spectrum of the background is close to k −1 predicted by inverse cascade theories.

Journal of Physics: Conference Series, 2011

We have conducted high resolution, high Reynolds number Direct Numerical Simulations (DNS) of the... more We have conducted high resolution, high Reynolds number Direct Numerical Simulations (DNS) of the Rayleigh-Taylor (RT) instability on the 0.5 petaflop, 150k compute cores BG/L Dawn supercomputer at Lawrence Livermore National Lab. This includes a suite of simulations with Atwood number ranging from 0.04 to 0.9 and grid size of 1024^2 by 4096, and a high resolution simulation of grid size 4096^3 and Atwood number of 0.75. After the layer width has developed substantially, additional branched simulations have been run under reverse gravity and zero gravity conditions. The simulations provide an extensive database to study Rayleigh-Taylor turbulence, including mixing layer growth rate and self-similar behavior, turbulence and mixing asymmetries, and spectral characteristics. Individual terms in the moments transport equations are recorded to develop and validate turbulence closure models.

Computer Graphics Forum, 2011

We present analysis and visualization of flow data from a high-resolution simulation of the dynam... more We present analysis and visualization of flow data from a high-resolution simulation of the dynamical behavior of the global ocean. Of particular scientific interest are coherent vortical features called mesoscale eddies. We first extract high-vorticity features using a metric from the oceanography community called the Okubo-Weiss parameter. We then use a new circularity criterion to differentiate eddies from other non-eddy features like meanders in strong background currents. From these data, we generate visualizations showing the three-dimensional structure and distribution of ocean eddies. Additionally, the characteristics of each eddy are recorded to form an eddy census that can be used to investigate correlations among variables such as eddy thickness, depth, and location. From these analyses, we gain insight into the role eddies play in large-scale ocean circulation.

Recent numerical simulations of protoplanetary disks using the compressible Navier-Stokes equatio... more Recent numerical simulations of protoplanetary disks using the compressible Navier-Stokes equations with radiative heat transport have shown large-scale vortex formation and positive angular momentum transport. In particular, Klahr and Bodenheimer (2003) observed global baroclinic instabilities in the presence of a radial entropy gradient. To gain a better understanding of the physical basis of these results, we have derived a simplified protoplanetary disk model based on the anelastic equation which includes the necessary components for vortex formation due to baroclinic instabilities. The model equations for entropy and vorticity include radiative damping, entropy gradients, and are coupled by a baroclinic term. A numerical model of these equations has been created to investigate the effects of the radial entropy gradient on vortex formation. The model is two dimensional pseudo-spectral on an annulus and uses Fourier-Chebyshev basis functions. Our simplified numerical model will b...

Applied Mathematics and Computation, 2002

We develop a one-dimensional, nonlinear, nonlocal model that governs the advection and dispersion... more We develop a one-dimensional, nonlinear, nonlocal model that governs the advection and dispersion of a chemical solute that reacts with a porous, mineral fabric to produce a change in porosity and a change in mineralogy. The flow is either driven by a pressure gradient, consistent with Darcy's law, or an imposed boundary velocity. Constitutive equations based on geometric considerations relate volume changes to the replacement reactions that occur. Numerical methods are used to analyze the behavior of the system. Ó

The Astrophysical Journal, 2007

The factors affecting vortex growth in convectively stable protoplanetary disks are explored usin... more The factors affecting vortex growth in convectively stable protoplanetary disks are explored using numerical simulations of a two-dimensional anelastic-gas model that includes baroclinic vorticity production and radiative cooling. The baroclinic feedback, in which anomalous temperature gradients produce vorticity through the baroclinic term and vortices then reinforce these temperature gradients, is found to be an important process in the rate of growth of vortices in the disk. Factors that strengthen the baroclinic feedback include fast radiative cooling, high thermal diffusion, and large radial temperature gradients in the background temperature. When the baroclinic feedback is sufficiently strong, anticyclonic vortices form from initial random perturbations and maintain their strength for the duration of the simulation, for over 600 orbital periods. Based on both simulations and a simple vortex model, we find that the local angular momentum transport due to a single vortex may be inward or outward, depending on its orientation. The global angular momentum transport is highly variable in time and is sometimes negative and sometimes positive. This result is for an anelastic-gas model and does not include shocks that could affect angular momentum transport in a compressible-gas disk.

Physics of Fluids, 2006

We investigate the interaction of two ellipsoidal vortices in the three-dimensional quasigeostrop... more We investigate the interaction of two ellipsoidal vortices in the three-dimensional quasigeostrophic fluid equations by first studying a reduced model of vortex interaction, the ellipsoidal moment model, and second by comparing the results to corresponding numerical simulations. The ellipsoidal moment model approximates the interaction of two ellipsoidal lumps of potential vorticity by a finite-degree-of-freedom Hamiltonian system. This approximation is derived explicitly in the natural moment coordinate system to first order in the ratio of the size of the vortices to their separation. Using this Hamiltonian system for the case of initially spheroidal identical vortices, the linear stability of vertically aligned vortices is analyzed. A new dynamical criterion for vortex merger and alignment is proposed and shown to give a clear and reasonable boundary for vortex merger. A similar boundary is shown to exist in the size of the largest Lyapunov exponent, although not in the chaotic region as measured by the 0-1 test of Gottwald and Melbourne ͓Proc. R. Soc. London, Ser. A 460, 603 ͑2004͔͒. There is no such sharp boundary for vortex alignment in this reduced model. A series of numerical experiments confirms the accuracy of the merger criterion used in the ellipsoidal moment model. The numerical simulations also suggest a mechanism for understanding the process of vortex alignment in terms of vortex Rossby waves.

Physics of Fluids, 2006

We present numerical simulations of decaying two-dimensional ͑2D͒ and three-dimensional quasigeos... more We present numerical simulations of decaying two-dimensional ͑2D͒ and three-dimensional quasigeostrophic ͑3D QG͒ turbulence. The resulting vorticity fields are decomposed into three components: the vortex cores, the strain cells, and the background. In 2D, the vortex cores induce five times the energy as the background, while in 3D QG the background plays a more dominant role and induces the same amount of energy as the vortex cores, quantifying previous observations that 3D QG has a more active filamentary background. The probability density function of the total velocity field is nearly Gaussian in 3D QG but significantly less so in 2D. In both 2D and 3D QG, the velocities induced by the vortex cores and the strain cells are non-Gaussian. In both 2D and 3D QG turbulence, the enstrophy spectrum of the background is close to k −1 predicted by inverse cascade theories.

Journal of Physics: Conference Series, 2011

We have conducted high resolution, high Reynolds number Direct Numerical Simulations (DNS) of the... more We have conducted high resolution, high Reynolds number Direct Numerical Simulations (DNS) of the Rayleigh-Taylor (RT) instability on the 0.5 petaflop, 150k compute cores BG/L Dawn supercomputer at Lawrence Livermore National Lab. This includes a suite of simulations with Atwood number ranging from 0.04 to 0.9 and grid size of 1024^2 by 4096, and a high resolution simulation of grid size 4096^3 and Atwood number of 0.75. After the layer width has developed substantially, additional branched simulations have been run under reverse gravity and zero gravity conditions. The simulations provide an extensive database to study Rayleigh-Taylor turbulence, including mixing layer growth rate and self-similar behavior, turbulence and mixing asymmetries, and spectral characteristics. Individual terms in the moments transport equations are recorded to develop and validate turbulence closure models.

Computer Graphics Forum, 2011

We present analysis and visualization of flow data from a high-resolution simulation of the dynam... more We present analysis and visualization of flow data from a high-resolution simulation of the dynamical behavior of the global ocean. Of particular scientific interest are coherent vortical features called mesoscale eddies. We first extract high-vorticity features using a metric from the oceanography community called the Okubo-Weiss parameter. We then use a new circularity criterion to differentiate eddies from other non-eddy features like meanders in strong background currents. From these data, we generate visualizations showing the three-dimensional structure and distribution of ocean eddies. Additionally, the characteristics of each eddy are recorded to form an eddy census that can be used to investigate correlations among variables such as eddy thickness, depth, and location. From these analyses, we gain insight into the role eddies play in large-scale ocean circulation.

Recent numerical simulations of protoplanetary disks using the compressible Navier-Stokes equatio... more Recent numerical simulations of protoplanetary disks using the compressible Navier-Stokes equations with radiative heat transport have shown large-scale vortex formation and positive angular momentum transport. In particular, Klahr and Bodenheimer (2003) observed global baroclinic instabilities in the presence of a radial entropy gradient. To gain a better understanding of the physical basis of these results, we have derived a simplified protoplanetary disk model based on the anelastic equation which includes the necessary components for vortex formation due to baroclinic instabilities. The model equations for entropy and vorticity include radiative damping, entropy gradients, and are coupled by a baroclinic term. A numerical model of these equations has been created to investigate the effects of the radial entropy gradient on vortex formation. The model is two dimensional pseudo-spectral on an annulus and uses Fourier-Chebyshev basis functions. Our simplified numerical model will b...