Turnover Time Scale Research Articles

PRE-MAIN SEQUENCE EVOLUTIONS OF SOLAR ABUNDANCE LOW MASS STARS

We present the Pre-Main Sequence (PMS) evolutionary tracks of stars with <TEX>$0.065{\sim}5.0M_{\odot}$</TEX>. The models were evolved from the PMS stellar birthline to the onset of hydrogen burning in the core. The convective turnover timescales which enables an observational test of theoretical model, particulary in the stellar dynamic activity, are also calculated. All models have Sun-like metal abundance, typically considered as the stars in the Galactic disk and the star formation region of Population I star. The convection phenomenon is treated by the usual mixing length approximation. All evolutionary tracks are available upon request.

The X-ray activity-rotation relation of T Tauri stars in Taurus-Auriga

Context. The Taurus-Auriga star-forming complex hosts the only population of T Tauri stars in which an anticorrelation of X-ray activity and rotation period has been observed. Aims. We aim to explain the origin of the X-ray activity‐rotation relation in Taurus-Auriga. We also aim to put the X-ray activity of these stars into the context of the activity of late-type mai n-sequence stars and T Tauri stars in the Orion Nebula Cluster. Methods. We have used XMM-Newton’s European Photon Imaging Cameras to perform the most sensi tive survey to date of Xray emission (0.3-10 keV) from young stars in Taurus-Auriga. We investigated the dependences of X-ray activity measures ‐ X-ray luminosity, LX, its ratio with the stellar luminosity, LX/L⋆, and the surface-averaged X-ray flux, FXS ‐ on rotation period and compared them with predictions based solely on the observed dependence of LX on a star’s L⋆ and whether it is accreting or not. We tested for differences in the distributions of LX/L⋆ of fast and slow rotators, accretors and non-accretors, and compared the dependence of LX/L⋆ on the ratio of the rotation period and the convective turnover timescale, the Rossby number, with that of late-type main-sequence stars. Results. We found significant anticorrelations of LX and FXS with rotation period, but these could be explained by the typically higher stellar luminosity and effective temperature of fast-rotators in Taurus-Auriga and a near-linear dependence of LX on L⋆. We found no evidence for a dependence of LX/L⋆ on rotation period, but for accretors to have lower LX/L⋆ than non-accretors at all rotation periods. The Rossby numbers of accretors and non-accretors were found to be the same as those of late-type main-sequence stars showing saturated X-ray emission. Conclusions. Non-accreting T Tauri stars show X-ray activity entirely consistent with the saturated activity of fast-rotating late -type main-sequence stars. Accreting T Tauri stars show lower X-ray activity, but this cannot be attributed to their slower ro tation.

Anisotropic Cascades in Interstellar Medium Turbulence

Anisotropic turbulent cascades in the solar wind and interstellar medium (ISM) are investigated using three-dimensional incompressible magnetohydrodynamic (MHD) simulations with a numerical resolution of 2563. In the absence of an external magnetic field (B0 = 0), the anisotropy in the MHD turbulent fluctuations is mediated primarily by the local magnetic field. The latter leads to a disparity in the spectral transfer of energy along and across the local mean magnetic field. While the anisotropic cascades give rise to the relationship ∥ ∝ between the parallel (∥ ~ 1/k∥) and perpendicular (⊥ ~ 1/k⊥) length scales of the eddies relative to the local magnetic field, the global energy is found to obey a Kolmogorov-like k-5/3 anisotropic spectrum in our simulations where turbulence is predominantly subcritical. In the latter, the turbulent cascades are dominated by the nonlinear eddy turnover timescales compared to the linear Alfven wave periods. The critical-balance criterion is therefore not necessarily satisfied in fully developed, strong, anisotropic, high plasma-β magnetofluid ISM turbulence.

Mean-field view on geodynamo models

Mean-field theory provides a useful description of magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In mean-field theory, the coefficients occurring in the expansion of the mean electromotive force in terms of the mean field and its derivatives are used to analyse and to simulate dynamo action. In this study, we consider dynamo processes in a rotating spherical shell similar to the Earth`s outer core; mean fields are then defined by azimuthal averaging. We present two different techniques for determining mean-field coefficients and apply both to a simulation of rotating magnetoconvection and a simple quasi-stationary dynamo (the benchmark example). In both examples, the tensorial mean-field coefficients are highly anisotropic and demonstrate the existence of an α2 -mechanism along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the benchmark example. The first technique is also applied to two highly time-dependent dynamos, one exhibiting a strongly columnar and the other a fully developed convection pattern. The resulting time-averaged mean-field coefficients resemble those obtained in the magnetoconvection and benchmark example which indicates that similar dynamo processes take place. The temporal fluctuations of mean-field coefficients occur on the convective turnover timescale. These fluctuations are particularly large in the fully developed regime, because the velocity field lacks any equatorial symmetry.With the aim of comparing mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all the previously determined mean-field coefficients has been constructed. In the magnetoconvection and benchmark example, the match between direct numerical simulations and mean-field simulations is best if at least 17 mean-field coefficients are kept. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from a direct numerical simulation is in good agreement with the result given by the mean-field model. However, this match is not satisfactory in the benchmark example. Here, the traditional representation of the mean electromotive force including no higher than first-order derivatives is not justified. The lack of a clear scale separation renders the traditional mean-field approach inappropriate in this example.

On spectral scaling laws for incompressible anisotropic magnetohydrodynamic turbulence

A heuristic model is given for anisotropic magnetohydrodynamics turbulence in the presence of a uniform external magnetic field B0ê‖. The model is valid for both moderate and strong B0 and is able to describe both the strong and weak wave turbulence regimes as well as the transition between them. The main ingredient of the model is the assumption of constant ratio at all scales between the linear wave period and the nonlinear turnover time scale. Contrary to the model of critical balance introduced by Goldreich and Sridhar [Astrophys. J. 438, 763 (1995)], it is not assumed, in addition, that this ratio be equal to unity at all scales. This allows us to make use of the Iroshnikov–Kraichnan phenomenology; it is then possible to recover the widely observed anisotropic scaling law k‖∝k⊥2∕3 between parallel and perpendicular wave numbers (with reference to B0ê‖) and to obtain for the total-energy spectrum E(k⊥,k‖)∼k⊥−αk‖−β the universal prediction, 3α+2β=7. In particular, with such a prediction, the weak Alfvén wave turbulence constant-flux solution is recovered and, for the first time, a possible explanation to its precursor found numerically by Galtier et al. [J. Plasma Phys. 63, 447 (2000)] is given.

Drizzle in Stratiform Boundary Layer Clouds. Part I: Vertical and Horizontal Structure

Abstract Detailed observations of stratiform boundary layer clouds on 12 days are examined with specific reference to drizzle formation processes. The clouds differ considerably in mean thickness, liquid water path (LWP), and droplet concentration. Cloud-base precipitation rates differ by a factor of 20 between cases. The lowest precipitation rate is found in the case with the highest droplet concentration even though this case had by far the highest LWP, suggesting that drizzle can be severely suppressed in polluted clouds. The vertical and horizontal structure of cloud and drizzle liquid water and bulk microphysical parameters are examined in detail. In general, the highest concentration of r &amp;gt; 20 μm drizzle drops is found toward the top of the cloud, and the mean volume radius of the drizzle drops increases monotonically from cloud top to base. The resulting precipitation rates are largest at the cloud base but decrease markedly only in the upper third of the cloud. Below cloud, precipitation rates decrease markedly with distance below base due to evaporation, and are broadly consistent in most cases with the results from a simple sedimentation–evaporation model. Evidence is presented that suggests evaporating drizzle is cooling regions of the subcloud layer, which could result in dynamical feedbacks. A composite power spectrum of the horizontal spatial series of precipitation rate is found to exhibit a power-law scaling from the smallest observable scales to close to the maximum observable scale (∼30 km). The exponent is considerably lower (1.1–1.2) than corresponding exponents for LWP variability obtained in other studies (∼1.5–2), demonstrating that there is relatively more variability of drizzle on small scales. Singular measures analysis shows that drizzle fields are much more intermittent than the cloud liquid water content fields, consistent with a drizzle production process that depends strongly upon liquid water content. The adiabaticity of the clouds, which can be modeled as a simple balance between drizzle loss and turbulent replenishment, is found to decrease if the time scale for drizzle loss is shorter than roughly 5–10 eddy turnover time scales. Finally, the data are compared with three simple scalings derived from recent observations of drizzle in subtropical stratocumulus clouds.

Evolutionary status of UV Piscium and its comparison with other short period RS CVn binaries

From the derived elements of UV Piscium, the evolutionary status of both of its components are compared with the Schaller et al. models and also with other main sequence systems having spectral types of late F to K range. From these models the ages of the components of UV Psc are determined. The Rossby number, which is a measure of chromospheric activity, has been derived from the convective turnover time scales and also from the age estimates.

What Causes the Divergences in Local Second-Order Closure Models?

Abstract It has been known for three decades that in the case of buoyancy-driven flows the widely used second-order closure (SOC) level-2.5 turbulence models exhibit divergences that render them unphysical in certain domains. This occurs when the dimensionless temperature gradient Gh (defined below) approaches a critical value Gh(cr) of the order of 10; thus far, the divergences have been treated with ad hoc limitations of the typewhere τ is the eddy turnover time scale, g is the gravitational acceleration, α is the coefficient of thermal expansion, T is the mean potential temperature, and z is the height. It must be noted that large eddy simulation (LES) data show no such limitation. The divergent results have the following implications. In most of the ∂T/∂z &amp;lt; 0 portion of a convective planetary boundary layer (PBL), a variety of data show that τ increases with z, −∂T/∂z decreases with z, and Gh decreases with z. As one approaches the surface layer from above, at some zcr (∼0.2H, H is the PBL height), Gh approaches Gh(cr) and the model results diverge. Below zcr, existing models assume the displayed equation above. Physically, this amounts to artificially making the eddy lifetime shorter than what it really is. Since short-lived eddies are small eddies, one is essentially changing large eddies into small eddies. Since large eddies are the main contributors to bulk properties such as heat, momentum flux, etc., the artificial transformation of large eddies into small eddies is equivalent to underestimating the efficiency of turbulence as a mixing process. In this paper the physical origin of the divergences is investigated. First, it is shown that it is due to the local nature of the level-2.5 models. Second, it is shown that once an appropriate nonlocal model is employed, all the divergences cancel out, yielding a finite result. An immediate implication of this result is the need for a reliable model for the third-order moments (TOMs) that represent nonlocality. The TOMs must not only compare well with LES data, but in addition, they must yield nondivergent second-order moments.

On Local Isotropy in Stratified Homogeneous Turbulence

This paper examines the postulate of local isotropy in stratified homogeneous turbulence from a theoretical point of view. The study is based on a priori analysis of the evolution equations governing single-point turbulence statistics that are formally consistent with the Navier--Stokes equations. The Boussinesq approximation has been utilized to account for the effect of buoyancy---a simplifying assumption which constitutes an excellent approximation for the case considered here. The study concludes that the hypothesis of local isotropy is formally inconsistent with the Navier--Stokes equations in homogeneous stratified turbulence. An estimate is provided that suggests that local isotropy may constitute only a physically justifiable approximation in the limit of a clear-cut separation between the time scales associated with the imposed buoyancy and the turbulent eddy turnover time scale. This is unlikely to happen in most flows, at least those not too far from equilibrium. The results also suggest that the dynamical dependence of the small-scale turbulence on large-scale anisotropies associated with imposed density stratification is significantly stronger than that caused by an imposed mean straining.

Numerical simulations of kinematic dynamo action

Numerical simulations of kinematic dynamo action in steady and three-dimensional ABC flows are presented with special focus on the difference in growth rates between cases with single and multiple periods of the prescribed velocity field. It is found that the difference in growth rate (apart from a trivial factor stemming from a scaling of the rate of strain with the wavenumber of the velocity field) is due to differences in the recycling of the weakest part of the magnetic field. The single wavelength classical ABC-flow experiments impose stronger symmetry requirements, which results in a suppression of the growth rate. The experiments with larger wave number achieve growth rates that are more compatible with the turn-over time scale by breaking the symmetry of the resulting dynamo-generated magnetic field. Differences in topology in cases with and without stagnation points in the imposed velocity field are also investigated, and it is found that the cigar-like structures that develop in the classical A = B = C dynamos are replaced by ribbon structures in cases where the flow is without stagnation points.

Numerical simulations of surface convection in a late M-dwarf

Based on detailed 2D and 3D numerical radiation-hydrodynamics (RHD) simulations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of a prototypical late-type M-dwarf (Teff~2800K log(g)=5.0, solar chemical composition). The RHD models predict stellar granulation qualitatively similar to the familiar solar pattern. Quantitatively, the granular cells show a convective turn-over time scale of ~100s, and a horizontal scale of 80km; the relative intensity contrast of the granular pattern amounts to 1.1%, and root-mean-square vertical velocities reach 240m/s at maximum. Deviations from radiative equilibrium in the higher, formally convectively stable atmospheric layers are found to be insignificant allowing a reliable modeling of the atmosphere with 1D standard model atmospheres. A mixing-length parameter of alpha=2.1 provides the best representation of the average thermal structure of the RHD model atmosphere while alternative values are found when fitting the asymptotic entropy encountered in deeper layers of the stellar envelope alpha=1.5, or when matching the vertical velocity field alpha=3.5. The close correspondence between RHD and standard model atmospheres implies that presently existing discrepancies between observed and predicted stellar colors in the M-dwarf regime cannot be traced back to an inadequate treatment of convection in the 1D standard models. The RHD models predict a modest extension of the convectively mixed region beyond the formal Schwarzschild stability boundary which provides hints for the distribution of dust grains in cooler (brown dwarf) atmospheres.

Disruption of a compressed vortex

The generation and breakdown of a tumbling motion are measured with particle image velocimetry in a model compression machine. The tumbling motion is a rotating flow which axis is perpendicular to the cylinder axis. The experimental set-up and the measurement procedure are described. The analysis of intake and compression strokes is presented. We first analyze the data by using phase averaging. Balances of mean and turbulent kinetic energy, of mean vorticity are presented. Effects of curvature and flow separation are clear during intake. The disruption of the vortex during the compression is a gradual process. Two three-dimensional separated regions appear first and are due to adverse pressure gradients induced by the vortex. Beyond a volumetric ratio of order two, the mean kinetic energy is transferred to turbulence within a short time scale, which is of the order of the vortex turnover time scale. The turbulence then decreases at the beginning of the expansion stroke. By analyzing instantaneous flow fields and by using proper orthogonal decomposition, we identify the fluctuations of the vortex correlated at a large scale. These fluctuations are amplified during the compression stroke. During the breakdown, they are correlated with fluid ejection from the vortex to the separated regions. We thus show that the vortex breakdown may involve several types of instability (elliptical instability but also centrifugal instability).

Small-scale magnetic fields on late-type M-dwarfs

We performed kinematic studies of the evolution of small-scale magnetic fields in the surface layers of M-dwarfs. We solved the induction equation for a prescribed velocity field, magnetic Reynolds number ReM, and boundary conditions in a Cartesian box, representing a volume comprising the optically thin stellar atmosphere and the uppermost part of the optically thick convective envelope. The velocity field is spatially and temporally variable, and stems from detailed radiationhydrodynamics simulations of convective flows in a proto-typical late-type M-dwarf (Teff = 2800 K, log g = 5.0, solar chemical composition, spectral type ≈M6). We find dynamo action for ReM ≥ 400. Growth time scales of the magnetic field are comparable to the convective turn-over time scale (≈150 sec). The convective velocity field concentrates the magnetic field in sheets and tubular structures in the inter-granular downflows. Scaling from solar conditions suggests that field strengths as high as 20 kG might be reached locally. Perhaps surprisingly, ReM is of order unity in the surface layers of cooler M-dwarfs, rendering the dynamo inoperative. In all studied cases we find a rather low spatial filling factor of the magnetic field.

Direct numerical simulation of turbulence–mean field interactions in a stably stratified fluid

Freely decaying turbulent flows in a stably stratified fluid are simulated with a pseudo-spectral numerical code solving the fully nonlinear Navier–Stokes equations under the Boussinesq approximation with periodic boundary conditions. The flow is decomposed into a turbulent field and a horizontal mean flow ū(z, t) defined as the average of the horizontal velocity component in a horizontal plane at height z and time t. Similarly, the density field is decomposed into a turbulent field and a (stable) mean density profile ρ(z, t) defined as the average of the density field in a horizontal plane at height z and time t. Attention is paid to the effect of the turbulent velocity field on an initial z-periodic horizontal mean flow (Simulation A) or an initial z-periodic perturbation of the mean density profile (Simulation B). Both A and B are performed under conditions of moderate and strong stratification and are compared to the non-stratified simulations.Simulation A shows that the turbulence–mean flow interaction is strongly affected by the buoyancy forces. In the absence of a stratification, the mean flow perturbation decays rapidly due to the turbulent diffusion of momentum. When a moderate stratification is applied, the mean flow perturbation decays much more slowly whereas it oscillates and grows with time when the stratification is strong. These results are interpreted by defining a time-dependent eddy viscosity. Whereas the eddy viscosity coefficient has positive values in the non-stratified simulation, it is affected by the buoyancy forces and decreases after a period of order N−1. For large times, the eddy diffusivity oscillates and its time-averaged value over a few turnover timescales is positive but small when the stratification is moderate, and roughly zero when the stratification is strong. These results are interpreted by defining a time-dependent eddy viscosity. Whereas the eddy viscosity coefficient has positive values in the non-stratified simulation, it is affected by the buoyancy forces and decreases after a period of order N−1 in the stratified simulations (where N is the Brunt–Väisälä frequency associated with the background linear stratification). At large time, we find that the eddy viscosity remains roughly zero when the stratification is moderate, whereas it oscillates but remains persistently negative in the strongly stratified case, which causes the horizontal mean flow to accelerate.We conclude that the presence of a stable stratification strongly affects the temporal behaviour of the mean quantities ū and ρ in turbulent flows and partly explains the formation of horizontal layers in stratified geofluids such as oceans and atmospheres.

The geodynamo as a bistable oscillator

Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating α reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ∝(1 − a 2)2, subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2−3) × 105 year, is shown to imply a secular variation of the axial dipole moment of ∼ 15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.

The role of electron density in magnetic turbulence

Inertial range energy transfer, decorrelation, and energy spectra are studied analytically and numerically for strongly anisotropic magnetohydrodynamic (MHD) turbulence augmented by electron density evolution. The model is relevant to interstellar turbulence and magnetic turbulence in fusion devices. For long wavelengths (compared to the ion gyroradius), magnetic and kinetic energies are equipartitioned through interactions that decorrelate on the Alfvénic time scale. Internal energy transfer is governed by advection and decorrelates on the eddy turnover time scale. For short wavelengths, the roles of internal and kinetic energy reverse. Magnetic and internal energies are equipartitioned by the kinetic Alfvén interaction, while kinetic energy evolves under a decoupled fluid straining interaction. The spectral indices for magnetic, kinetic, and internal energies are −3/2, −3/2, and −7/4 for long wavelengths, and −2, −5/3, and −2 for short wavelengths.

Production and consumption of methyl halides in a freshwater lake

The concentrations of the methyl halides CH3Cl and CH3Br in Lake Washington and its tributary streams were measured during the period 1994–1998. Strong seasonal variation was observed. In summer, the surface mixed layer in the middle of the lake was found to be generally undersaturated for CH3Cl but consistently supersaturated for CH3Br relative to air-water gas equilibrium; meanwhile, the deep waters (zmax - 65 m) of the summertime lake were found to be depleted to near zero levels for both compounds. In winter, the methyl halides were observed to be vertically well mixed throughout the water column and strongly undersaturated in both species. A simple mass-balance box model indicates that the wintertime lake (T = 8°C) is a net sink for atmospheric methyl halides with estimated loss rates of ~2.6–3.2 pM d−1 for CH3Cl (1 pM = 10−12 mol L−1) and 0.09–0.13 pM d−1 for CH3Br, probably because of unspecified microbiological processes. In summer, the mass balance model indicates that there is a net source of CH3Br in the surface mixed layer (0.17–0.25 pM d−1), as required to maintain the observed strong supersaturation. However, the summer surface waters are apparently a sink for CH3Cl, (1.9–2.9 pM d−1), with enhanced biological production compensated by larger combined microbial and chemical sinks terms. In summer, methyl halide concentrations in the deep waters continue to decrease exponentially at the observed wintertime rate, while both production and loss rates in the surface waters are likely much faster than in winter, resulting in much shorter turnover timescales. An order-of-magnitude extrapolation of these Lake Washington methyl halide fluxes to a global source/sink from freshwater lakes implies a negligible contribution (<0.05%) with respect to the currently estimated global budgets of these gases.

A numerical study of the effect of periodic nutrient supply on pathways of carbon in a coastal upwelling regime

A size-based ecosystem model was modified to include periodic upwelling events and used to evaluate the effect of episodic nutrient supply on the standing stock, carbon uptake, and carbon flow into mesozooplankton grazing and sinking flux in a coastal upwelling regime. Two ecosystem configurations were compared: a single food chain made up of net phytoplankton and mesozooplankton (one autotroph and one heterotroph, A1H1), and three interconnected food chains plus bacteria (three autotrophs and four heterotrophs, A3H4). The carbon pathways in the A1H1 simulations were under stronger physical control than those of the A3H4 runs, where the small size classes are not affected by frequent upwelling events. In the more complex food web simulations, the microbial pathway determines the total carbon uptake and grazing rates, and regenerated nitrogen accounts for more than half of the total primary production for periods of 20 days or longer between events. By contrast, new production, export of carbon through sinking and mesozooplankton grazing are more important in the A1H1 simulations. In the A3H4 simulations, the turnover time scale of the autotroph biomass increases as the period between upwelling events increases, because of the larger contribution of slow-growing net phytoplankton. The upwelling period was characterized for three upwelling sites from the alongshore wind speed measured by the NASA Scatterometer (NSCAT) and the corresponding model output compared with literature data. This validation exercise for three upwelling sites and a downstream embayment suggests that standing stock, carbon uptake and size fractionation were best supported by the A3H4 simulations, while the simulated sinking fluxes are not distinguishable in the two configurations.

Annual Cycle and Interannual Variability of Ecosystem Metabolism in a Temperate Climate Embayment

We have studied the net and gross metabolism of Tomales Bay, a temperate climate estuary in northern California. Tomales Bay has proved to be heterotrophic, implying that the bay oxidizes a subsidy of organic carbon from outside the system, in excess of inorganic nutrients supplied to it from outside and in addition to material cycling within it. Net organic oxidation releases dissolved inorganic nutrients, and the system exports these dissolved inorganic products. Dissolved inorganic phosphorus is exported to the ocean via mixing and constitutes the most direct record of net ecosystem production (NEP). Excess dissolved inorganic nitrogen is lost to denitrification. Excess dissolved inorganic carbon largely results in alkalinity elevation and hydrographic export of alkalinity due to sulfate reduction. The negative NEP of this system results in little release of CO2 to the atmosphere, because of this alkalinity elevation. A major purpose of the study was to ascertain the relative importance of various sources of organic material supplied to the system from outside its boundaries and undergoing net reactions within it. In order to address the question, we used stoichiometrically linked whole-system budgets of carbon, nitrogen, and phosphorus. The difference between dissolved inorganic phosphorus (DIP) fluxes to and from the bay is a measure of net internal sources or sinks of DIP and is used as a quantitative index of NEP, with the assumption that the C:P ratio of organic matter is constant (∼106:1). The system is thus defined in terms of water column dissolved material composition; this definition includes time, as well as space. Net changes in the standing stocks of dissolved materials can originate from (spatial) transport to or from the system or from internal (temporal) transformations between the dissolved and particulate materials (i.e., changes in organic storage). Over the 8-yr study, the system respired 12 mmol·m−2·d−1 more organic C than the internal system primary production of ∼100 mmol·m−2·d−1. The system is thus heterotrophic by ∼10%, with substantial seasonality in the extent of heterotrophy. By deconvoluting the time series of NEP into a seasonal cycle and interannual variation, we infer that terrestrial and marine sources each account for about half of the carbon required to support negative NEP in this system, but with quite different turnover time scales. Temporal response of NEP to terrigenous input appears to be extremely modulated, so that there is no obvious immediate (same year) response to extreme interannual variation in terrigenous organic loading. In contrast, NEP responds both interannually and seasonally to marine organic inputs. We interpret the differences in response to loading of terrestrial vs. marine organic matter as reflecting differences in the reactivity of these carbon reservoirs.

The Theoretical Calculation of the Rossby Number and the ``Nonlocal'' Convective Overturn Time for Pre-Main-Sequence and Early Post-Main-Sequence Stars

This paper provides estimates of convective turnover timescales for Sun-like stars in the pre-main-sequence and early post-main-sequence phases of evolution, based on up-to-date physical input for the stellar models. In this first study, all models have solar abundances, which is typical of the stars in the Galactic disk, where most of the available data have been collected. A new feature of these models is the inclusion of rotation in the evolutionary sequences, thus making it possible to derive theoretically the Rossby number for each star along its evolutionary track, based on its calculated rotation rate and its local convective turnover time near the base of the convection zone. Global turnover times are also calculated for the complete convection zone. This information should make possible a new class of observational tests of stellar theory that were previously impossible with semiempirical models, particularly in the study of stellar activity and in research related to angular momentum transfer in stellar interiors during the course of stellar evolution.