# Arrangementer - Side 5

**Three-dimensional instability of solitary water waves**

Flow induced vibration (FIV) is a recent discipline in Flow Assurance which focuses on the piping and equipment vibrations caused by the internal flow of gas, oil and/or water in subsea production systems (SPS). Those vibrations may cause fatigue failure at weak spots in the piping such as welds and tees. Due to recent incidents and ever-increasing production rates and velocities, FIV is now considered as a major limiting factor in the design and operation of SPS. Based on real cases and ongoing projects, this presentation provides an introduction to the following aspects: fluid-structure interaction mechanism, fatigue mechanism, design requirements for SPS, analysis tools and vibration monitoring techniques.

Muligheter for samarbeid med DHI innen forskning, PhD og master-prosjekter.

The symposium is a follow-up of two highly successful previous symposia, held 14-15 October 2008 in the Norwegian Academy in Oslo and 1-2 November 2010 in RSE in Edinburgh. Topics of this year's symposium include: internal waves, ocean surface waves and tsunamis reflecting the activities in the current research projects of the Norwegian and Scottish groups.

Wave measurements are traditionally performed in one of two locations: either at the sea surface or from below the surface. Both have their challenges and benefits.

Nortek is among those offering a subsurface wave measurement solution. This is done with acoustic Doppler current profilers. The presentation will discuss how subsurface wave measurements have evolved in the last decade. An emphasis will be placed on the challenges that exist and what has been done to expand the limits and improve the performance.

Thierry Coupez is professor at Mines - Paristech

We will take a look at ideas for Mechanics Academy (MA), a freely-accessible web-based resource for anyone aiming to learn mechanics.

Harish Narayanan is at SIMULA.

Patrick J. Lynett is from the University of Southern California.

Randall J. LeVeque, Applied Mathematics Department University of Washington

Lateral-torsional buckling of elastic structures under combined loading will be considered in this seminar. This problem has been first reported in the habilitation thesis of Prandtl dated 1899. Closed-form solutions based on Bessel's functions are available for some speciﬁc types of loading. However, numerical methods such as the Finite Element Methods (FEM) or other approximate methods are needed in the general case. More generally, approximation of the buckling curve (limit of the stable domain in the loading parameters space) is investigated from the stationary property of the Rayleigh’s quotient. The approximation is then compared to a numerical approach, namely the iterative method of Vianello and Stodola. Closed-form solutions give upper bounds with relative error less than 0.2%. It is shown that the stable domain of the loading parameter space is convex. The Papkovitch–Schaefer theorem proven in 1934 is extended for this specific problem, despite the nonlinear dependence of the equilibrium equations on the loading parameters for the one-dimensional system. The boundary of the stable domain is clearly nonlinear, but this nonlinearity is weak. It is shown that Dunkerley’s lower bound is relevant for the two structural cases considered, and the maximum relative error induced by such a lower bound is lower than 2%. Prandtl's linear approximation is then validated approximately one century later the pioneer works of Prandtl devoted to elastic instability.

Noël Challamel is Professor at the Department of Civil Engineering (LIMATB), University of South-Brittany, Lorient, France, and Marie Curie fellow at the Department of Mathematics, University of Oslo, Oslo, Norway.

The fundamental mechanisms of plasticity in inorganic glasses are distinctly different from those in crystalline metals. Whereas dislocations and their mobility require plasticity in metals, mechanisms responsible for permanent deformation in glasses are to be looked at the atomistic scale. The lecture will deal with this and will involve topics such as for instance constitutive material laws, plasticity theory, dislocation theory, computational mechanics, multiscale analysis, finite element methods, crack modelling, etc.

Vincent Keryvin is professor at Department of Materials Engineering (LIMATB), University of South-Brittany, Lorient, France.

This seminar will be focused on some elementary structural systems such as the cantilever beam. The cantilever is an old problem in structural mechanics already investigated by Galileo (1638) from equilibrium and strength arguments. This structural paradigm will be reconsidered here using buckling, post-buckling and inelastic theory. We will first present some fundamental buckling results for axially loaded columns. This model covers the case of a tree under its own weight or gives an answer to Babel mythology, at least from the stability theory point of view. This in-plane buckling problem in presence of distributed and concentrated axial forces has been recently exactly solved using hypergeometric functions. The post-buckling behavior associated with a nonlinear boundaryvalue problem will be also discussed using some asymptotic and numerical methods. The out-of-plane buckling problem of this cantilever beam will be further investigated. The lateral-torsiona l buckling problem of Prandtl (1899) dealing with the stability boundary of a beam loaded by its own weight and a concentrated force will be also solved. The convexity theorem of Papkovitch and Schaefer (1934) will be shown for these structural problems. The seminar will be concluded by the inelastic analysis of the beam in bending. We will show the need to develop a nonlocal plasticity law to describe the post-failure behavior of a beam in presence of softening. Wood’s paradox (1968) is overcome by using a nonlocal plasticity model. The Galileo problem is then revisited in the light of nonlocal mechanics. Applications of such theoretical studies can be found in the field of civil engineering at the macro scale (reinforced concrete design, timber beams, steel or composite beams…), but also at micro- or nano-scales including for instance nanostructures.

Challamel is Professor of Civil Engineering, University of South Brittany, Lorient, France, and Marie Curie Fellow in solid mechanics (faststoffmekanikk) at UiO (2011/2012).

Volume tracking is a popular method for the computation of two phase flow problems. In this talk we present a reformulation of volume tracking in two dimensions in terms of an explicit tracking of the interface between the two immiscible phases. This allows for a higher order accurate representation of the interface with respect to the spatial discretization while conserving the mass up to roundoff precision.

Joris Verschaeve is postdoc at the Mechanics Division, Department of Mathematics, University of Oslo.

Ocean Engineering (OE) is considered by many to be a matured field which is mainly controlled by the oil industries. However, due to the growing interdiciplinary nature of OE, it presents new exciting challenges for scientists and engineers with a solid background in topics like hydrodynamics, acoustics, physio-chemistry as well as electro-kinetics, electromagnetics and control theory. Some practical examples will be discussed.

Touvia Miloh is professor at Tel Aviv University.

An idealized mathematical model of tsunami evolution in deep sea and across the continental shelf is proposed. The initial value problem in deep sea is related to the well known Cauchy- Poisson problem, and the tsunami propagation across the continental shelf is derived using the linearized shallow water equations.

When analyzing different cases of tsunamis in deep sea it was found that tsunamis evolve into two basic wave types. One resembles a single wave and the other a wave packet. The analysis of different cases of tsunamis at the shoreline reveals that the continental shelf, due to its geometrical properties, serves as a tsunami amplifier, producing tsunami amplitudes up to 20 times larger than those at the edge of the continental shelf.

A comparison with tsunami measurements suggests that the idealized model may be used for a reliable assessment of the principle hydrodynamic properties of the tsunami, such as the tsunami amplitude and its half- period.

The new mathematical model for tsunami evolution is used to derive a synthetic tsunami database for the southern part of the Eastern Mediterranean coast. Information about coastal tsunami amplitudes, half-periods, currents, and inundation levels is presented.

Michael Stiassnie is professor at the Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology.

Simulations of Fluid-Solid interactions (FSI) are becoming more common as faster computers enables the study of larger models including both fluids and solids. In many applications it is of significant importance to determine the impact that a flowing fluid has on the mechanical structure surrounding it. Vortex-induced vibrations can give structural failure due to fatigue, but it can also produce undesired acoustic noise. During the seminar, several examples of FSI problems and solutions will be demonstrated. The examples include the study of flow induced vibrations in a compressor exhaust, the dynamic flow of oil through a filter, the impact of water waves on a submerged object, etc.

Large-eddy simulations are also advancing in the industrial CFD society. RANS modeling has shown to be insufficient in many complex flow situations, and LES has proven to provide answers to many fundamental questions in turbulent flows. A brief demonstration of an example with flow over a wing profile is presented. Using LES, it is possible to extract valuable information regarding lift, drag, etc., but it is also possible to visualize the turbulent structures evolving from the boundary layer on the wing.

Love Håkansson is at EDR - Engineering Data Resources

Turbulence is complex flow phenomenon with a wide range of scales of motion. Even though there is advancements in measurement technologies, the tools we use in the laboratories are often not adequate to extract all the information necessary for understanding and characterizing this flow. How-wire anemometry has been used by researcher for many decades due to its high temporal resolution. Even though it has good temporal resolution, it can only provide single point data. One also needs to be careful while using hot-wires because it has its own limitations given different flow configurations. In this talk, we will see some examples of hot-wire measurements in shear flow turbulence. Namely we will look at axisymmetric wake, turbulent boundary layers, and wake boundary layer interactions. Each of these measurements requires different setups and different adjustments. We will discuss what we can measure, how we can measure, how we can calibrate and how we should interpret the results.

Murat Tutkun is at the Defense Research Establishment (FFI) and Ecole Centrale de Lille, France

Recent findings show that moderate mixing levels typical of mid-latitude can erode or even remove the Arctic cold halocline layer and that internal wave induced mixing is enhanced in the absence of sea ice. In a seasonally ice-free Arctic Ocean increased levels of mixing, sufficient to remove the cold halocline layer, can be expected as a result of wind energy input over large areas of open water. The ice is then easily exposed to the relatively warm Atlantic water, possibly leading to a strong positive feedback. I will report on insight gained from field work conducted during the International Polar Year. Detailed finescale and turbulence measurements were made from drifting ice in the central Arctic and in the southern Yermak Plateau located in the Marginal Ice Zone northwest of Svalbard. Observations are analyzed to describe the characteristics of internal waves and turbulent mixing in the Arctic Ocean. The role of diapycnal mixing away from abyssal plains is discussed for the Arctic Ocean and regional heat budget and ice cover.

Ilker Fer is at the Department of Geophysics at UiB

This paper presents a Bayesian hierarchical space-time stochastic model for significant wave height. The model has been fitted by data for an area in the North Atlantic ocean and aims at describing the temporal and spatial variability of significant wave height in this area. It could also serve as foundation for further extensions used for long-term prediction of significant wave height and future return periods of extreme significant wave heights. The main model and preliminary simulation results will be presented. Furthermore, a discussion of possible model extensions and future work will be included.

Erik Vanem is at the Statistics division of the Department of Mathematics at UiO

We present a fast marching level set method for reservoir simulation based on a fractional flow formulation of two-phase, incompressible, immiscible flow in two or three space dimensions. The method uses a fast marching approach and is therefore considerably faster than conventional finite difference methods. The fast marching approach compares favorably with a front tracking method as regards both efficiency and accuracy. In addition, it maintains the advantage of being able to handle changing topologies of the front structure.

Co-authored with Knut-Andreas Lie and Kenneth Karlsen

Nils Henrik Risebro is professor at CMA