Daniel R. Lynch

A wave equation model for finite element tidal computations

Abstract A shallow water wave equation is developed from the primitive two-dimensional shallow water equation. A finite element model based on this equation and the primitive momentum equation is developed. A finite difference formulation is used in the time domain which allows the model to be implicit or explicit while still centered in time. Results obtained with linear triangles and quadratic quadrilaterals are reported, and compare well with analytic solutions. The model incorporates all of the economical advantages of earlier models, and errors due to short wavelength spatial noise are suppressed without recourse to artificial means.

Comprehensive coastal circulation model with application to the Gulf of Maine

Abstract A state-of-the-art finite element model is described and applications are shown for the Gulf of Maine. The model is three-dimensional (hydrostatic) with a free surface, fully nonlinear, incorporates advanced turbulence closure and operates in tidal time. Variable horizontal and vertical resolution are facilitated by the use of unstructured meshes. Solutions for the Gulf of Maine illustrate performance in the context of several isolated nonlinear processes. Composite solutions for March–April and July–August time periods are recorded under climatological forcing. The solutions exhibit a general cyclonic central Gulf circulation, a coastal current with several branch points and anticyclonic circulation around Georges Bank. Each of these features is seasonally modulated. The surface circulation is in general agreement with surface drift observations. The circulation at depth shows the combined influence of deep basin topography and baroclinicity.

Seasonal mean circulation in the Yellow Sea } a model-generated climatology

The three-dimensional climatological circulation is computed for the Yellow and Bohai Seas in a series of six bimonthly realizations. The model (QUODDY, Lynch et al., Continental Shelf Res. 16(7) (1996) 875) is nonlinear, tide-resolving, and baroclinic with level 2.5 turbulence closure. Data inputs include seasonal hydrography, seasonal mean wind and river input, and oceanic tides. Results for winter and summer exhibit two distinct circulation modes. In winter, strongnortherly wind drives southward flow at the surface and alongboth Korean and Chinese coasts. This is compensated by deep return flow } the Yellow Sea Warm Current } in the central trough of the Yellow Sea, penetrating to the Bohai. The Changjiang discharge exits to the southwest in winter, trapped alongthe Chinese coast. In summer, a water mass produced by winter cooling } the Yellow Sea Cold Water } is isolated in the deep central trough, setting up cyclonic circulation over the eastern Yellow Sea. Summer winds from the south drive northeastward flow alongthe Chinese coast. The net result is a qualitative reversal of the winter pattern. The Changjiang discharge is driven offshore toward the Korean Strait by the summer wind. The winter and summer circulations are partitioned dynamically amongtidal rectification, baroclinic pressure g radients, wind response, and river input from the Changjiang. Wind dominates the winter pattern. In summer, baroclinic pressure gradients dominate the eastern Yellow Sea; with wind, tidal rectification, and input from the Changjiang dominant to the west of the cyclonic gyre. The seasonal cycle indicates that January and March exhibit the same basic winter pattern. May is quiescent, followed by July which defines the summer mode. September shows the same general summer pattern, with features shifted westward. November is a transition period followed by winter conditions. # 2001 Elsevier Science Ltd. All rights reserved.

Unified approach to simulation on deforming elements with application to phase change problems

Abstract Several different approaches to simulation on deforming finite elements are shown to generate the same weighted residuals formulation for the evolution of the dependent variables. Control of node motion by means of mesh stretching in two dimensions is illustrated in the context of phase change problems. Simulation of problems with large phase boundary excursions shows good agreement with analytic solutions.

Finite element simulation of flow in deforming regions

Abstract A finite element technique for solving multidimensional flow problems with moving boundaries is developed by means of Galerkins procedure. The method accounts automatically for continuous grid deformation during simulation, and utilizes finite difference techniques in the time domain. In the absence of grid deformation, the method reduces to the standard Galerkin finite element formulation. Utility of the approach is demonstrated by application to one- and two-dimensional flow problems.

Coupling of finite element and moment methods for electromagnetic scattering from inhomogeneous objects

A hybrid formulation which combines the method of moments (MM) with the finite element method (FEM) to solve electromagnetic scattering and/or absorption problems involving inhomogeneous media is discussed. The basic technique is to apply the equivalence principle and transform the original problem into interior and exterior problems, which are coupled on the exterior dielectric body surface through the continuities of the tangential electric field and magnetic field. The interior problem involving inhomogeneous medium is solved by the FEM, and the exterior problem is solved by the MM. The coupling of the interior and exterior problems on their common surface results in a matrix equation for the equivalent current sources for the interior and exterior problems. Combining advantages of both methods allows complicated inhomogeneous problems with arbitrary geometry to be treated in a straightforward manner. The validity and accuracy of the formulation are checked by two-dimensional numerical results, which are compared with the exact eigenfunction solution, the unimoment solution, and Richmonds pure moment solution. >

The M2 Tide and Its Residual on the Outer Banks of the Gulf of Maine

Abstract Tidal computations are reported for the Gulf of Maine with emphasis on its seaward banks. Georges Bank, Browns Bank, Nantucket Shoals, and the nearshore region off Cape Sable. The model is 3D and nonlinear, with quadratic vertical viscosity; stratification is ignored. The objective is to establish a theoretical baseline for tidal and residual currents on detailed topography against which seasonal changes may be examined. Two triangular meshes are used. The base case corresponds to earlier studies with roughly 6-km resolution on the banks. A more refined and extended mesh provides resolution at 2–3 km in critical areas and has boundaries farther removed from the banks. Both meshes provide very good fits with observed M2 elevations. Comparison of computed and observed M2 current profiles at 76 sites reveals general agreement that improves with resolution. For the refined mesh and the 48 sites with records exceeding 60 days, average deviations for M2 ellipse parameters are (6.1, 4.7) cm s−1 for the ...

Spatially-explicit individual based modeling of marine populations: A review of the advances in the 1990s

Abstract The utility of individual based models (IBMs) is that properties of ecological systems can be derived by considering the properties of individuals constituting them. Individual differences may be physiological, behavioral or may arise from interactions among individuals. The differences result in unique life histories, which when considered as a whole give rise to growth and size distributions that provide a measure of the state of the population. Early IBMs generally did not consider the effect of a spatially variable physical environment. Recent advances in ocean circulation models that include realistic temporal and spatial variation of currents, turbulence, light, prey, etc., have enabled IBMs to be embedded in model flow fields and for unique, sometimes behaviorally modified, Lagrangian trajectories to be computed. The explicit consideration of realistic spatial heterogeneity provides an additional factor that contributes to the differentiation among individuals, to variances in population structure, and ultimately to our understanding of the recruitment process. This is particularly important in marine environments where fronts, boundary layers, pycnoclines, gyres and other smaller spatial features have been hypothesized to play a significant role in determining vital rates and population structure. In this paper we will review the status of research on spatially-explicit IBMs, their successes, limitations and future developments. Examples will be drawn from approaches used in the past decade in GLOBEC, FOCI, SABRE and other programs.

Diagnostic model for baroclinic, wind-driven and tidal circulation in shallow seas

Abstract A three-dimensional diagnostic model for continental shelf circulation studies is presented. The model is based on the linearized hydrodynamic equations subject to surface stress, density gradient, and remote (boundary) forcing. Finite elements are used to resolve real topography. Solutions are obtained in the frequency domain, including the limit of zero frequency. A test case based on analytic solutions for tidal front circulation demonstrates the successful representation of sensitive baroclinic circulation. Representative applications to the Gulf of Maine region, including the Bay of Fundy, Georges Bank, and a portion of the Scotian Shelf, are shown for wind, along-shelf transport, and tidal front circulation on Georges Bank.

Seasonal variation of the three-dimensional residual circulation on Georges Bank

The seasonal variation of the low-frequency circulation in the Georges Bank region is studied numerically by computing six bimonthly circulation fields subject to forcing from the barotropic M2 tide, mean baroclinic pressure gradients, and mean wind stresses. The model is three dimensional, diagnostic, and nonlinear, with quadratic vertical eddy viscosity that is stratification-dependent. Tidal forcing is imposed at the boundary of the domain, and an extensive set of density and wind data is used to determine climatological mean forcings. The magnitude of the M2 tidally rectified around-bank velocities and transports is sensitive to stratification influences on the eddy viscosity, with up to a 50% intensification relative to computations which assume no influences. The dependence occurs through both the local advective tidal stress terms and the large-scale barotropic pressure field. The six bimonthly solutions (January–February, March–April, May–June, July–August, September–October, November–December) indicate important contributions from tidal rectification, baroclinic pressure gradients, and mean wind stress to the seasonal intensification of the Georges Bank gyre. Tidal rectification and baroclinicity are the dominant forcings, while wind stress generates opposing around-bank flow and cross-bank surface drift in winter. Overall, the solutions are in approximate agreement with observed Eulerian around-bank currents and transports, although there are both local and bank-wide discrepancies. The seasonal intensification of recirculation around Georges Bank is well produced by the model, with estimates of the recirculating transport increasing from under 0.02 Sv (January–February) to over 0.13 Sv (September–October).