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Around Hopen Island, the satellite images and experiments with drifting buoys describe the movement of the drifting ice and depict tidally generated trapped motion. An analytical solution is applied to investigate the trapping phenomenon. A general solution is achieved by the superposition of the incident and reflected (scattered) waves for an elliptically shaped island above the critical latitude. The incident wave simulates the tidal wave propagation toward the island and its prominent feature, an amphidromic point located to the southeast from Hopen Island. The analytical solution for the reflected wave is constructed in elliptic coordinates. Tide amplitudes and cophase lines are analyzed in the island’s vicinity and compared to observations and numerical model results. A simulated drift of Lagrangian water particles constructed with the help of analytical solutions reproduces well the observed clockwise trapped motion of the drifting buoy near Hopen Island. Since the resonance may amplify the semidiurnal incident tide, we have also investigated the natural modes of water oscillations near the island. While this paper focuses on the details of the model used at the specific site of Hopen Island, a similar trapping analysis can be applied to circular or elliptic islands that have a small scale relative to the barotropic Rossby deformation radius. Significance Statement This study aims to understand how the semidiurnal tide propagates and generates strong currents near Hopen Island in the Barents Sea. The trapping of the semidiurnal (M2) tide around Hopen Island leads to an organized dipole structure in sea level, which rotates clockwise. The dipole generates maximum amplitudes of water surface elevation and the strong current near the south and north tips of the island. The abrupt sea level change induced by the dipole sets up often violent currents, which, together with drifting ice, can be dangerous for navigation. The strong tidal currents generate permanent clockwise circulation around the islands, which is essential for biological life and waste disposal as material disposed of near the islands will be trapped for an extended time. Our investigation elucidates the role of dipoles in the local enhancement of tides around the islands.

The Synchronous Reluctance Machine (SynRM) is an electrical machine in which the useful electromagnetic torque is produced due to rotor saliency. Its high power- and torque-to-mass ratio and very good efficiency make it a cheap and simple alternative for permanent magnet or induction motors, e.g. in electromobility applications. However, because of magnetic nonlinearities, the rotational speed and torque control of a SynRM is a nontrivial task. In the paper, a control algorithm based on a Hamiltonian mathematical model is presented. The model is formulated using measurement results, obtained by the drive controller. An algorithm is tested in the drive system consisting of a SynRM with the classical rotor and a fast prototyping card. The drive dynamic response in transient states is very good, but the proposed algorithm does not ensure the best efficiency after steady state angular velocity is achieved.

In this paper, a novel, composite material is proposed based on ferromagnetic wires immersed in a polymer that is well suited for 3D printing. The magnetic properties of this material are examined using FEM and compared with the properties of a more traditional composite based on magnetic powder. For a 50% ferromagnetic volume in the material, the proposed composite has a 67% higher value of saturation magnetic flux density and 87% higher value of maximum permeability, compared with the powder-based material. The authors believe that the proposed material could be used in the manufacturing of small electromechanical devices such as energy harvesters, thus vastly widening the possible fields of application related to 3D printing techniques.

Tsunamis are one of the most catastrophic natural hazards that can devastate coastal regions. Most common mechanisms that generate tsunamis are undersea earthquakes and submarine landslides. However, in enclosed basins, such as fjords, reservoirs, and lakes, subaerial landslides can also generate devastating tsunamis with similar or worse consequences, because of a more efficient wave generation. Here, we present the validation of a three-dimensional (3D) numerical model, TSUNAMI3D, by comparing numerical results with a set of subaerial landslide laboratory experiments carried out in the large tsunami wave basin at the Oregon State University (OSU). Results obtained from the laboratory experiments show that subaerial landslides generate highly non-linear waves with complex wave patterns and runup, challenging existing numerical models. The 3D numerical model is first verified with a commercial code, FLOW3D, to obtain a compromise between the model’s spatial-time resolution accuracy and computational cost. Second, the 3D numerical model and the commercial code are validated with a set of OSU laboratory experiments comprising three different layouts or basin configurations, namely, fjord, curved headland, and basin-wide. Simplified material rheology and key parameters required for modeling subaerial landslides are defined. Numerical models’ relative errors are estimated and analyzed, and the models’ limitations are discussed. In general, numerical models’ relative errors are found to be acceptable in most of the validation tests except those tests located close to the wave generation region. Validation results confirm that the 3D numerical models with simplified landslide rheology can be used to understand and reproduce the complex non-linear wave propagation and runup generated by subaerial landslides. Thus, TSUNAMI3D can help assess tsunami hazards in communities located in proximity to potential subaerial landslides. Also, the set of physical experiments can be used for further numerical validation efforts, helping tsunami organizations, e.g., the National Tsunami Hazard Mitigation Program, to amend existing or develop better numerical models and thus, improve inundation/evacuation mapping products that would save lives and property.

The paper presents the estimation methodology for uncertainties of magnetic flux linkage measurements, when the flux linkage and current functions with respect to time are obtained instead of single values of these quantities. The computed uncertainties are then used to estimate the quality of an approximation of a current-flux characteristic in the mathematical model of an electrical machine when the approximation is based on the results of measurements.

The paper presents an algorithm for the construction of an approximation of a highly nonlinear current-flux characteristic of a synchronous reluctance machine. Such an approximation is required in a Hamiltonian model of an electric machine and the constructed approximation is suited to be used in such a model. It employs a simplicial approximation based on irregular points sets in the spaces of currents and fluxes. The sets are constructed by the iterative insertion of new points. Initially the sets contain an arbitrarily small number of elements. The insertion is based on an approximation error calculation. Based on the sets containing possibly small number of elements, the proposed procedure leads to smooth and precise approximation. Due to the nonlinearity of the approximated characteristics, ambiguities can occur. A method for the triangulation refinement of the sets of currents and fluxes that eliminates them is also presented. In the paper, a reluctance machine model using the constructed approximation is described and compared with a model using the approximation based on regular sets

In the paper a control algorithm of an electrical machine, that is based on its hamiltonian mathematical model described in the dq0 reference frame, is introduced. The algorithm is designed to be specifically useful to control Synchronous Reluctance Machines. In the algorithm flux linkage values in the direct and quadrature axis are treated as state variables. Those flux linkage values and the electromagnetic torque are estimated using the aforementioned model. The algorithm is divided into two modes, first to ensure fast reaching of the commanded angular velocity and second to ensure stable operation of the drive when it is obtained. Additional criterion used in the control algorithm is to minimize the ohmic losses in the phase windings. In the paper the way of formulation of the needed mathematical model by the drive controller, based on the measurement results, is also presented. The performance of the algorithm is examined numerically.

This dissertation describes the formulation, verification, and validation of a dispersive wave model with a shock-capturing scheme, and its implementation for basin-wide evolution and coastal runup of tsunamis using two-way nested computational grids. The depth-integrated formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. The semi-implicit, finite difference solution captures flow discontinuities associated with bores or hydraulic jumps through a momentum conservation scheme, which also accounts for energy dissipation in the wave breaking process without the use of an empirical model. An upwind scheme extrapolates the free surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This eliminates depth extrapolation errors and greatly improves the model stability, which is essential for computation of energetic breaking waves and runup. The vertical velocity term associated with non-hydrostatic pressure also describes tsunami generation and transfer of kinetic energy due to dynamic seafloor deformation. A depth-dependent Gaussian function smooths bathymetric features smaller than the water depth to improve convergence of the implicit, non-hydrostatic solution. A two-way grid-nesting scheme utilizes the Dirichlet condition of the non-hydrostatic pressure and both the velocity and surface elevation at the grid interface to ensure propagation of dispersive waves and discontinuities through computational grids of different resolution. The inter-grid boundary can adapt to topographic features to model wave transformation processes at optimal resolution and computational efficiency. The computed results show very good agreement with data from previous laboratory experiments for wave propagation, transformation, breaking, and runup over a wide range of conditions. The present model is applied to the 2009 Samoa Tsunami for demonstration and validation. These case studies confirm the validity and effectiveness of the present modeling approach for tsunami research and impact assessment. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models.

First, we investigated some aspects of tsunami–tide interactions based on idealized numerical experiments. Theoretically, by changing total ocean depth, tidal elevations influence the speed and magnitude of tsunami waves in shallow regions with dominating tidal signals. We tested this assumption by employing a simple 1-D model that describes propagation of tidal waves in a channel with gradually increasing depth and the interaction of the tidal waves with tsunamis generated at the channel's open boundary. Important conclusions from these studies are that computed elevations by simulating the tsunami and the tide together differ significantly from linear superposing of the sea surface heights obtained when simulating the tide and the tsunami separately, and that maximum tsunami–tide interaction depends on tidal amplitude and phase. The major cause of this tsunami–tide interaction is tidally induced ocean depth that changes the conditions of tsunami propagation, amplification, and dissipation. Interactions occur by means of momentum advection, bottom friction, and variable water flux due to changing total depth and velocity. We found the major cause of tsunami–tide interactions to be changing depth. Secondly, we investigate tsunami–tide interactions in Cook Inlet, Alaska, employing a high-resolution 2-D numerical model. Cook Inlet has high tides and a history of strong tsunamis and is a potential candidate for tsunami impacts in the future. In agreement with previous findings, we find that the impacts of tsunamis depend on basin bathymetries and coastline configurations, and they can, in particular, depend on tsunami–tide interactions. In regions with strong tides and tsunamis, these interactions can result in either intensification or damping of cumulative tsunami and tide impacts, depending on mean basin depth, which is regulated by tides. Thus, it is not possible to predict the effect of tsunami–tide interaction in regions with strong tides without making preliminary investigations of the area. One approach to reduce uncertainties in tsunami impact in regions with high tides is to simulate tsunamis together with tidal forcing.

This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright © 2008 John Wiley & Sons, Ltd.

A numerical model for the global tsunamis computation constructed by Kowalik et al. (2005), is applied to the tsunami of 26 December, 2004 in the World Ocean from 80°S to 69°N with spatial resolution of one minute. Because the computational domain includes close to 200 million grid points, a parallel version of the code was developed and run on a Cray X1 supercomputer. An energy flux function is used to investigate energy transfer from the tsunami source to the Atlantic and Pacific Oceans. Although the first energy input into the Pacific Ocean was the primary (direct) wave, reflections from the Sri Lankan and eastern shores of Maldives were a larger source. The tsunami traveled from Indonesia, around New Zealand, and into the Pacific Ocean by various routes. The direct path through the deep ocean to North America carried miniscule energy, while the stronger signal traveled a considerably longer distance via South Pacific ridges as these bathymetric features amplified the energy flux vectors. Travel times for these amplified energy fluxes are much longer than the arrival of the first wave. These large fluxes are organized in the wave-like form when propagating between Australia and Antarctica. The sources for the larger fluxes are multiple reflections from the Seychelles, Maldives and a slower direct signal from the Bay of Bengal. The energy flux into the Atlantic Ocean shows a different pattern since the energy is pumped into this domain through the directional properties of the source function. The energy flow into the Pacific Ocean is approximately 75% of the total flow to the Atlantic Ocean. In many locations along the Pacific and Atlantic coasts, the first arriving signal, or forerunner, has lower amplitude than the main signal which often is much delayed. Understanding this temporal distribution is important for an application to tsunami warning and prediction.

Basic tsunami physics of propagation and run-up is discussed for the simple geometry of a channel. Modifications of a numerical technique are suggested for the long-distance propagation and for the nonlinear pro- cesses in tsunami waves. The principal modification is application of the higher order of approximations for the first derivative in space. Presently, tsunami calculations employ the high resolution 2D and 3D models for generation and runup processes, while propagation is resolved by the reg- ular 2D models. Such approach requires boundary conditions which will seamlessly connect the high resolution calculations to the propagation models. These conditions are described with the help of the method of characteristics.

Tidally-generated, trapped motions can signie cantly enhance and modify sea level and currents in the island proximity. The analytical solution for incident waves interacting with a cylindrical island with a circular sill has been constructed to investigate this phenomenon. To derive solutions for the scattering problems simple Sverdrup and Kelvin waves are used as incident waves. The amplie cation of the signal along the island perimeter has shown to be a function of frequency, relative dimensions of the island and the circular sill surrounding the island, relative sill depth, and the bottom friction. Although the incident diurnal tide may be amplie ed through the resonant response, this resonance occurs in the shallow water where the bottom friction damps the effect. The dispersion equation shows that the geometry of the problem favors amplie cation of semidiurnal tides. Analytical solutions obtained by superposition of the incident and scattered waves around an island are used to explain the observed peculiarities of tides in the vicinity of the Pribilof Islands, Bering Sea.

Basic tsunami physics of propagation and run-up is discussed for the simple geometry of a channel. We will try to understand how linear and nonlinear processes occurring in a tsunami should influence approach taken to numerical computations.

Observations in the region of the Pribilof Islands and Canyon (PIC) reveal a clockwise circulation around the group of islands and around each of the two largest islands, St. Paul and St. George. Six current meters deployed around St. Paul Island revealed a steady clockwise flow around the island, which was strongest south of the island and weakest to the east. We use a high-resolution tidal model in the PIC region to show that this flow pattern results from tidal rectification over the shallow topography tides. Tidal residual currents of 10-15 cm s - were predicted by the model, compared to mean currents of 5-20 cm s - observed at the mooring sites. Both diurnal and semidiurnal tidal oscillations contribute to the clockwise circulation around the islands. In the diurnal band the enhanced currents occur also at the shelf slope where a tidal wave generates a shelf wave due to resonance with topography. In the PIC region the main shelf wave occurs in the Pribilof Canyon where both observations and measurements show enhancement of the diurnal tidal currents.

Diurnal tidal waves K1 and O1 were studied using a primitive equation ocean circulation model with fine vertical resolution. The study focused on Kashevarov Bank, a shallow submarine bank at the northern continental slope of the Sea of Okhotsk. Owing to resonance, the currents over the bank are 20–30 times stronger than the off-bank currents. The large current amplitudes of the basic tidal waves K1 and O1, through nonlinear interactions, generate residual currents and new oscillations in the semidiurnal, fortnightly and other bands. The model predicts a strong clockwise residual circulation, with barotropic and baroclinic components. The latter is about 50% of the total residual flow over the bank top. To elucidate the role of various terms in maintenance of the residual motion, the time-averaged momentum and heat balance equations were analyzed. The time-averaged flow over the bank top is ageostrophic, and the horizontal advection is dominant in the tidal rectification. To demonstrate the influence of the tides on the thermohaline structure over Kashevarov Bank, horizontally uniform and vertically stratified initial temperature and salinity distributions were considered. Strong tidal mixing results in an almost homogeneous thermohaline structure and well-developed internal tides over the bank summit. This fact demonstrates the role of tides in establishing the observed homogeneous stratification over Kashevarov Bank.

Eight major tidal constituents in the Sea of Okhotsk have been investigated using a numerical solution of tidal equations on a 59 space grid. The tides are dominated by the diurnal constituents. Diurnal tidal currents are enhanced in Shelikhov Bay and Penzhinskaya Guba, at Kashevarov Bank, in proximity to the Kuril Islands and at a few smaller locations. The major energy sink for diurnal tides (over 60% of the total energy) is Shelikhov Bay and Penzhinskaya Guba. The major portion of semidiurnal tide energy is dissipated in the northwestern region of the Sea of Okhotsk and in Shelikhov Bay and Penzhinskaya Guba. Nonlinear interactions of diurnal currents are investigated through K1 and O1 constituent behavior over Kashevarov Bank. These interactions generate residual circulation of the order of 10 cm s 21, major oscillations at semidiurnal and fortnightly periods (13.66 days), and higher harmonics of basic tidal periods. The M2 tidal current, caused by the nonlinear interaction of the diurnal constituents over Kashevarov Bank, constitutes approximately a half of the total M2 tide current there. The fortnightly current, through nonlinear interactions, also influences basic diurnal tidal currents by inducing fortnightly variations in the amplitude of these currents.

Oceanic tidal angular momentum (OTAM) is calculated for the four major tides of the Arctic Ocean, based on the tidal elevations and current velocities from a recent two-dimensional numerical hydrodynamic model. The presented OTAM tables are meant to be complementary to other modeling studies that use satellite altimetry (which cannot observe Arctic Ocean tides because of ice cover and limited satellite inclinations). Although the Arctic Ocean's influence on earth rotation is, as may be expected, relatively small, the rapid advancement of the subject now calls for such small contributions to be explicitly accounted for.

Diurnal tidal constituents K1 and O1 are calculated in the Nordic seas with a numerical space grid of about 10 km. This allows resolution of the structure of enhanced tidal currents generated by near-resonant topographic vorticity waves at the Yermak Plateau. The resonance properties of the Yermak Plateau are investigated in the period range 20–30 h. The main resonance peak is close to the 26-h period, and the resonance curve envelops a wide range of periods. This broad resonance peak explains the enhancement of both diurnal tidal components separated by a 2-h difference and the stability of the resonance phenomena. The model results describe well the observed flow pattern over the Yermak Plateau, including the current ellipse rotation.

A steady state diagnostic numerical model is used to describe the circulation in the Alaska Coastal Current. The Alaska Coastal Current extends northwards from the Columbia River around the Gulf of Alaska where it becomes a relatively high speed flow. It is characterized by low salinities created by high rates of coastal fresh water discharge. The diagnostic numerical model developed used hydrographic data with spatial resolution of 3.7 km. The results are compared with vertically averaged profiling current meter measurements. The alongshore current components agree quite well while the cross-shelf components occasionally differ not only in magnitude but also in their sign. The model also predicts an increase in the alongshore flow in the offshore regions. This variation is verified by the current meter data. Vertical profiles of the current were compared with the model flows with favorable results in the alongshore direction and a less certain outcome in the offshore flow. While the alongshore flow is well represented by the model, the cross-shelf motion is poorly represented. This could be a contrast between the high speed alongshore flows as compared with the relatively weak cross-shelf flow. The bottom topography also plays an important role in controlling the shelf circulation here.

[1] Crescent City (CC) is particularly susceptible to tsunami attack. The combination of tsunami signal enhancement by both distant bathymetric features and local nearshore resonance seems to be responsible for this behavior. Application of global tsunami propagation models to the Kuril Islands Tsunami of November 2006 in the companion paper (Kowalik et al., 2008) delineated the importance of distant bathymetric features for both tsunami wave amplification and for increased duration of the tsunami arriving at CC. These distant features were responsible for delivering the late, high-energy signal, which was delayed by 2 hours from the predicted arrival time. Additional local amplification and increased duration are caused by the shelf bathymetry adjacent to CC. As the initial tsunami arrives at CC, the shelf trapping mechanism tends to excite the gravest of the natural modes. This oscillation is slowly shifted toward the natural mode closest to the period of the incident tsunami wave packet. Short-duration wave trains tend to influence the tsunami response at CC harbor in such a way that 1 hour after the first wave arrival a much stronger wave will be generated owing to the tendency of the shelf to initially ring at the frequency of the gravest mode. Practical implications of distant and local amplification relate to the potential hazard near CC, highlighting the need for awareness of the tsunami signal duration. In this respect, two timescales are important for this event: the 2-hour time delay due to distant bathymetric features and the 1-hour delay due to local offshore bathymetry.

[1] A numerical model for the global tsunami computation constructed by Kowalik et al. (2005, 2007a) is applied to the tsunami of November 15, 2006 in the northern Pacific with spatial resolution of one minute. Numerical results are compared to sea level data collected by Pacific DART buoys. The tide gauge at Crescent City (CC) recorded an initial tsunami wave of about 20 cm amplitude and a second larger energy packet arriving 2 hours later. The first energy input into the CC harbor was the primary (direct) wave traveling over the deep waters of the North Pacific. Interactions with submarine ridges and numerous seamounts located in the tsunami path were a larger source of tsunami energy than the direct wave. Travel time for these amplified energy fluxes is longer than for the direct wave. Prime sources for the larger fluxes at CC are interactions with Koko Guyot and Hess Rise. Tsunami waves travel next over the Mendocino Escarpment where the tsunami energy flux is concentrated owing to refraction and directed toward CC. Local tsunami amplification over the shelf break and shelf are important as well. In many locations along the North Pacific coast, the first arriving signal or forerunner has lower amplitude than the main signal, which often is delayed. Understanding this temporal distribution is important for an application to tsunami warning and prediction. As a tsunami hazard mitigation tool, we propose that along with the sea level records (which are often quite noisy), an energy flux for prediction of the delayed tsunami signals be used.

] More than 130years ago,theAustrian Arctic explorer,Carl Weyprecht [Weyprecht and Ihne, 1913] (who discov-ered Franz Josef Land, an archipelago north of Russia, andwho advanced a successful scheme for international coop-eration in polar science—the International Polar Year con-cept) postulated that a number of fundamental problems ofmeteorology and geophysics could be solved near theEarth’spoles.Thishypothesisisstillvalidinthe21stcenturybecause the Arctic is recognized as a region where globalclimate change signals are amplified. The model-basedconclusion of Manabe and Stouffer [1994] that the firstsigns of climate change could be detected in the Arctic hasbeen corroborated by numerous other model results [e.g.,Holland and Bitz, 2003; Symon et al., 2005]. On the otherhand, it has been demonstrated that model conclusions maybe highly uncertain and that model estimates of futureclimate change differ significantly from model to model.In order to reduce these uncertainties, it is important tovalidate and to improve models. The latter is the first majorgoal of the Arctic Ocean Model Intercomparison Project(AOMIP). The second major AOMIP goal is to investigatevariability of the Arctic Ocean and sea ice at seasonal todecadal timescales, and identify mechanisms responsible forthe observed changes. Some of the latest AOMIP activitiesassociated with these project goals arereflected inthe papersof this special section.[

[1] Vertical and spatial variability of tidal currents in the northern part of the Bering Sea near St. Lawrence Island were examined using observations made at 17 new and historical current meter mooring locations. The semidiurnal currents dominate over the diurnal currents. Semidiurnal currents exhibit a seasonal modulation with currents being somewhat stronger during the summer and fall when the density structure displays two-layer stratification. Diurnal currents exhibit a weak semiannual modulation. Examination of the vertical structure of tidal currents shows that maximum semidiurnal currents are observed in the upper or middle layers down to a depth of about 20 m, and below this depth the energy of the semidiurnal currents decreases rapidly. However, the energy of diurnal band currents remains almost constant with depth, decreasing only in close proximity to the bottom. Rotary spectral analysis applied to the records shows further differences: the M2 clockwise (CW) component of rotation dominates in the upper and middle water column but the counterclockwise component (CCW) dominates near the bottom. Interpretation of these observed results points to the different bottom boundary layers (BBL) for the CW and CCW motions in addition to the role of density stratification in organizing the BBL. We compare results of a vertically averaged two-dimensional model to the observationally derived tidal ellipse parameters and show that the barotropic formulation provides a first-order description of the tidal regime within the domain.

In this work a numerical modeling method is used to study tsunami waves generated by the Great Alaska earthquake of 1964, and their impact on Kodiak Island communities. The numerical model is based on the nonlinear shallow water equations of motion and continuity which are solved by a finite-difference method. We compare two different source models for the 1964 deformation. It is shown that the results of the near-field inundation modeling strongly depend on the slip distribution within the rupture area. These results are used for evaluation of the tsunami hazard for the Kodiak Island communities.