Many nearshore fish and invertebrate populations are overexploited even when apparently coherent management structures are in place. One potential cause of mismanagement may be a poor understanding and accounting of stochasticity, particularly for stock recruitment. Many of the fishes and invertebrates that comprise nearshore fisheries are relatively sedentary as adults but have an obligate larval pelagic stage that is dispersed by ocean currents. Here, we demonstrate that larval connectivity is inherently an intermittent and heterogeneous process on annual time scales. This stochasticity arises from the advection of pelagic larvae by chaotic coastal circulations. This result departs from typical assumptions where larvae simply diffuse from one site to another or where complex connectivity patterns are created by transport within spatially complicated environments. We derive a statistical model for the expected variability in larval settlement patterns and demonstrate how larval connectivity varies as a function of different biological and physical processes. The stochastic nature of larval connectivity creates an unavoidable uncertainty in the assessment of fish recruitment and the resulting forecasts of sustainable yields.coastal oceanography ͉ fisheries ͉ marine ecology N earshore ecosystems host a wide variety of marine organisms and are among the most productive environments on Earth. Yet many species harvested from these ecosystems are overfished (1-3), a problem that is especially acute for those invertebrates and fishes with a relatively sedentary adult life stage. One potential cause of overfishing is mismanagement because of a poor understanding and accounting of stochasticity in these systems (4,5). Stochasticity caused by climate variations has long been known to influence the dynamics of ocean ecosystems and the fisheries they support (6). Climate variation affects rates of fecundity and recruitment by altering water temperature, coastal circulation patterns, or the availability of spawning grounds (7,8); such effects can be understood and, given sufficient data, may be predictable. Here, we introduce a mechanism that generates stochasticity in spatial and temporal patterns of larval transport on annual time scales. This stochasticity is inherently unpredictable because of the chaotic nature of coastal circulations and the relatively short larval time scales.Many harvested fish and invertebrates from nearshore ecosystems have a life cycle that includes a pelagic larval stage that can last up to months and a localized benthic adult stage (9, 10). These relatively sedentary adults release hundreds to millions of larvae that are advected and dispersed by ocean currents as they develop competency to settle (9-13). Spawning releases can occur continuously over months or in a few short events. Biotic factors, such as active swimming and vertical migration, also contribute to movement patterns (12,14,15). A small fraction of the larvae settle at suitable sites, and an even smaller fraction recruit to adult...

A conceptual framework for analysing the energetics of density-stratified Boussinesq fluid flows is discussed. The concept of gravitational available potential energy is used to formulate an energy budget in which the evolution of the background potential energy, i.e. the minimum potential energy attainable through adiabatic motions, can be explicitly examined. For closed systems, the background potential energy can change only due to diabatic processes. The rate of change of background potential energy is proportional to the molecular diffusivity. Changes in the background potential energy provide a direct measure of the potential energy changes due to irreversible diapycnal mixing. For open systems, background potential energy can also change due to boundary fluxes, which can be explicitly measured. The analysis is particularly appropriate for evaluation of diabatic mixing rates in numerical simulations of turbulent flows. The energetics of a shear driven mixing layer is used to illustrate the analysis.

Basin-scale internal waves provide the driving forces for vertical and horizontal fluxes in a stratified lake below the wind-mixed layer. Thus, correct modeling of lake mixing and transport requires accurate modeling of basinscale internal waves: examining this capability with a hydrostatic, z-coordinate three-dimensional (3D) numerical model at coarse grid resolutions is the focus of this paper. It is demonstrated that capturing the correct thermocline forcing with a 3D mixed-layer model for surface dynamics results in a good representation of low-frequency internal wave dynamics. The 3D estuary and lake computer model ELCOM is applied to modeling Lake Kinneret, Israel, and is compared with field data under summer stratification conditions to identify and illustrate the spatial structure of the lowest-mode basin-scale Kelvin and Poincaré waves that provide the largest two peaks in the internal wave energy spectra. The model solves the unsteady Reynolds-averaged Navier-Stokes equations using a semi-implicit method similar to the momentum solution in the TRIM code with the addition of quadratic Euler-Lagrange discretization, scalar (e.g., temperature) transport using a conservative flux-limited approach, and elimination of vertical diffusion terms in the governing equations. A detailed description is provided of turbulence closure for the vertical Reynolds stress terms and vertical turbulent transport using a 3D mixed-layer model parameterized on wind and shear energy fluxes instead of the convential eddy viscosity/diffusivity assumption. This approach gives a good representation of the depth of the mixed-layer at coarse vertical grid resolutions that allows the internal waves to be energized correctly at the basin scale.Wind stresses, surface heating, and density currents form the driving energy fluxes of a stratified lake. The basin-scale energy flux from the wind is of particular interest because of its dominant role in setting the thermocline in motion, which, in the absence of inflows and outflows, is the primary energy store for transport and mixing below the wind-mixed layer. Thus, modeling the basin-scale internal wave behavior is an a priori requirement to modeling and quantifying the flux paths of nutrients in a stratified lake (Imberger 1994). This paper takes a first step in this direction by analyzing our ability to model basin-scale internal waves that are seen in Lake Kinneret, Israel.Energy flux path in a stratified lake-Energy flux through a stratified lake has a fundamental dependence on forced and free baroclinic motions. The wind imparts both momentum and turbulent kinetic energy (TKE) to the water in the surface layer. The TKE distributes momentum vertically in the 1 Corresponding author

We define the rate at which a scalar θ mixes in a fluid flow in terms of the flux of θ across isoscalar surfaces. This flux θd is purely diffusive and is, in principle, exactly known at all times given the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to make the calculation of this flux very difficult. In this paper, we derive an exact expression relating the instantaneous diascalar flux to the average squared scalar gradient on an isoscalar surface which does not require knowledge of the spatial structure of the surface itself. To obtain this result, a time-dependent reference state θ(t,z*.) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the reference state due to diffusion is shown to equal the divergence of the diffusive flux, i.e. (∂/∂z*)θd.This result provides a mathematical framework that exactly separates diffusive and advective scalar transport in incompressible fluid flows. The relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn–Cox model. Estimation of water mass transformation from oceanic microstructure profiles and determination of the time-dependent mixing rate in numerically simulated flows are discussed.