Investigation of gravity-driven coatal currents

We summarize a study that compares experimental laboratory data for gravity-driven coastal surface currents with corresponding theoretical results obtained from a new geostrophic model describing such currents. It is found that experiment and theory are, generally, in good agreement

A three-dimensional spectral element model for the solution of the hydrostatic primitive equations

We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical flows. The highlights of this new model include unstructured grids, dual h– p paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear flow rectification, respectively. The first of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and finite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of flow around a submarine canyon. The aforementioned tests demonstrate the good performance of the model in the idealized/process-oriented limits

To continue or discontinue: Comparisons of continuous and discontinuous Galerkin formulations in a spectral element ocean model

The discontinuous Galerkin method is implemented in the spectral element ocean model to replace a continuous Galerkin discretization of the continuity and the tracer evolution equations. The aim is to improve the model’s local conservation properties, and thus its performance in advection-dominated flows. The new model is validated against several oceanic benchmark problems, particularly ones that feature frontal structures and under-resolved features. Comparisons confirm the advantages of the DGM, including enhanced model robustness

Wind driven general circulation of the Mediterranean Sea simulated with a Spectral Element Ocean Model

This work is an attempt to simulate the Mediterranean Sea general circulation with a Spectral Finite Element Model. This numerical technique associates the geometrical flexibility of the finite elements for the proper coastline definition with the precision offered by spectral methods. The model is reduced gravity and we study the wind-driven ocean response in order to explain the large scale sub-basin gyres and their variability. The study period goes from January 1987 to December 1993 and two forcing data sets are used. The effect of wind variability in space and time is analyzed and the relationship between wind stress curl and ocean response is stressed. Some of the main permanent structures of the general circulation (Gulf of Lions cyclonic gyre, Rhodes gyre, Gulf of Syrte anticylone) are shown to be induced by permanent wind stress curl structures. The magnitude and spatial variability of the wind is important in determining the appearance or disappearance of some gyres (Tyrrhenian anticyclonic gyre, Balearic anticyclonic gyre, Ionian cyclonic gyre). An EOF analysis of the seasonal variability indicates that the weakening and strengthening of the Levantine basin boundary currents is a major component of the seasonal cycle in the basin. The important discovery is that seasonal and interannual variability peak at the same spatial scales in the ocean response and that the interannual variability includes the change in amplitude and phase of the seasonal cycle in the sub-basin scale gyres and boundary currents. The Coriolis term in the vorticity balance seems to be responsible for the weakening of anticyclonic structures and their total disappearance when they are close to a boundary. The process of adjustment to winds produces a train of coastally trapped gravity waves which travel around the eastern and western basins, respectively in approximately 6 months. This corresponds to a phase velocity for the wave of about 1 m/s, comparable to an average velocity of an internal Kelvin wave in the area

Comparison of advection schemes for high-order h–p finite element and finite volume methods

We review and compare advection schemes designed for high-order finite element/finite volume methods. The emphasis is on studying, by numerical examples, the properties of these schemes in terms of accuracy, and monotonicity, and their viability for oceanic applications. The schemes reviewed are classical spectral element, Taylor Galerkin Least Square method, the Discontinuous Galerkin method and high-order finite volume method. The latter two schemes exhibit a definite robustness due to their small, but finite, inherent numerical dissipation. They also prove the most flexible since their discontinuous representation of the solution allows easy implementations of flux limiting or adaptive procedure. Finally, an ad-hoc but simple adaptive procedure is presented to illustrate DGM’s potential; this procedure proved to be extremely effective at controlling Gibbs oscillations in 1D but was too dissipative on the Hecht problem

Euler–Lagrange equations for the spectral element shallow water system

We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with which elemental assembly and mass averaging are applied in the forward and in the adjoint systems. Our derivation can be extended to obtain an adjoint for any Galerkin finite element and spectral element system. We begin the derivations using a linear wave equation in one dimension. We then apply our technique to a two-dimensional shallow water ocean model and test it on a classic double-gyre problem. The spectral element forward and adjoint ocean models can be used in a variety of inverse applications, ranging from traditional data assimilation and parameter estimation, to the less traditional model sensitivity and stability analyses, and ensemble prediction. Here the Euler–Lagrange equations are solved by an indirect representer algorithm

A comparison between laboratory and numerical simulations of gravity-driven coastal currents with a geostrophic theory

Laboratory and numerical simulations of buoyant, gravity-driven coastal currents are summarized and compared to the inviscid geostrophic theory of Thomas \& Linden 2007. {Thomas, P. J. and Linden, P.F. 2007. Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model. {J. Fluid Mech.} {578}, 35-65}. The lengths, widths and velocities of the buoyant currents are studied. Agreement between the laboratory and numerical experiments and the geostrophic theory is found to depend on two non-dimensional parameters which characterize, respectively, the steepness of the plumes isopycnal interface and the strength of horizontal viscous forces (quantified by the horizontal Ekman number). The best agreement between experiments (both laboratory and numerical) and the geostrophic theory are found for the least viscous flows. At elevated values of the horizontal Ekman number, laboratory and numerical experiments depart more significantly from theory

The Nature of the Cold Filaments in the California Current System

Data from the Coastal Transition Zone (CTZ) experiment axe used to describe the velocity fields and water properties associated with cold filaments in the California Current. Combined with previous field surveys and satellite imagery, these show seasonal variability with maximum dynamic height ranges and velocities in summer and minimum values in late winter and early spring. North of Point Arena (between 39 degrees N and 42 degrees N) in spring-summer the flow field on the outer edge of the cold water has the character of a meandering jet, carrying fresh, nutrient-poor water from farther north on its offshore side and cold, salty, nutrient-rich water on its inshore side. At Point Arena in midsummer, the jet often flows offshore and continues south without meandering back onshore as strongly as it does farther north. The flow field south of Point Arena in summer takes on more of the character a field of mesoscale eddies, although the meandering jet from the north continues to be identifiable. The conceptual model for the May-July period between 36 degrees N and 42 degrees N is thus of a surface jet that meanders through and interacts with a field of eddies; the eddies are more dominant south of 39 degrees N, where the jet broadens and where multiple jets and filaments are often present. At the surface, the jet often separates biological communities and may appear as a barrier to cross-jet transport, especially north of Point Arena early in the season (March-May). However, phytoplankton pigment and nutrients are carried on the inshore flank of the jet, and pigment maxima are sometimes found in the core of the jet. The biological effect of the jet is to define a convoluted, 100 to 400-km-wide region next to the coast, within which much of the richer water is contained, and also to carry some of that richer water offshore in meanders along the outer edge of that region.The CTZ program was funded by the Coastal Sciences Program of the Office of Naval Research (Code 1122CS). Support for PTS was provided by ONR grants N00014-87K0009 and N00014-90J1115, with additional support provided by NASA grants NAGW-869 and NAGW-1251