Seminarer - Side 9

Jan Erik H. Weber, Department of Geosciences, University of Oslo Göran Broström, Norwegian Meteorological Institute, Oslo Nonlinear density-driven convection in a conditionally unstable fluid is studied theoretically. The novelty here is that the destabilizing basic density gradient is expressed in terms of the vertical perturbation velocity through a unit step function. This is done by introducing a one-way source step function due to phase transitions in the equation for the perturbation density. Then we can model the fact that the density-gradient is unstable when the perturbation vertical velocity is upward (positive), and stable when the vertical perturbation velocity is downward (negative), characterizing conditional stability. Linear analytical solutions as well as numerical results for nonlinear two-dimensional steady convection are presented.

Jan Erik Weber is professor at Department of Geosciences

A theoretical model for propagation of internal waves under an ice cover is developed. The sea water is considered to be inviscid, non-rotating, and incompressible and the Brunt-Väisälä frequency is supposed to be constant. The ice is considered of uniform thickness, with constant values of Young's modulus, Poisson's ratio, density and compressive stress in the ice. The boundary conditions are such that the normal velocity at the bottom is zero and, at the undersurface of the ice, the linearized kinematical and dynamic boundary conditions are satisfied. We present and analyze explicit solutions for the internal waves under the ice cover and the dispersion equations. It is shown that when the frequency is near, but smaller than the Brunt-Vaisela frequency the ice deflections can be considerable. The theoretical results are compared with experimental data for the Arctic regions.

Sergey Muzylev is at the Shirsov Institute of Oceanology, Moscow

The study is based on field measurements since 2002. We analyze the transport of Antarctic Bottom Water in Deep Channels of the Atlantic: Vema Channel (31deg S), Romanche Fracture Zone (0 deg) and Vema Fracture Zone (11 deg N). The flow of bottom water in the Vema Channel can reach 4 mln. sq. m per second and the velocity is as high as 60 cm/s. The transport and velocities in the Romanche Fracture Zone and Vema Fracture Zone are smaller and do not exceed 500 th. sq. m per sec. The major penetration of bottom waters to the Northeastern Atlantic basins occurs through the Vema FZ but not through the Romanche FZ because strong tidal internal waves on the slopes of the Mid-Atlantic Ridge near Romanche FZ exceed 50 m, while at the Vema FZ they are approximately 20 m. Such difference in mixing of bottom waters with the overlying North Atlantic Deep water results in the fact the deep Northeastern Atlantic basins are filled with the bottom water transported through the Vema FZ.

Eugene Morozov is proessor at the Shirshov Institute of Oceanology, Moscow

This presentation concerns the mathematical formulation of steady surface gravity waves in a Lagrangian description of motion. It will be demonstrated that classical second-order Lagrangian Stokes-like approximations do not represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time, i.e. without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of same order.

Didier Clamond has been a post.-doc. at the Department at Mathematics, UiO. He is now faculty member at the University of Nice, Sophia-Antipolis.

The talk deals with the stability of water waves in a shear flow. A carefully designed numerical solver enables to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a shear-velocity of 1 m/s). The main finding is the appearance of a second unstable mode which quite often turns out to be the dominant one. A comparison between results from the viscous model (Orr-Sommerfeld equations), and those of the inviscid model (Rayleigh equations), for 18cm long waves, reveals some similarity in the structure of the eigenfunctions, but a significant difference in the imaginary part of the eigenvalues (i.e. the growth-rate). It is found that the growth-rate for the viscous model is 10 fold larger than that of the inviscid one.

Michael Stiassnie er professor ved Technion, Israel

M. Stiassnie , A. Regev, and Y. Agnon: The stability and long-time evolution of narrow spectra homogeneous seas subject to inhomogeneous disturbances is studied. Specifically, we study unidirectional spectra, where according to classical homogeneous theory (i.e. the Kinetic equation), no spectral evolution is expected. In the region of instability , recurrent evolution is discovered. This behavior is qualitatively different from recent work on discrete spectra that exhibited irreversible widening of narrow spectra. The inhomogeneous structure of the unstable modes that leads to the recurrent evolution is revealed.

Technip is a world-class player in engineering, technologies and construction services for oil and gas, petrochemical and other industries. With a workforce of > 22,000 people worldwide, and annual revenues of almost 7 billion euros, TECHNIP ranks among the 5 major players in full-service engineering and construction services in the field of hydrocarbons and petrochemicals. Technip Norge is a specialist offshore / subsea construction company with offices in Oslo ( Stabekk ), Stavanger and Haugesund plus a pipeline fabrication yard in Orkanger. Using a fleet of specialist vessels the main areas of activity in Norway are projects for the engineering, procurement, supply and installation of rigid pipelines, flexible risers and subsea structures plus all necessary activities related to this, such as diving, ROV operations, offshore survey, trenching and rock-dumping. The presentation will give a general introduction to the company, our special areas of technical expertise and a brief summary of some of the challanges experienced on one of our recent projects.

Tim Crome is Engineering Manager in Technip Norge AS

Presentasjonen omhandler fokus, hovedsamarbeidspartnere, og om hvordan mekanikk kan bidra til den nye SFFen

Hans Petter Langtangen er utdannet på mekanikk og var ansatt på Matematisk institutt før han flyttet til IFI og etterhvert SIMULA senteret. Langtangen er leder av den nye SFFen

Stratified flow phenomena are prevalent throughout the oceans. We present the results of laboratory experiments that study several ocean inspired problems, including: the settling of marine snow, spontaneous propulsion of asymmetric objects and the generation of internal wave beams by topography. These experiments cover a large range of physical scales, from as small as 100 microns for the settling of marine snow to several meters for internal wave generation, emphasizing the richness of interesting and important research problems is stratified flow

Dr. Tom Peacock of Dept. of Mechanical Engineering, MIT is a visitor at the BILAT-program. He is an expert on theoretical physics, and does currently theoretical, experimental and field work on internal waves in the ocean.

 

 

Short presentation of Shell Technology Norway, STN STN strategy and focusing areas Typical Subsea and cleaner production activities Typical RD projects A typical field development project, Ormen Lange STN RD challenges

In a recent Ph.D. project the possibility of applying the Discontinuous Galerkin spectral/hp element method for the next generation of Boussinesq-type models has been investigated. These numerical methods have reached a level of maturity that turns them into an attractive alternative to the existing Boussinesq-type models, which traditionally have been based on finite difference methods in structured domains. In particular, we seek to take advantage of the geometrical flexibility of spectral/hp finite element methods to enable us to solve wave problems in increasingly complex environments. A nodal discontinuous Galerkin finite element method (DG-FEM) is used for the spatial discretization to solve a recently derived set of high-order Boussinesq-type equations [1] in complex and curvilinear geometries, and thereby amends the application range of previous numerical models. The new Boussinesq method allows for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep waters, and to demonstrate and investigate the applicability of the model both linear and nonlinear test cases have been considered where water waves interact with bottom-mounted fully reflecting structures. References [1] Madsen, P. A., Bingham, H. B. and Liu, H. 2002 A new Boussinesq method for fully nonlinear waves from shallow to deep water. J. Fluid Mech. 462, pp. 1-30.

Dr. Allan Engsig-Karup is at Coastal, Maritime and Structural Engineering Technical University of Denmark (DTU) Lyngby, Denmark.

Oljeindustrien i Norge startet opp på 70-tallet, dvs. at mange av de konstruksjoner som står i nordsjøen nå er over 30år gamle. Ny teknologi gjør at oljeselskapene kan ta ut mer olje og gass av reservoarene enn det som opprinnelig var planlagt. Dessuten finner de nye felt som utvinnes via undervannsteknologi, men som fordrer behandling på eksisterende konstruksjoner. Dette gjør at levetiden til eksisterende konstruksjoner må forlenges. Forlengelse av levetid for store komplekse konstruksjoner er en av kjernevirksomhetene til konstruksjonsavdelingen i FORCE Technology. Ved bruk av avanserte berengningsmodeller/programmer bistår vi våre kunder med å evaluere nye miljølaster (bølger, vind, strøm etc.), nye vekter og ikke minst konstruksjonens integritet som følge av disse nye endringene. Foredraget vil gi eksempler på noen prosjekter FORCE jobber med, programmer vi bruker og teorien bak noen av disse.  Vi ønsker ikke minst studenter velkommen til seminaret. Både interesserte på bachelor- og masterstudiet. Det vil være mulighet for en samtale med FORCE etter foredraget med tanke på mulig ansettelse i FORCE. Klikk herfor mer informasjon.

 

Air-sea interaction plays a vital role in modulating weather and climate from global scales down to scales of the smallest surface waves. Ultimately, the bulk parameterization of air-sea fluxes in coupled atmosphere-ocean models depends on small scale processes. In this talk I will present results of ongoing air-sea interaction research at Scripps that uses both traditional atmospheric measurements of heat flux along with infrared imaging of the sea surface to study wave-modulated heat flux and surface turbulence. These measurements were made off the Scripps Pier and from R/P FLIP off the coast of California. A second set of experiments was undertaken in the Gulf of Tehuantepec, on the Pacific coast of Mexico, which is well known for the regular occurrence of high winds in winter which blow through the mountain gap at the head of the gulf out over the Pacific. In February 2004, we conducted a 4-week campaign of airborne measurements of the development of the wave field and wind field with fetch out to approximately 500 km offshore. The primary aim of the experiment was to measure the coupled development of the wave field and wind field, including the statistics of surface wave breaking for an improved understanding of the dissipation of surface waves and their role in air-sea fluxes. We used the NSF/NCAR C130 with its standard suite of meteorological measurements, GPS dropsondes and AXBTs, along with the NASA Airborne Terrain Mapper (ATM) used as a scanning LIDAR for surface wave measurement, and a video imaging package for measuring whitecaps. I will present an overview of the experiment and the results so far pertaining to the evolution of the surface wave field, wave breaking and extreme wave statistics.

Ken Melville is professor at the Scripps Institution of Oceanography, University of California and is an international expert on air-sea interaction.

In order to secure the safety of ships travelling along the Norwegian coast, several fine-scale wave models have been applied for the most dangerous wave areas, such as the Steady State Irregular Wave Model (STwave) and a refraction model (www.met.no: kyst_og_hav). Lately, the model Simulating Waves Nearshore (SWAN) from TUDelft, The Netherlands, was employed to forecast waves in Trondheim ship lane. SWAN is a spectral wave model, similar to WAM, developed for shallow water or coastal areas by including depth-induced wave breaking, triad wave-wave interaction and an implicit numerical scheme that allows SWAN to run efficiently on high horizontal resolution. At met.no, SWAN was set up with 418x150 grid points and a 500mx500m grid cell size. It receives spectra on the outer boundaries from met.no's operational version of WAM and is driven by winds from a 4 km x 4 km atmospheric model. The model has furthermore the option to include varying current fields (refraction, blocking, and frequency shift) which we would like to test. Current fields can be obtained from an ocean or tidal model. We will present our experience with SWAN and results so far of comparing the forecasted wave parameters with those from a buoy located at Stor-Fosna in the ship lane. Acknowledgements: The work is performed in collaboration with the Norwegian Coastal Authorities (Kystverket).

The temporal evolution of the energy spectrum of a field of random surface gravity waves in deep water is investigated by means of direct numerical simulations of the deterministic primitive equations. The detected rate of change of the spectrum is shown to be proportional to the cubic power of the energy density and agree quite well with the nonlinear energy transfer $S_{nl}$ as predicted by Hasselmann. In spite of the fact that use of various asymptotic relations which are valid only for $t\to\infty$ or integration with respect to time over a time scale much longer than $O({\rm period}\times (ak)^{-2})$ are necessary in the derivation of Hasselmann's $S_{nl}$, it is clearly demonstrated that the rate of change of the spectrum given by the numerical simulation agrees quite well with Hasselmann's $S_{nl}$ at every instant of ordinary time scale comparable to the period. The result implies that the four-wave resonant interactions control the evolution of the spectrum at every instant of time, while non-resonant interactions do not make any significant contribution even in a short-term evolution. It is also pointed out that the result may call for a reexamination of the process of derivation of the kinetic equation for the spectrum.