OS41A-01 INVITED
Ocean Models and Proper Orthogonal Decomposition
The increasing computational developments and the better understanding of mathematical and physical systems resulted in an increasing number of ocean models. Long time ago, modelers were like a secret organization and recognize each other by using secret codes and languages that only a select group of people was able to recognize and understand. The access to computational systems was reduced, on one hand equipment and the using time of computers were expensive and restricted, and on the other hand, they required an advance computational languages that not everybody wanted to learn. Now a days most college freshman own a personal computer (PC or laptop), and/or have access to more sophisticated computational systems than those available for research in the early 80's. The resource availability resulted in a mayor access to all kind models. Today computer speed and time and the algorithms does not seem to be a problem, even though some models take days to run in small computational systems. Almost every oceanographic institution has their own model, what is more, in the same institution from one office to the next there are different models for the same phenomena, developed by different research member, the results does not differ substantially since the equations are the same, and the solving algorithms are similar. The algorithms and the grids, constructed with algorithms, can be found in text books and/or over the internet. Every year more sophisticated models are constructed. The Proper Orthogonal Decomposition is a technique that allows the reduction of the number of variables to solve keeping the model properties, for which it can be a very useful tool in diminishing the processes that have to be solved using "small" computational systems, making sophisticated models available for a greater community.
OS41A-02
Large scale and small-scale components of stratified flows and their mathematical images
Fine structure of atmosphere and hydrosphere is registered by different methods in the environment and observed in laboratory tanks where waves, vortices and flows are modelled The goal of the talk is to describe a mechanism of a fine flow structure formation in a continuously stratified fluid by the examples of internal waves produced by free or forced oscillations of compact bodies. In mathematical modelling based on the set of fundamental governing equations including continuity, Navier- Stokes, Fourier, Fick and state equations with initial and boundary conditions are solved for given particular geometry of the problem. When doing so, a structure of transient diffusion induced flows on a sphere in a continuously stratified fluid is calculated and evolable velocity and density fields are analysed. Flow produced by an oscillating or uniformly moving obstacle (sloping strip, disk, cylinder, sphere) is calculated in linear approximation taking into account viscosity and diffusivity effects. Visualized patterns of flow manifest complex flow structure. Regular components of solutions describe internal waves. Singular components describe boundary layers and their analogues in the fluid interior, which are placed on some characteristics of corresponding Euler problem. In general case there are two viscous singular solutions. One corresponds to classical Stokes periodic flow on the oscillating plane, while the other has no analogues in the uniform fluid. In frame of homogeneous fluid approximation two boundary layers turn to be identical and merged. That leads to insolvability of 3D Navier-Stokes equations both for compressible and incompressible fluids. Additionally, there is combined, or separated, salinity boundary layer, too. In non-linear analysis all regular and singular flow components interact directly upon each other. Presented solutions of linear and weakly non-linear problems of 2D and 3D periodic and attached (lee) internal wave generation match laboratory data rather well. With source oscillation amplitude increase, singular components are being visualized in by the schlieren instrument as the envelopes of the wave beams. Interaction between singular components results in formation of the interfaces in a fluid body bounding fast vortex jets running to the source. Complete classification of 3D periodic flows including the waves and several kinds of the distinguished singular components is presented. Data extrapolation on the environment conditions is discussed.
OS41A-03
A subtlety in forcing eddy resolving ocean models with applied wind stress
High-resolution satellite-mounted scatterometers provide surface wind data containing wealth of new information not included by conventional surface wind measurements, which makes it a more accurate representation of the boundary condition needed for oceanic models. We examine it in the real data that neglecting the ocean current dependence in the wind will increase wind power input to the oceanic general circulation by 29% and can even reverse the sign of the power input in some places of strong ocean currents. An experiment is designed to illustrate a possible pitfall in applying a scatterometer-derived wind stress in modeling ocean circulation. It is that a scatterometer-derived wind stress will lead to spurious energy sources almost as large as that from applying surface wind stress neglecting the ocean current dependence when applied to models directly. We also explain how to avoid this pitfall, and provide the necessary data.
OS41A-04
On the Heat Budget in the Equatorial Pacific in the 1/4 of Degree OCCAM Simulation.
The use of ocean models is an essential tool to improve our knowledge of the different processes that occur in the ocean. I present a study focussed on developing a better understanding of the key physical processes affecting the heat balance in the equatorial tropical Pacific Ocean. The approach I have adopted in this is to look in detail at the different heat flux contributions, in the Ocean Circulation and Climate Advanced Model (OCCAM). Using the model output, I analysed the strength of the equatorial circulation and looked into the importance of each term of the heat balance equation. I further evaluated the importance of each term of the advection scheme used in the model and analysed the Philander and Pacanowski (1981) vertical mixing scheme. Every five days the model archived an instantaneous value of the state of the ocean and a 5-day mean value. I made use of both outputs to make an estimate of the high frequency term, which in the context of my analysis represents physical processes not captured by the available model output.I carried out an analysis of the variations in time of the different processes that contribute to the vertical mixing close to the equator. One of the main findings was the presence of instability processes during the first half of the year with higher period than the Tropical Instability Waves in the eastern equatorial Pacific ocean.
OS41A-05
A Pretty Good Sponge
Comparisons are made of the effectiveness of sponge formulations for the suppression of outgoing waves at the edges of two-dimensional open computational domains. Results using perfectly matched layers (PML) are compared to those of a pretty good sponge (PGS). PGS has cabilities nearly matching those of the PML, while being much easier to implement. Evaluations have been made in the context of the linear and non-linear rotating shallow water wave equations with and without imposed background flows. With background flow, PGS becomes a very specific type of nudging or forcing sponge or flow relaxation scheme. An example of internal wave generation over a ridge shows the extendibility of PGS to three dimensional baroclinic problems. Together results show that PGS is an effective and computationally simple way to arrest outgoing waves in a large class of limited domain, ocean wave scattering problems.
OS41A-06 INVITED
Nonhydrostatic effects of nonlinear internal wave propagation in the South China Sea
It is well known that internal tides are generated over steep topography at the Luzon Strait on the eastern
boundary of the South China Sea. These internal tides propagate westward and steepen into trains of weakly
nonlinear internal waves that propagate relatively free of dissipation until they interact with the continental shelf on
the western side of the South China Sea, some 350 km from their generation point. The rate at which the internal
tide transforms into trains of nonlinear waves depends on the Froude number at the generation site, which is
defined as the ratio of the barotropic current speed to the local internal wave speed. Large Froude numbers lead
to rapid evolution of wave trains while low Froude numbers generate internal tides that may not evolve into wave
trains before reaching the continental shelf. Although the evolution into trains of weakly nonlinear waves results
from the delicate interplay between nonlinear steepening and nonhydrostatic dispersion, the steepening process
is represented quite well, at least from a qualitative standpoint, by hydrostatic models, which contain no explicit
nonhydrostatic dispersion. Furthermore, hydrostatic models predict the propagation speed of the leading wave in
wave trains extremely well, indicating that its propagation speed depends very weakly on nonlinear or dispersive
effects. In order to examine how hydrostatic models introduce dispersion that leads to the formation of wave
trains, we simulate the generation and evolution of nonlinear waves in the South China Sea with and without the
hydrostatic approximation using the nonhydrostatic model SUNTANS, which can be run in either hydrostatic or
nonhydrostatic mode. We show that the dispersion leading to the formation of wave trains in the hydrostatic
model results from numerically-induced dispersion that is implicit in the numerical formulation of the advection
terms. While the speed of the leading wave in the wave trains is correct, the amplitude and number of waves in
the wave trains is not correctly computed by the hydrostatic model. This has important implications for the
predictability of wave amplitude upon arrival at the continental shelf using hydrostatic models.
http:suntans.stanford.edu
OS41A-07
Nonhydrostatic Modeling of the Transformation and Interaction of Nonlinear Internal Waves in the South China Sea
Nonlinear internal waves (NLIWs) are generated at the Luzon Straits. As these waves propagate across the South China Sea their amplitudes increase and they steepen forming solitary wave trains. These waves impinge on the slope of the Dong Sha Plateau where they under go significant transformations and interact with locally generated NLIWs. These transformations from waves of depression to waves of elevation and from solitary waves to multi-crested waves are highly nonlinear and nonhydrostatic. Furthermore the interactions with locally generated waves are complex and also nonhydrostatic. We study the transformation and interactions of these waves using local, nested nonhydrostatic models which are in turn nested inside hydrostatic models. This method allows the use of high resolution nonhydrostatic models which would be computationally prohibitive if used over the entire South China Sea. However it requires that the open boundary values for the nonhydrostatic models be a hybrid of the values from the hydrostatic models, which predict the phase of the NLIWs well but underpredict the amplitude, and values from a semi- analytic model which more correctly predicts the amplitude. Low resolution results have shown the transformation from waves of depression to waves of elevation and have demonstrated the interaction of the solitary wave trains with the topography.
OS41A-08
Stability of Internal Gravity Waves in Sheared Inertial Currents
Observations of the oceanic internal wave field exhibit characteristic spectral peaks near the local inertial frequency. Near-inertial internal gravity waves are characterized by nearly horizontal currents with a flow direction that oscillates at the inertial frequency. In this work, we consider the stability of near-inertial waves in the limit of infinite horizontal scale and constant shear and stratification and pose the question: Are there small-scale internal gravity waves of infinitesimal amplitude that grow exponentially within such a flow? The stability problem is addressed using Floquet theory and the results are examined within a three-dimensional parameter space defined by the characteristic frequencies of the problem; the buoyancy frequency, the shear and the free-wave frequency of an infinitesimal test-wave, all normalized by the inertial frequency. Growth rates are computed numerically and distinct zones of instability are identified. A principal finding is that for particular combinations of shear, stratification and rotation, internal wave disturbances of all frequencies grow exponentially on the inertial time scale even when the neccessary condition for steady KH instability (N2 / S2 < ¼) is not satisfied. In the limit of vanishing shear, the zones of instability collapse to a discrete set of unstable waves. These waves further divide into those with frequencies such that they are periodic at the inertial period and those that are periodic at twice the inertial period.