Since the first discovery of an extrasolar planet around a solar-type star, observers have detected over 500 planets outside the solar system. Many of these planets have Jovian masses and orbit their host stars in orbits of only a few days, the so-called 'Hot Jupiters'. At such close proximity to their parent stars, strong tidal interactions between the two bodies are expected to cause significant secular spin-orbit evolution. This thesis tackles two problems regarding the tidal evolution of short-period extrasolar planets. In the first part, we adopt a simple model of the orbit-averaged effects of tidal friction, to study the tidal evolution of planets on inclined orbits. We also analyse the effects of stellar magnetic braking. We then discuss the implications of our results for the importance of Rossiter-Mclaughlin effect observations. In the second part, we study the mechanisms of tidal dissipation in solar-type stars. In particular, internal gravity waves are launched at the interface of the convection and radiation zones of such a star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star is studied, primarily using numerical simulations, in both two and three dimensions. We find that the waves undergo instability and break above a critical amplitude. A model for the tidal dissipation that results from this process is presented, and its validity is verified by numerical integrations of the linear tidal response, in an extensive set of stellar models. The dissipation is efficient, and varies by less than an order of magnitude between all solar-type stars, throughout their main-sequence lifetimes, for a given planetary orbit. The implications of this mechanism for the survival of short-period extrasolar planets is discussed, and we propose a possible explanation for the survival of all of the extrasolar planets currently observed in short-period orbits around F, G and K stars. We then perform a stability analysis of a standing internal gravity wave near the centre of a solar-type star, to understand the early stages of the wave breaking process in more detail, and to determine whether the waves are subject to weaker parametric instabilities, below the critical amplitude required for wave breaking. We discuss the relevance of our results to our explanation for the survival of short-period planets presented in the second part of this thesis. Finally, we propose an alternative mechanism of tidal dissipation, involving the gradual radiative damping of the waves. Based on a simple estimate, it appears that this occurs even for low mass planets. However, it is in conflict with current observations since it would threaten the survival of all planets in orbits shorter than 2 days. We discuss some hydrodynamic instabilities and magnetic stresses which may prevent this process.

The breaking of internal solitary waves (ISWs) of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. The simulations were performed for a wide range of boundary slopes S∈[0.01,0.3] and wave slopes. Over steep slopes (S≥0.1), three distinct breaking processes were observed; surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary layer separation, respectively. Over mild slopes (S≤0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation after it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental timescale. The breaker type was characterized in wave slope S_w versus S space and the reflection coefficient (R), modeled as a function of the internal Iribarren number, was in agreement with other studies. The same 2D model was applied to investigate boundary layer separation-driven global instability, which is shown to play an important role in breaking of shoaling ISWs. The simulations were conducted with waves propagating over a flat bottom and shoaling over relatively mild (S=0.05) and steep (S=0.1) slopes. Combining the results over flat and sloping boundaries, a unified criterion for vortex shedding is proposed, which depends on the momentum thickness Reynolds number and the non-dimensionalized ISW-induced pressure gradient at the point of separation. The criterion is generalized to a form that may be readily computed from field data and compared to published laboratory and field observations. During vortex shedding, the bed shear stress, vertical velocity and near-bed Reynolds stress were elevated, implying potential for sediment re-suspension. Laboratory experiments were also performed to study three-dimensionality (3D) of global instability. Our results agree with previous laboratory experiments, using the proposed pressure gradient parameter and Reynolds number. The 3D effects prevent the vortices from ascending as high as they do in 2D simulations. The instabilities were not able to re-suspend sediments with 20 µm median diameters, which suggests applying lighter sediments, as finer sediments will be cohesive and dynamically different. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2011-12-23 15:03:29.76

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23149号 / 工博第4793号 / 新制||工||1750(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 平石 哲也, 准教授 馬場 康之, 教授 森 信人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

A dynamic simulation of the response of an inflatable dam subjected to a flood was carried out to determine the survivability envelope of the dam where it can operate without rupture, or overflow. A fully nonlinear free-surface flow was applied in two dimensions using a mixed Eulerian-Lagrangian formulation. An ABAQUS finite element model was used to determine the dynamic structural response of the dam. The problem was solved in the time domain which allows the prediction of a number of transient phenomena such as the generation of upstream advancing waves, and dynamic structural collapse. Stresses in the dam material were monitored to determine when rupture occurs. An iterative study was performed to find the service envelope of the dam in terms of the internal pressure and the flood Froude number for two flood depths. It was found that the driving parameter governing failure of the dam was the internal pressure. If this pressure is too low, the dam overflows; if this pressure is too high, the dam ruptures. The fully nonlinear free-surface flow over a semi-circular bottom obstruction was studied numerically in two dimensions using a similar solution formulation as that used in the previous study. A parametric study was performed for a range of values of the depth-based Froude number up to 2.5 and non-dimensional obstacle heights up to 0.9. When wave breaking does not occur, three distinct flow regimes were identified: subcritical, transcritical and supercritical. When breaking occurs it may be of any type: spilling, plunging or surging. In addition, for values of the Froude number close to 1, the upstream solitary waves break. A systematic study was undertaken, to define the boundaries of each type of breaking and non-breaking pattern, and to determine the drag and lift coefficients, free surface profile characteristics and transient behavior. / Master of Science

Les récentes paramétrisations utilisées dans les modèles spectraux de vagues offrent des résultats intéressants en termes de prévision et rejeux des états de mer. Cependant, de nombreux phénomènes physiques présents dans ces modèles sont encore mal compris et donc mal modélisés, notamment le terme de dissipation lié au déferlement des vagues.Le travail présenté dans cette thèse vise dans un premier temps à analyser et critiquer les paramétrisations existantes de la dissipation, au travers de la modélisation explicite des propriétés du déferlement sous-jacentes. Du constat de l’échec de ces paramétrisations à reproduire les observations in situ et satellite du déferlement, une nouvelle méthode d’observation et d’analyse des déferlements est proposée à l’aide de systèmes de stéréo vidéo. Cette méthode permet l’observation des déferlements sur des surfaces de mer reconstruites à haute résolution par stéréo triangulation. Ainsi, une méthode complète de reconstruction des surfaces de mer en présence de vagues déferlantes est proposée et validée. La détection des vagues déferlantes sur les images et leur reprojection sur les surfaces reconstruites est également discutée. Bien que peu d’acquisitions soient disponibles, les différents paramètres observables grâce à l’utilisation de la stéréo vidéo sont mis en avant. Ce travail montre l’intérêt des systèmes vidéo stéréo pour une meilleure observation et compréhension du déferlement des vagues, pour le développement des paramétrisations de la dissipation dans les modèles spectraux de vague. / The recent parameterizations used in spectral wave models provide today interesting results in terms of forecast and hindcast of the sea states. Nevertheless, many physical phenomena present in these models are still poorly understood and therefore poorly modeled, in particular the dissipation source term due to breaking. First, the work presented in this thesis is aimed at analyzing and criticizing the existing parameterizations of the dissipation through the explicit modeling of the underlying properties of breaking. The finding of the failure of these parameterizations to reproduce the in situ and satellite observations, a new method for the observation and the analysis of breaking is proposed using stereo video systems . This method allows the observation of breaking waves on the high-resolution stereo-reconstructed sea surfaces. Therefore, a complete method for reconstruction of the sea surfaces in the presence of breaking waves is proposed and validated.The detection of breaking waves on the images and their reprojection on reconstructed surface is also discussed. Although too few acquisitions are available to draw firm results, an overview of the various observable parameters through the use of stereo video is given.This work shows the importance of stereo video systems to a better observation and understanding of the breaking waves, required in order to improve dissipation source term in spectral wave models.

The SUPERTANK dataset is analyzed to examine the upper limit of beach change in response to elevated water level induced by wave runup. Thirty SUPERTANK runs are investigated, including both erosional and accretionary wave conditions under random and monochromatic waves. Two experiments, one under a spilling and one under a plunging breaker-type, from the Large-Scale Sediment Transport Facility (LSTF) are also analyzed. The upper limit of beach change approximately equals the maximum vertical excursion of swash runup. Exceptions to this direct relationship are those with beach or dune scarps when gravity-driven changes, i.e., avalanching, become significant. The vertical extent of wave runup, Rmax, above mean water level on a beach without a scarp is found to approximately equal the significant breaking wave height, Hbs. Therefore, a simple formula Rmax = Hbs is proposed. The linear relationship between maximum runup and breaking wave height is supported by a conceptual derivation. This predictive formula reproduced the measured runup from a large-scale 3-dimensional movable bed physical model. Beach and dune scarps substantially limit the uprush of swash motion, resulting in a much reduced maximum runup. Predictions of wave runup are not improved by including a slope-dependent surf-similarity parameter. The limit of wave runup is substantially less for monochromatic waves than for random waves, attributed to absence of low-frequency motion for monochromatic waves.

This study reports on a new formulation of the spectral dissipation source term Sds for wind-wave modelling applications. This new form of Sds features a nonlinear dependence on the local wave spectrum, expressed in terms of the azimuthally integrated saturation parameter B(k)=k^4 F(k). The basic form of this saturation-dependent Sds is based on a new framework for the onset of deep-water wave breaking due to the nonlinear modulation of wave groups. The new form of Sds is succesfully validated through numerical experiments that include exact nonlinear computations of fetch-limited wind-wave evolution and hindcasts of two-dimensional wave fields made with an operational wind-wave model. The newly-proposed form of Sds generates integral spectral parameters that agree more closely with observations when compared to other dissipation source terms used in state-of-the-art wind-wave models. It also provides more flexibility in controlling properties of the wave spectrum within the high wavenumber range. Tests using a variety of wind speeds, three commonly-used wind input source functions and two alternative full-development evolution limits further demonstrate the robustness and flexibility of the new saturation-dependent dissipation source term. Finally, improved wave hindcasts obtained with an implementation of the new form of Sds in a version of the WAM model demonstrate its potential usefulness in operational wind-wave forecasting applications.

Nearshore processes on barred beaches are studied with a process-based numerical model. The two major goals of the study are to expand the body of knowledge about nearshore processes on barred beaches gaining a better understanding of the physical mechanisms affecting bar migration events and to enhance the numerical model in order to accomplish realistic simulations of bar migration events on storm time scales. The numerical model is used to study the effect of physical processes on the hydrodynamics and morphodynamics in the nearshore environment. The numerical model system consists of a linear spectral refraction-diffraction model, REF/DIF S, a quasi-3D nearshore circulation module, SHORECIRC, energetics-based sediment transport models, and a morphological evolution model. A laboratory experiment with an offshore bar migration case followed by an onshore bar migration case is used for modeling purposes and verifications. A number of enhancements are made to the wave and circulation modules of the numerical model system specifically for simulations on barred beaches. The model modifications and enhancements are: a combined breaking wave parameter with a spatial variation in the wave model, a method accounting for breaking wave persistence in the wave model, a method accounting for the new breaker roller lag in the wave model, the dynamic pressure component in the radiation stress forcing, a roller contribution with different depth variation options for the short wave forcing in the circulation model, wave height instead of water depth as the turbulent length scale in the eddy viscosity calculations in the circulation model, and a slope term for the default sediment transport formula. The effect of surface shape parameter and the roller face angle on radiation stress and mean water level predictions are investigated. In reality, the organized wave energy is transferred to roller development over a transition distance and the roller does not immediately contribute to the radiation stresses; therefore, showing the importance of the roller lag mechanism for mean water level predictions. The cross-shore variation of the vertical momentum balance is studied to observe the variation of forcing agents of the undertow current. The cross-shore pressure gradient is the most dominant forcing term affecting the depth structure of the undertow current. The effect of different depth variations of the roller contribution to the short wave forcing on the undertow current is investigated. The mechanism accounting for breaking wave persistence and the mechanism accounting for the roller lag are shown to be important for predictions of the undertow currents on barred beaches. The skewed wave orbital velocities are introduced to the linear wave model by an empirical parametrization method and are found to contribute strongly to the onshore bar migration. The enhancements made to the wave dissipation and roller are found to significantly affect the predicted migration of the bar as well as the maintainance of the trough.

Στην παρούσα διατριβή παρουσιάζεται η αριθμητική μέθοδος προσομοίωσης μεγάλων κυμάτων (LWS), για τη μελέτη της τυρβώδους ροής που αναπτύσσεται κατά τη θραύση κυμάτων (θραύση εκχείλισης) πάνω από πυθμένα σταθερής κλίσης. Κατά τη μέθοδο LWS, οι μεγάλες κλίμακες των τυρβωδών διακυμάνσεων της ταχύτητας και της ελεύθερης επιφάνειας επιλύονται αριθμητικά, ενώ η επίδραση των μικρών κλιμάκων λαμβάνεται υπόψη με τη χρήση υποπλεγματικού (subgrid scale ή SGS) μοντέλου τάσεων, αντίστοιχο της μεθόδου προσομοίωσης μεγάλων δινών LES. Η θραύση εκχείλισης προσομοιώνεται από τη δράση των SGS τάσεων, οι οποίες δημιουργούν το στρόβιλο θραύσης και παράγουν εγκάρσια στροβιλότητα στο μέτωπο του κύματος. Η μέθοδος LWS εφαρμόζεται σε σύζευξη με τις εξισώσεις Euler και των αντιστοίχων μη-γραμμικών οριακών συνθηκών. Επιπλέον, ως σημείο αναφοράς χρησιμοποιείται η προσομοίωση της θραύσης εκχείλισης με μοντέλο επιφανειακού στροβίλου, κατά το οποίο η επίδραση του στροβίλου θραύσης υπολογίζεται εμπειρικά. Το μοντέλο προσαρμόζεται στις εξισώσεις δισδιάστατης μη συνεκτικής ροής, με τη χρήση κατάλληλα τροποποιημένων οριακών συνθηκών. Παρουσιάζονται αποτελέσματα δισδιάστατης ροής, κατά τη θραύση κύματος κάθετα στην ακτογραμμή, και τρισδιάστατης ροής, κατά τη θραύση κύματος κάθετα και υπό γωνία ως προς την ακτογραμμή. Γενικά, τα αποτελέσματα της ελεύθερης επιφάνειας και του πεδίου ταχυτήτων στη ζώνη απόσβεσης, κατά την θραύση κυμάτων κάθετα στην ακτογραμμή και πάνω από πυθμένα κλίσης 1/35, δείχνουν ικανοποιητική συμφωνία με τις αντίστοιχες πειραματικές μετρήσεις. Ωστόσο, παρά την ασθενή μεταβολή της ροής εγκάρσια στην ακτογραμμή, παρατηρείται ότι, λόγω της τρισδιάστατης δομής του στροβίλου, ο μηχανισμός της θραύσης προσομοιώνεται ικανοποιητικότερα από τη μέθοδο LWS, όταν αυτή συνδυάζεται με τρισδιάστατο πεδίο ροής. Τέλος, εξετάζεται η διάδοση και η θραύση κυμάτων πάνω από πυθμένα σταθερής κλίσης 1/35, τα οποία προσπίπτουν στην ακτογραμμή υπό γωνία 42,45 μοιρών σε μεγάλο βάθος. Οι κορυφογραμμές του κύματος θραύονται σταδιακά και η δράση των SGS τάσεων παράγει εγκάρσια και διαμήκη στροβιλότητα. Ο στρόβιλος θραύσης αναπτύσσεται κατά μήκος των θραυομένων κορυφογραμμών, με γωνία προσανατολισμού αντίστοιχη της γωνίας πρόσπτωσης κύματος στη γραμμή θραύσης. / A method named Large Wave Simulation is presented, for the study of turbulent flow that develops during wave breaking (spilling breakers) over a constant-slope bed. According to LWS method, large scales of velocity field and free-surface elevation are numerically resolved, whereas the corresponding subgrid scale (SGS) effects are accounted for by a SGS stress model, equivalent to the ones used in Large Eddy Simulation (LES) method. Spilling breaking is simulated by a SGS stress field that creates an eddy breaker and produces spanwise vorticity at the breaking wave front. LWS method is used in conjuction with the Euler equation and the corresponding nonlinear boundary conditions. Moreover, as a reference, a surface roller (SR) model is used for the simulation of spilling breaking, which necessitates empirical parameters, for the calculation of the eddy breaker effect. The SR model is adapted for two-dimensional, inviscid but rotational free-surface flow, by use of appropriately modified boundary conditions. Results of two-dimensional flow during breaking waves, propagating perpendicularly to the shoreline, are presented, as well as results of threedimensional flow during breaking waves, propagating perpendicularly and obliquely to the shoreline. In the case of waves breaking perpendicularly to the shoreline over a constant slope (1/35) bed, free-surface elevation and velocities results are in accordance with existing experimental data. However, despite of the flow being weakly dependent to the cross-shore direction, due to the fact that the eddy breaker is three-dimensional, LWS method performs better when combined with a three-dimensional flow field. Finally, oblique wave propagation (42,45 degrees at deep water) and breaking over a constant-slope (1/35) bed is simulated. Wave crestlines break gradually and the effect of the SGS stress field produces spanwise (longshore) and streamwise (cross-shore) vorticity. The eddy breaker develops along the breaking wave front and its orientation follows the shape of the breaking crestlines.

Video based remote sensing techniques are well suited to collect spatially resolved wave images in the surf zone with breaking waves and dynamic bathymetric changes. An advanced video-based depth inversion method is developed to remotely survey bathymetry in the surf zone. The present method involves image processing of original wave image sequences, wave property estimation based on linear feature extraction from the processed image sequences, and is combined with a nonlinear depth inversion model. The original wave image sequences are processed through video image frame differencing and directional low-pass filtering schemes to remove wave-breaking-induced foam noise having high frequencies in the surf zone. The features of individual crest trajectories are extracted from the processed and rectified image sequences, i.e. processed image cross-shore timestacks, by tracking pixels of high intensity within an interrogation window of a Radon-transform-based line-detection algorithm. The wave celerity is computed using space-time information of the extracted trajectories of individual wave crests in the cross-shore timestack domain. The presented retrieval of nearshore bathymetry from video image sequences is based on a nonlinear depth inversion using the nonlinear shallow water wave theory. The nonlinear wave amplitude dispersion effects at the breaker points are determined by combining the nonlinear shallow water celerity equation with a wave breaker criterion, thereby computing water depths iteratively from the celerity measured from the video data. The water depths estimated at the breaker points present initial bathymetric anchor points. Bathymetric profiles in the surf zone are inverted by calculating wave heights dissipated after wave breaking with a wave dissipation model and wave heights shoaled before wave breaking with a wave shoaling model. The continuous wave amplitude dispersion effects are subtracted from the measured celerity profiles, resulting in nearshore bathymetric profiles. The nonlinear depth inversion derived bathymetric estimates from nearshore imagery match the measured values with a biased mean depth error of about +0.06m in the depth range of 0.1 to 3m. In addition, the wave height estimates by the depth inversion model are comparable to the in-situ measured wave heights with a biased mean wave height error of about +0.14m. The present depth inversion method based on optical remote-sensing supports coastal management, navigation, and amphibious operations.