Jeffrey B. Weiss

Anisotropy and coherent vortex structures in planetary turbulence

High-resolution numerical simulations were made of unforced, planetary-scale fluid dynamics. In particular, the simulation was based on the quasi-geostrophic equations for a Boussinesq fluid in a uniformly rotating and stably stratified environment, which is an idealization for large regions of either the atmosphere or ocean. The solutions show significant discrepancies from the long-standing theoretical prediction of isotropy. The discrepancies are associated with the self-organization of the flow into a large population of coherent vortices. Their chaotic interactions govern the subsequent evolution of the flow toward a final configuration that is nonturbulent.

Temporal scaling behavior of decaying two‐dimensional turbulence

Decaying two‐dimensional turbulence is characterized by the emergence of coherent vortices, which subsequently dominate the evolution. The temporal scaling behavior of the flow is analyzed using a scaling theory, a long‐time integration of the fluid equations, and a dissipative, modified point‐vortex model that represents the turbulence as a system of interacting coherent structures. Good agreement is found in the behavior of average vortex properties, low‐order moments of the flow fields, and the form of self‐similar evolution.

Revisiting freely decaying two-dimensional turbulence at millennial resolution

We study the evolution of vortex statistics in freely decaying two-dimensional turbulence at very large Reynolds number. The results obtained here confirm that the peak vorticity inside vortex cores is conserved and that the number of vortices as a function of time, N(t), decreases as a power law. In addition, the numerical findings are consistent with the predictions of the scaling theories proposed by Carnevale et al. [Phys. Rev. Lett. 66, 2735 (1991)] and Weiss and McWilliams [Phys. Fluids A 5, 608 (1993)]. We also obtain new evidence for a self-similar distribution of vortex radii and circulations, that suggests the possibility of a generic statistical behavior of the decaying phase of two-dimensional turbulence at high Reynolds number.

Vortex merging in quasi-geostrophic flows

We study symmetric vortex merger in quasi-geostrophic flows using numerical simulations with high vertical resolution. We analyse the effect of varying the vertical aspect ratio of the vortices and compare with the barotropic case. During the merging of potential vorticity cores with small aspect ratio, we observe the birth of secondary instabilities on the filaments. This is a new phenomenon not seen in baroclinic simulations having low vertical resolution. Passive Lagrangian tracers are used to explore the transport of fluid parcels during vortex merger, to provide a detailed view of the flow evolution, and to determine the value of the critical merging distance for baroclinic vortices.

The vortices of homogeneous geostrophic turbulence

A coherent-vortex analysis is made of a computational solution for the free decay of homogeneous, Charney-isotropic geostrophic turbulence at large Reynolds number. The method of analysis is a vortex detection and measurement algorithm that we call a vortex census. The census demonstrates how, through non-conservative interactions among closely approaching vortices, the vortex population evolves towards fewer, larger, sparser, and more weakly deformed vortices. After emergence from random initial conditions and a further period of population adjustment, there is a period of approximately self-similar temporal evolution in the vortex statistics. This behaviour is consistent with a mean-vortex scaling theory based on the conservation of energy, vortex extremum, and vortex aspect ratio. This period terminates as the population approaches a late-time non-turbulent end-state vortex configuration. The end state develops out of merger and alignment interactions among like-sign vortices, and even during the scaling regime, local clusters of nearly aligned vortices are common.

Lagrangian dynamics in high-dimensional point-vortex systems

We study the Lagrangian dynamics of systems of N point vortices and passive particles in a two-dimensional, doubly periodic domain. The probability distribution function of vortex velocity, pN, has a slow-velocity Gaussian component and a significant high-velocity tail caused by close vortex pairs. In the limit for N→∞, pN tends to a Gaussian. However, the form of the single-vortex velocity causes very slow convergence with N; for N≈106 the non-Gaussian high-velocity tails still play a significant role. At finite N, the Gaussian component is well modeled by an Ornstein-Uhlenbeck (OU) stochastic process with variance σN=N ln N/2π. Considering in detail the case N=100, we show that at short times the velocity autocorrelation is dominated by the Gaussian component and displays an exponential decay with a short Lagrangian decorrelation time. The close pairs have a long correlation time and cause nonergodicity over at least the time of the integration. Due to close vortex dipoles the absolute dispersion differ...

Eddies and vortices in ocean basin dynamics

A wind-driven, closed-basin quasi-geostrophic ocean model is computed at very high horizontal resolution to study the effect of increasing Reynolds number (Re) on eddy variability. Five numerical simulations are performed with identical configurations, varying only in horizontal resolution and viscosity coefficient (and therefore Re). Qualitative changes in the structure of eddy variability are evident in the dramatic increase of isolated vortex structures at the highest Re. While the time-mean kinetic energy is relatively independent of Re, the vortex emergence contributes to a continual increase with Re of eddy kinetic energy and meridional vorticity flux. The rate of increase slows somewhat at the highest Re, indicating the possibility of a regime where eddy variability becomes insensitive to further increases in Re.

Rates, pathways, and end states of nonlinear evolution in decaying two‐dimensional turbulence: Scaling theory versus selective decay

A recently proposed scaling theory of two‐dimensional turbulent decay, based on the evolutionary pathway of successive mergers of coherent vortices, is used to predict the rate and end state of the evolution. These predictions differ from those based on the selective‐decay hypothesis and traditional ideas of spectrum evolution, and they are in substantially better agreement with numerical solutions at large Reynolds number.

Co-occurrence of Northern and Southern Hemisphere Blocks as Partially Synchronized Chaos

Abstract Teleconnections between the midlatitudes of the Northern and Southern Hemispheres are diagnosed in National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis data and separately in European Centre for Medium-Range Weather Forecasts reanalysis data. The teleconnections are manifested as a small but significant tendency for blocking to occur simultaneously in the two hemispheres, though at different longitudes and different relative latitudes, during boreal winters over the period 1979–94 in both datasets. One way to explain the correlations between blocking events is as an instance of synchronized chaos, the tendency of some coupled chaotic systems to synchronize, permanently or intermittently, regardless of initial conditions. As the coupling is weakened, the systems no longer synchronize completely, but small correlations between the states of the coupled systems are observed instead. In previous work, such behavior was observed in an idealized coupled-hemi...

A wavelet-packet census algorithm for calculating vortex statistics

A generalized wavelet-packet based technique for decomposing signals into coherent and noncoherent parts is presented. The method is tested on the vorticity field of numerical simulations of weakly decaying two-dimensional turbulence. The easily recognizable coherent vortex structures that emerge are systematically filtered from the solution. Once extracted, various properties of the vortices, such as their number, size, circulation, and peak value are computed. The results compare well with a similar study [J. Fluid Mech. 219, 361 (1990); Phys. Fluids 5, 608 (1993)], which employs a complex pattern recognition technique based exclusively on a priori knowledge of the properties of the solution—that is, the features typical of the resulting vortex structures. The similarity of the results is encouraging, suggesting that the wavelet packet technique, by absorbing much of the complexity into the mathematical features of the transform itself, can provide an efficient, standardized tool that is readily extendi...