Resonant Activation of Population Extinctions

Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's demographic stochasticity and environmental noise remain poorly understood. Here, we model environmental forcing as a stochastic fluctuation between two states, one with a higher death rate than the other. We find that in general there exists a rate of fluctuations that minimizes the mean time to extinction, a phenomenon previously dubbed "resonant activation." We develop a heuristic description of the phenomenon, together with a criterion for the existence of resonant activation. Specifically the minimum extinction time arises as a result of the system approaching a scenario wherein the severity of rare events is balanced by the time interval between them. We discuss our findings within the context of more general forms of environmental noise, and suggest potential applications to evolutionary models.Comment: 12 pages, 7 Figures, Accepted for publication in Physical Review

Scaling laws for convection and jet speeds in the giant planets

Three-dimensional studies of convection in deep spherical shells have been used to test the hypothesis that the strong jet streams on Jupiter, Saturn, Uranus, and Neptune result from convection throughout the molecular envelopes. Due to computational limitations, these simulations must adopt viscosities and heat fluxes many orders of magnitude larger than the planetary values. Several numerical investigations have identified trends for how the mean jet speed varies with heat flux and viscosity, but no previous theories have been advanced to explain these trends. Here, we show using simple arguments that if convective release of potential energy pumps the jets and viscosity damps them, the mean jet speeds split into two regimes. When the convection is weakly nonlinear, the equilibrated jet speeds should scale approximately with F/nu, where F is the convective heat flux and nu is the viscosity. When the convection is strongly nonlinear, the jet speeds are faster and should scale approximately as (F/nu)^{1/2}. We demonstrate how this regime shift can naturally result from a shift in the behavior of the jet-pumping efficiency with heat flux and viscosity. Moreover, the simulations hint at a third regime where, at sufficiently small viscosities, the jet speed becomes independent of the viscosity. We show based on mixing-length estimates that if such a regime exists, mean jet speeds should scale as heat flux to the 1/4 power. Our scalings provide a good match to the mean jet speeds obtained in previous Boussinesq and anelastic, three-dimensional simulations of convection within giant planets over a broad range of parameters. When extrapolated to the real heat fluxes, these scalings suggest that the mass-weighted jet speeds in the molecular envelopes of the giant planets are much weaker--by an order of magnitude or more--than the speeds measured at cloud level.Comment: 23 pages, 10 figures, in press at Icaru

Jovian vortices and jets

We explore the conditions required for isolated vortices to exist in sheared zonal flows and the stability of the underlying zonal winds. This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming infinite; however, this model differs from the usual layer model because the lower layer is not assumed to be motionless but has a steady configuration of alternating zonal flows [1]. Steady state vortices are obtained by a simulated annealing computational method introduced in [2], generalized and applied in [3] in fluid flow, and used in the context of magnetohydrodynamics in [4-6]. Various cases of vortices with a constant potential vorticity anomaly atop zonal winds and the stability of the underlying winds are considered using a mix of computational and analytical techniques

Convectively driven shear and decreased heat flux

We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh-B\'enard convection, focusing on its ability to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($Pr$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($Ra$) sufficiently, and we explore the resulting convection for $Ra$ up to $10^{10}$. When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $Ra\to\infty$. The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $Ra$. When the large-scale shear is present with $Pr\lesssim2$, the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $Ra$ for $Pr=1$. When the shear is present with $Pr\gtrsim3$, the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $Ra$, but the growth rates are slower than any previously reported for Rayleigh-B\'enard convection without large-scale shear. We find the Nusselt numbers grow proportionally to $Ra^{0.077}$ when $Pr=3$ and to $Ra^{0.19}$ when $Pr=10$. Analogies with tokamak plasmas are described.Comment: 25 pages, 12 figures, 5 video

Biological effects of Gulf Stream meandering

A modeling study was conducted to examine the effects of time-dependent mesoscale meandering of a jet on nutrient—phytoplankton—zooplankton (NPZ) dynamics. The jet was represented as a quasi-geostrophic flow using the method of contour dynamics. Two cases for biology were examined: 1) plankton in a mixed layer of fixed depth and 2) plankton at the base of a mixed layer (i.e., pycnocline) of variable depth. When the mixed layer depth is fixed, nutrient upwelling and dilution of the phytoplankton and zooplankton populations occur along the northward branch of the meander. The additional nutrients and reduced grazing pressure leads to significant enhancement (10–20%) of the phytoplankton production and biomass, while the zooplankton biomass decreases similarly. For plankton on a material surface of variable depth, phytoplankton growth in the pycnocline is increased by the higher light levels encountered during along-isopycnal upwelling. The nutrients decrease and the zooplankton mass in the pycnocline increases by a small amount downstream of the phytoplankton peak. Although the biological enhancements found are not large, the results suggest that vertical motions resulting from mesoscale oceanographic features such as jet meanders and mid-ocean eddies can be an important source of new nutrients for oceanic plankton production

Data management for JGOFS: Theory and design

The Joint Global Ocean Flux Study (JGOFS), currently being organized under the auspices of the Scientific Committee for Ocean Research (SCOR), is intended to be a decade long internationally coordinated program. The main goal of JGOFS is to determine and understand on a global scale the processes controlling the time-varying fluxes of carbon and associated biogenic elements in the ocean and to evaluate the related exchanges with the atmosphere, sea floor and continental boundaries. 'A long-term goal of JGOFS will be to establish strategies for observing, on long time scales, changes in ocean biogeochemical cycles in relation to climate change'. Participation from a large number of U.S. and foreign institutions is expected. JGOFS investigators have begun a set of time-series measurements and global surveys of a wide variety of biological, chemical and physical quantities, detailed process-oriented studies, satellite observations of ocean color and wind stress and modeling of the bio-geochemical processes. These experiments will generate data in amounts unprecedented in the biological and chemical communities; rapid and effortless exchange of these data will be important to the success of JGOFS

Time-Dependent Eddy-Mean Energy Diagrams and Their Application to the Ocean

Insight into the global ocean energy cycle and its relationship to climate variability can be gained by examining the temporal variability of eddy–mean flow interactions. A time-dependent version of the Lorenz energy diagram is formulated and applied to energetic ocean regions from a global, eddying state estimate. The total energy in each snapshot is partitioned into three components: energy in the mean flow, energy in eddies, and energy temporal anomaly residual, whose time mean is zero. These three terms represent, respectively, correlations between mean quantities, correlations between eddy quantities, and eddy-mean correlations. Eddy–mean flow interactions involve energy exchange among these three components. The temporal coherence about energy exchange during eddy–mean flow interactions is assessed. In the Kuroshio and Gulf Stream Extension regions, a suppression relation is manifested by a reduction in the baroclinic energy pathway to the eddy kinetic energy (EKE) reservoir following a strengthening of the barotropic energy pathway to EKE; the baroclinic pathway strengthens when the barotropic pathway weakens. In the subtropical gyre and Southern Ocean, a delay in energy transfer between different reservoirs occurs during baroclinic instability. The delay mechanism is identified using a quasigeostrophic, two-layer model; part of the potential energy in large-scale eddies, gained from the mean flow, cascades to smaller scales through eddy stirring before converting to EKE. The delay time is related to this forward cascade and scales linearly with the eddy turnover time. The relation between temporal variations in wind power input and eddy–mean flow interactions is also assessed

Parametric instability in oscillatory shear flows

Author Posting. © Cambridge University Press, 2003. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 481 (2003): 329-353, doi:10.1017/S0022112003004051.In this article we investigate time-periodic shear flows in the context of the two-dimensional vorticity equation, which may be applied to describe certain large-scale atmospheric and oceanic flows. The linear stability analyses of both discrete and continuous profiles demonstrate that parametric instability can arise even in this simple model: the oscillations can stabilize (destabilize) an otherwise unstable (stable) shear flow, as in Mathieu's equation (Stoker 1950). Nonlinear simulations of the continuous oscillatory basic state support the predictions from linear theory and, in addition, illustrate the evolution of the instability process and thereby show the structure of the vortices that emerge. The discovery of parametric instability in this model suggests that this mechanism can occur in geophysical shear flows and provides an additional means through which turbulent mixing can be generated in large-scale flows.F.P.’s and G.F.’s research was supported by grants from NSF, OPP- 9910052 and OCE-0137023. J.P.’s research is supported in part by a grant from NSF, OCE-9901654

Rotating convection : 1995 Summer Study Program in Geophysical Fluid Dynamics

The 1995 program in Geophysical Fluid Dynamics addressed "Rotating Convection," with particular emphasis on high-Rayleigh-number convection and on convection in the ocean.Funding was provided by the National Science Foundation under Grant No. OCE-8901012

Gravitational signature of Jupiter’s internal dynamics

Telescopic observations and space missions to Jupiter have provided vast information about Jupiter's cloud level winds, but the depth to which these winds penetrate has remained an ongoing mystery. Scheduled to be launched in 2011, the Jupiter orbiter Juno will make high-resolution observations of Jupiter's gravity field. In this paper we show that these measurements are sensitive to the depth of the internal winds. We use dynamical models ranging from an idealized thermal wind balance analysis, using the observed cloud-top winds, to a full general circulation model (GCM). We relate the depth of the dynamics to the external gravity spectrum for different internal wind structure scenarios. In particular, we predict that substantial Jovian winds below a depth of 500 km would lead to detectable (milligal-level) gravity anomalies with respect to the expected gravity for a planet in solid body rotation