Computational Kernel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations

Abstract. A practical scheme is proposed to explicitly introduce tides into ocean general circulation models (OGCM). In this scheme, barotropic linear response to the tidal forcing is calculated by the time differential equations modified for ocean tides, instead of the original barotropic equations of an OGCM. This allows for the usage of various parameterizations specified for tides, such as the self-attraction/loading (SAL) effect and energy dissipation due to internal tides, without unintentional violation of the original dynamical balances in an OGCM. Meanwhile, secondary nonlinear effects of tides, e.g., excitation of internal tides and advection by tidal currents, are fully represented within the framework of the original OGCM equations. That is, this scheme drives the OGCM by the barotropic linear tidal currents which are predicted progressively by a tuned tide model, instead of the equilibrium tide potential, without large additional numerical costs. We incorporated this scheme into Meteorological Research Institute Community Ocean Model and executed test experiments with a low-resolution global model. The results showed that the model can simulate both the non-tidal circulations and the tidal motion simultaneously. Owing to the usage of tidal parameterizations such as a SAL term, a root-mean-squared error in the tidal heights is found to be as small as 10.0 cm, which is comparable to that of elaborately tuned tide models. In addition, analysis of the speed and energy of the barotropic tidal currents is found to be consistent with that of past tide studies. The model also showed active excitement of internal tides and tidal mixing. In the future, the impacts of internal tides and tidal mixing should be examined using a model with a finer resolution, since explicit and precise introduction of tides into an OGCM is a significant step toward the improvement of ocean models.

Characteristics of Coupled Atmosphere-Ocean CO2 Sensitivity Experiments with Different Ocean Formulations

Comparison of electrostatic charge generation in gas-solid fluidized beds in turbulent versus pre-turbulent flow regime

A general method using multipliers for finding the conserved integrals admitted by any given partial differential equation (PDE) or system of partial differential equations is reviewed and further developed in several ways. Multipliers are expressions whose (summed) product with a PDE (system) yields a local divergence identity which has the physical meaning of a continuity equation involving a conserved density and a spatial flux for solutions of the PDE (system). On spatial domains, the integral form of a continuity equation yields a conserved integral. When a PDE (system) is variational, multipliers are known to correspond to infinitesimal symmetries of the variational principle, and the local divergence identity relating a multiplier to a conserved integral is the same as the variational identity used in Noether’s theorem for connecting conserved integrals to invariance of a variational principle. From this viewpoint, the general multiplier method is shown to constitute a modern form of Noether’s theorem in which the variational principle is not directly used. When a PDE (system) is non-variational, multipliers are shown to be an adjoint counterpart to infinitesimal symmetries, and the local divergence identity that relates a multiplier to a conserved integral is shown to be an adjoint generalization of the variational identity that underlies Noether’s theorem. Two main results are established for a general class of PDE systems having a solved-form for leading derivatives, which encompasses all typical PDE systems of physical interest. First, all non-trivial conserved integrals are shown to arise from non-trivial multipliers in a one-to-one manner, taking into account certain equivalence freedoms. Second, a simple scaling formula based on dimensional analysis is derived to obtain the conserved density and the spatial flux in any conserved integral, just using the corresponding multiplier and the given PDE (system). Also, a general class of multipliers that captures physically important conserved integrals such as mass, momentum, energy, angular momentum is identified. The derivations use a few basic tools from variational calculus, for which a concrete self-contained formulation is provided.

Finding an equivalence between two feedback control systems is treated as a problem in the theory of partial differential equation systems. The mathematical aim is to embed the Jakubzyk-Respondek, Hunt-Meyer-Su work on feedback linearization in the general theory of differential systems due to Lie, Cartan, Vessiot, Spencer, and Goldschmidt. We do this by using the functor taking control systems into differential systems, and studying the equivalence invariants of such differential systems. After discussing the general case, attention is focussed on the special situation of most immediate practical importance, the theory of feedback linearization. In this case, the general system for feedback equivalence becomes a system of linear partial differential equations. Conditions are found that the general solution of this system may be described in terms of a Frobenius system and certain differential-algebraic operations.

Low Reynolds number k-ϵ model is employed to demonstrate the Bejan's numerical heat and mass flow visualization in turbulent boundary layer regime. The governing turbulence kinetic energy and its dissipation rate equations are included along with conservation equations. The turbulent flow equations are highly nonlinear and coupled in nature, hence, an unconditionally stable Crank–Nicolson finite difference approach is deployed. The computer-generated heatlines, masslines, streamlines, and isotherms for different control parameters are analyzed in the turbulent flow regime. Average momentum, thermal, and concentration diffusion rates are increased upon the increment in in laminar regime and are decreasing with rising in turbulent regime. The stream, heat and masslines deviate more in turbulent regime when compared to laminar regime. Further, the kinetic energy and dissipation rate contours are deviated more in turbulent heat and mass flow regime for different values of . Mainly, in this research paper, the authors made an attempt to demonstrate the turbulent heat and mass flow visualization about a vertical plate using boundary layer approximations through LRN k-ϵ turbulence model.

Based on the theoretical spectral model of inertial internal wave breaking (fine structure) proposed previously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior below the surface mixed layer in the ocean general circulation model (OGCM) is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes (including inertial internal wave breaking product) on oceanic interior mixing is emphasized. We suggest that adding the inertial internal wave breaking mixing scheme (F-scheme for short) put forward in this paper to the turbulence mixing scheme of Canuto et al. (T-scheme for short) in the OGCM, except the region from 15°S to 15°N. The numerical results of F-scheme by using WOA09 data and an OGCM (LICOM, LASG/IAP climate system ocean model) over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation (AMOC) by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.

Nonlocally related partial differential equation (PDE) systems are important in the analysis of a given PDE system. In particular, they are useful for seeking nonlocal symmetries. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related PDE system. In this paper, a new and complementary method for constructing nonlocally related PDE systems is introduced. In particular, it is shown that each point symmetry of a PDE system systematically yields a nonlocally related PDE system. Examples include nonlinear reaction-diffusion equations, nonlinear diffusion equations, and nonlinear wave equations. The considered nonlinear reaction-diffusion equations have no local conservation laws. Previously unknown nonlocal symmetries are exhibited through our new symmetry-based method for two examples of nonlinear wave equations.

The exotic conformal Galilei algebra and nonlinear partial differential equations

Multi-scaling expansion in the systems integrable by the inverse scattering transform

Global climate modeling is one of the grand challenges of computational science, and ocean modeling plays an important role in both understanding the current climatic conditions and predicting the future climate change. Three-dimensional time-dependent ocean general circulation models (OGCMs) require a large amount of memory and processing time to run realistic simulations. Recent advances in computing hardware have dramatically affected the prospect of studying the global climate. The significant computational resources of massively parallel supercomputers promise to make such studies feasible. In addition to using advanced hardware, designing and implementing a well-optimized parallel ocean code will significantly improve the computational performance and reduce the total research time to complete these studies.In our present work, we chose the most widely used OGCM code as our base code. This OGCM is based on the Parallel Ocean Program (POP) developed in FORTRAN 90 on the Los Alamos CM-2 Connection Machine by the Los Alamos ocean modeling research group. During the first half of 1994, the code was ported to the Cray T3D by Cray Research using SHMEM-based message passing. Since the code on the T3D was still time-consuming when large problems were encountered, improving the code performance was considered essential.We have developed several general strategies to optimize the ocean general circulation model on the Cray T3D. These strategies include memory optimization, effective use of arithmetic pipelines, and usage of optimized libraries. The optimized code runs 2 to 2.5 times faster than the original code, which gives significant performance improvements for modeling large scaled ocean flows. Many test runs for both of the original and the optimized code have been carried out on the Cray T3D using various numbers of processors (1-256). Comparisons are made for a variety of real-world problems. A nearly linear scaling performance line is obtained for the optimized code, while the speed up data of the optimized code also shows excellent improvement over the original code.In addition to discussing the optimization of the code, we also address the issue of portability. Given the short life cycle of the massively parallel computer, usually on the order of three to five years, we emphasize the portability of the ocean model and the associated optimization routines across several computing platforms. Currently, the ocean modeling code has been ported successfully to the Hewlett Packard (HP)/Convex SPP-2000, and is readily portable to Cray T3E.This paper reports our efforts to optimize the parallel implementations of the oceanic model. So far, the work has focused on improving the load balancing and single node performance of the code on the Cray T3D. As a result, the atmosphere and ocean model components running side-by-side can achieve a performance level of slightly more than 10 GFLOPS on 512 processors of that machine. We have also developed a user-friendly coupling interface with atmospheric and biogeochemical models, in order to make the global climate modeling more complete and more realistic.

The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations. Meanwhile, homotopy perturbation method yields a very rapid convergence of the solution series in most cases. The developed method, variational homotopy perturbation method, took full advantage of both methods. In this study, we described an application of the variational homotopy perturbation method to solve systems of homogeneous partial differential equations. Here we consider some initial value problems of homogeneous partial differential equation systems with two and three variables. The results show that the obtained solution using this method was in agreement with the solution using the homotopy analysis method and variational iteration method, which prove the validity of the variational homotopy perturbation method when applied to systems of partial differential equations.

Since absorption of solar radiation plays a major role in heating the upper ocean layers, it is essential for modeling physical, chemical and biological processes (e.g., ocean general circulation or marine carbon cycle). In order to simulate the upper ocean thermal structures as realistically as possible, an ocean general circulation model (OGCM) requires accurate solar radiation data, used as the surface boundary condition. In this sense, it is important to recognize the quality of the solar radiation data being expected or suitable for OGCMs beforehand. The appropriate choice of absorption schemes of solar radiation is also important for ocean modeling in the upper ocean. The absorption of solar radiation is greatly affected by many factors, such as the wavelength of sunlight, the zenith angle and ocean optical properties in the ocean interior. Many absorption schemes have attempted to mimic these processes, but the impact of those schemes on the upper ocean thermal structures is not yet fully understood.

Diagnostic methods are defined in order to compare two numerical simulations of ocean dynamics in a region of freshwater influence. The first one is a river plume simulation based on a high resolution numerical configuration of the POM coastal ocean model in which mixing parametrizations have been previously defined. The second one is a simulation based on the NEMO Global Ocean Model used for climate simulations in its half-a-degree configuration in which a river inflow is represented as precipitation on two coastal grid cells. Both simulations are forced with the same freshwater inflows and wind stresses. The divergence of volumetric fluxes above and below the halocline are compared. Results show that when an upwelling wind blows, the two models display similar behavior although the impact of lack of precision can be observed in the NEMO configuration. When a downwelling wind blows, the NEMO Global Ocean configuration can not reproduce the coastally trapped baroclinic dynamics because its grid resolution is too coarse. To find a parametrization to help represent these dynamics in ocean general circulation models, a method based on energy conservation is investigated. This method shows that it is possible to link the energy fluxes provided by river inflows to the divergence of energy fluxes integrated over the grid cells of ocean general circulation models. A parametrization of the dynamics created by freshwater inflows is deduced from this method. This enabled creation of a box model that proved to have the same behavior as the fluxes previously computed from the high resolution configuration.

Steering of upper ocean currents and fronts by the topographically constrained abyssal circulation