Mark R. Petersen

BAROCLINIC VORTICITY PRODUCTION IN PROTOPLANETARY DISKS. I. VORTEX FORMATION

The formation of vortices in protoplanetary disks is explored via pseudospectral numerical simulations of an anelastic-gas model. This model is a coupled set of equations for vorticity and temperature in two dimensions that includes baroclinic vorticity production and radiative cooling. Vortex formation is unambiguously shown to be caused by baroclinicity, because (1) these simulations have zero initial perturbation vorticity and a nonzero initial temperature distribution, and (2) turning off the baroclinic term halts vortex formation, as shown by an immediate drop in kinetic energy and vorticity. Vortex strength increases with larger background temperature gradients, warmer background temperatures, larger initial temperature perturbations, higher Reynolds number, and higher resolution. In the simulations presented here, vortices form when the background temperatures are ~200 K and vary radially as r-0.25, the initial vorticity perturbations are zero, the initial temperature perturbations are 5% of the background, and the Reynolds number is 109. A sensitivity study consisting of 74 simulations showed that as resolution and Reynolds number increase, vortices can form with smaller initial temperature perturbations, lower background temperatures, and smaller background temperature gradients. For the parameter ranges of these simulations, the disk is shown to be convectively stable by the Solberg-Hoiland criteria.

BAROCLINIC VORTICITY PRODUCTION IN PROTOPLANETARY DISKS. II. VORTEX GROWTH AND LONGEVITY

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.

Role of global warming on the statistics of record-breaking temperatures.

We theoretically study the statistics of record-breaking daily temperatures and validate these predictions using both Monte Carlo simulations and 126 years of available data from the city of Philadelphia. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperature distribution in Philadelphia, as a function of the number of years of observation. We then consider the case of global warming, where the mean temperature systematically increases with time. Over the 126-year time range of observations, we argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events, a conclusion that is supported by numerical simulations and by the Philadelphia data. We also study the role of correlations between temperatures on successive days and find that they do not affect the frequency or magnitude of record temperature events.

An image-based approach to extreme scale in situ visualization and analysis

Extreme scale scientific simulations are leading a charge to exascale computation, and data analytics runs the risk of being a bottleneck to scientific discovery. Due to power and I/O constraints, we expect in situ visualization and analysis will be a critical component of these workflows. Options for extreme scale data analysis are often presented as a stark contrast: write large files to disk for interactive, exploratory analysis, or perform in situ analysis to save detailed data about phenomena that a scientists knows about in advance. We present a novel framework for a third option - a highly interactive, image-based approach that promotes exploration of simulation results, and is easily accessed through extensions to widely used open source tools. This in situ approach supports interactive exploration of a wide range of results, while still significantly reducing data movement and storage.

Forcing for statistically stationary compressible isotropic turbulence

Linear forcing has been proposed as a useful method for forced isotropic turbulence simulations because it is a physically realistic forcing method with a straightforward implementation in physical-space numerical codes [T. S. Lundgren, “Linearly forced isotropic turbulence,” Annual Research Briefs (Center for Turbulence Research, Stanford, CA, 2003), p. 461; C. Rosales and C. Meneveau, “Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,” Phys. Fluids 17, 095106 (2005)]. Here, extensions to the compressible case are discussed. It is shown that, unlike the incompressible case, separate solenoidal and dilatational parts for the forcing term are necessary for controlling the stationary state of the compressible case. In addition, the forcing coefficients can be cast in a form that allows the control of the stationary state values of the total dissipation (and thus the Kolmogorov microscale) and the ratio of dilatational to solenoidal di...

Adaptive Extraction and Quantification of Geophysical Vortices

We consider the problem of extracting discrete two-dimensional vortices from a turbulent flow. In our approach we use a reference model describing the expected physics and geometry of an idealized vortex. The model allows us to derive a novel correlation between the size of the vortex and its strength, measured as the square of its strain minus the square of its vorticity. For vortex detection in real models we use the strength parameter to locate potential vortex cores, then measure the similarity of our ideal analytical vortex and the real vortex core for different strength thresholds. This approach provides a metric for how well a vortex core is modeled by an ideal vortex. Moreover, this provides insight into the problem of choosing the thresholds that identify a vortex. By selecting a target coefficient of determination (i.e., statistical confidence), we determine on a per-vortex basis what threshold of the strength parameter would be required to extract that vortex at the chosen confidence. We validate our approach on real data from a global ocean simulation and derive from it a map of expected vortex strengths over the global ocean.

The LANS-α and Leray turbulence parameterizations in primitive equation ocean modeling

Ocean modeling presents several unique technical challenges: there is a tremendous range of spatial scales; the kinetic energy forcing scale occurs at the Rossby radius of deformation (20–100 km), which is often at or below the grid resolution; and mixing is strongly anisotropic, occurring primarily along nearly horizontal isopycnal surfaces. We present analysis and numerical results to show that the Lagrangian-averaged Navier–Stokes alpha (LANS-α) turbulence parameterization and, to a lesser extent, the Leray parameterization are well suited to ocean modeling. LANS-α and Leray are fundamentally different from purely dissipative turbulence models in that both LANS-α and Leray are more energetic and produce more eddy structure near the gridscale. This is consistent with expectation from linear stability analysis, where it has been shown that these models resolve the process of baroclinic instability on coarser meshes than standard Navier–Stokes. Formulations of LANS-α and Leray models for the primitive equations are presented. In an idealized ocean channel domain, LANS-α produces turbulence statistics in kinetic energy, eddy kinetic energy and temperature distributions that resemble a doubled-resolution simulation without LANS-α. Leray produces qualitatively similar results, but to a lesser degree than LANS-α. Finally, the Leray model is tested in a North Atlantic domain with realistic topography and forcing, and produces higher kinetic and eddy kinetic energy than the non-Leray model.

New phenomena in variable-density Rayleigh?Taylor turbulence

This paper presents several issues related to mixing and turbulence structure in buoyancy-driven turbulence at low to moderate Atwood numbers, A, found from direct numerical simulations in two configurations: classical Rayleigh–Taylor instability and an idealized triply periodic Rayleigh–Taylor flow. Simulations at A up to 0.5 are used to examine the turbulence characteristics and contrast them with those obtained close to the Boussinesq approximation. The data sets used represent the largest simulations to date in each configuration. One of the more remarkable issues explored, first reported in (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145–80), is the marked difference in mixing between different density fluids as opposed to the mixing that occurs between fluids of commensurate densities, corresponding to the Boussinesq approximation. Thus, in the triply periodic configuration and the non-Boussinesq case, an initially symmetric density probability density function becomes skewed, showing that the mixing is asymmetric, with pure heavy fluid mixing more slowly than pure light fluid. A mechanism producing the mixing asymmetry is proposed and the consequences for the classical Rayleigh–Taylor configuration are discussed. In addition, it is shown that anomalous small-scale anisotropy found in the homogeneous configuration (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145–80) and Rayleigh–Taylor turbulence at A=0.5 (Livescu et al 2008 J. Turbul. 10 1–32) also occurs near the Boussinesq limit. Results pertaining to the moment closure modelling of Rayleigh–Taylor turbulence are also presented. Although the Rayleigh–Taylor mixing layer width reaches self-similar growth relatively fast, the lower-order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. Since eddy diffusivity in the popular gradient transport hypothesis is proportional to the turbulent Reynolds number, the dissipation rate and turbulent transport have different length scales long after the onset of the self-similar growth for the layer growth. To highlight the importance of turbulent transport, variable density energy budgets for the kinetic energy, mass flux and density-specific volume covariance equations, necessary for a moment closure of the flow, are provided.

Verifying Scientific Simulations via Comparative and Quantitative Visualization

This article presents a visualization-assisted process that verifies scientific-simulation codes. Code verification is necessary because scientists require accurate predictions to interpret data confidently. This verification process integrates iterative hypothesis verification with comparative, feature, and quantitative visualization. Following this process can help identify differences in cosmological and oceanographic simulations.

Lateral Mixing in the Eddying Regime and a New Broad‐Ranging Formulation

We survey a number of issues associated with lateral dissipation in eddyresolving ocean models and present two effective techniques. The first is a specification of lateral viscosity that is closely related to that of Chassignet and Garraffo [2001], involving the combined application of biharmonic and Laplacian forms of viscosity. The specification can in principle be applied across a broad range of model resolution, although our testing was performed only at eddy-resolving scale where a relatively simple form suffices. The second is the implementation of the Lagrangian Averaged Navier Stokes (LANSα) alpha subgridscale turbulence scheme in a primitive equation ocean model, with our presentation here being largely a summary of the recent work of Hecht et al. [2008] and Petersen et al. [2008]. As an inherently non-dissipative turbulence parameterization, one can understand the higher levels of eddy variability with LANS-α as coming about through an increase in the effective Rossby radius of deformation.