Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model

To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few degrees of freedom such as multi-layer quasi-geostrophic and shallow-water models and relatively low-resolution (e.g., 4° horizontal resolution) primitive equation models. In this paper, we present a new approach in which continuation methods are combined with parallel numerical linear system solvers. With this implementation, we show that it is possible to compute steady states versus parameters (and perform fully implicit time integration) of primitive equation ocean models with up to a few million degrees of freedom.     

Numerical model simulations of continental shelf flows off northern California

The three-dimensional circulation on the continental shelf off northern California in the wind events and shelf transport (WEST) experiment region during summer 2001 is studied using the primitive equation regional ocean modeling system (ROMS). The simulations are performed with realistic topography and initial stratification in a limited-area domain with a high-resolution grid. Forcing consists of measured wind-stress and heat flux values obtained from a WEST surface buoy. The general response shows a southward coastal upwelling jet of up to and a weakening or reversal of currents inshore of the jet when upwelling winds relax. Model results are compared to WEST moored velocity and temperature measurements at five locations, to CODAR surface current observations between Pt. Reyes and Bodega Bay, and to hydrographic measurements along shipboard survey lines. The model performs reasonably well, with the highest depth-averaged velocity correlation (0.81) at the inshore mooring (40 m water depth) and lowest correlation (0.68) at the mid-depth mooring (90 m depth). The model shows generally stronger velocities than those observed, especially at the inshore moorings, and a lack in complete reversal of southward velocities observed when upwelling winds relax. The comparison of surface velocities with CODAR measurements shows good agreement of the mean and the dominant mode of variability. The hydrography compares closely at the southern and northern edges of the survey region (correlation coefficients between 0.90 and 0.97), with weaker correlations at the three interior survey lines (correlation coefficients between 0.44 and 0.76). Mean model fields over the summer upwelling period show slight coastal jet separation off Pt. Arena and significant separation off Pt. Reyes. The cape regions also experience relatively strong bottom velocities and nonlinearity in the surface flow. Across-shelf velocity sections examined along the shelf reveal a double jet structure that appears just north of Bodega Bay and shows the offshore jet strengthening to the south. We examine the dynamics during an upwelling and subsequent relaxation event in May 2001 in which the WEST measurements show evidence of a strong flow response. The alongshelf variability in the upwelling and relaxation response introduced by Pt. Reyes is evident. Analysis of term balances from the depth-averaged momentum equations helps to clarify the event dynamics in different regions over the shelf. A clear pattern in the nonlinear advection term is due to the spatial acceleration of the southward jet around the capes of Pt. Arena and Pt. Reyes during upwelling. Results from a three-dimensional Lagrangian analysis of water parcel displacement show significant southward displacement in the coastal jet region, including a strong signal from the double jet. Alongshelf variability in parcel displacements and upwelling source waters due to the presence of Pt. Arena and Pt. Reyes is also apparent from the Lagrangian fields. A cyclonic eddy-like recirculation feature offshore of Pt. Arena prior to the upwelling event causes large patches of onshore-displaced parcels. Additionally, across-shelf variability in the response of water parcels along the D line includes decreased vertical displacement and increased alongshelf displacement in the offshore direction.     

Coupled-dynamic analysis of floating structures with polyester mooring lines

A theory and numerical tool are developed for the coupled-dynamic analysis of a deepwater floating platform with polyester mooring lines. The formulas allow relatively large elongation and nonlinear stress–strain relationships, as typically observed in polyester fibers. The mooring-line dynamics are based on a rod theory and the finite element method (FEM), with the governing equations described in a generalized coordinate system. The original rod theory [Nordgren, R.P., 1974. On Computation of the Motion of Elastic Rods. Journal of Applied Mechanics, 41, 777–780] is generalized to allow larger elongation and nonlinear stress–strain relationship. The dynamic modulus of polyester is modeled following an empirical regression formula suggested by [Bosman, R.L.M., Hooker, J., 1999. The Elastic Modulus Characteristic of Polyester Mooring Ropes. In: Proceedings of the Offshore Technology Conference, OTC 10779. Houston, Texas], in which the axial stiffness is not constant, but depends on loading conditions. Two case studies, the static and dynamic behavior of a tensioned buoy and a classic spar with polyester mooring lines, are conducted. The time-domain simulation results are systematically compared with those from the original rod theory. The effects of large elongation and nonlinear stress–strain relations are separately assessed. It is seen that the mean offset, motions, and tension with polyester lines can be different from those by original rod theory with linear elastic lines.     

Nonlinear modeling of liquid sloshing in a moving rectangular tank

A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results.     

Dynamic analysis of vehicle–deck interactions

This paper presents the review and studies at various levels of problems concerning the authors’ previous research on the dynamics of vehicle–deck interactions. The various levels of study include the dynamic structural behavior of vehicle–deck systems, vehicle vibrations, damping effects of vehicles on structural systems, dynamic interactions between tire and deck surface, and vehicle securing on decks during ship motions, etc. The study includes analytical, numerical and experimental analysis. Practical problems encountered by Ro–Ro ship designers are addressed by discussing those analysis. It is shown that influences from the dynamics of vehicle–deck interactions are relevant to a number of aspects of issues, such as the excitation frequency range, how detailed information of the structural system response is required, the structure characteristics, and positions and orientations of vehicles on decks, etc. The study contributes to the knowledge for the naval architect and vehicle engineer on how significant the dynamics of vehicle–deck interactions are when dealing with relevant problems.