No description available.

No description available.

No description available.

Bed topography identification in open channel and glacier flows is of paramount importance for the study of the respective flows. In the former, the knowledge of the channel bed topography is required for modelling the hydrodynamics of open channel flows, fluvial hydraulics, flood propagation, and river flow monitoring. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features. While in the latter, usable bedrock topographic information is very important for glacier flow modellers to accurately predict the flow characteristics. Experimental techniques to infer the bed topography are usually used but are mostly time consuming, costly, and sometimes not possible due to geographical restrictions. However, the measurement of free surface elevation is relatively easy. Alternative to experimental techniques, it is therefore important to develop fast, easy-to-implement, and cost-effective numerical methods. The inverse of the classical hydrodynamic problem corresponds to the determination of hydraulic parameters from measurable quantities. The forward problem uses model parameters to determine measurable quantities. New one-shot and direct pseudo-analytical and numerical approaches for reconstructing the channel bed topography from known free surface elevation data is developed for one-dimensional shallow water flows. It is shown in this work that instead of treating this inverse problem in the traditional partial differential equation (PDE)-constrained optimization framework, the governing equations of the direct problem can be conveniently rearranged to obtain an explicit PDE for the inverse problem. This leads to a direct solution of the inverse problem which is successfully tested on a range of benchmark problems and experimental data for noisy and noiseless free surface data. It was found that this solution approach creates very little amplification of noise. A numerical technique which uses the measured free surface velocity to infer the channel bed topography is also developed. The one-dimensional shallow water equations along with an empirical relationship between the free surface and the depth averaged velocities are used for the inverse problem analysis. It is shown that after a series of algebraic manipulation and integration, the equation governing the inverse problem simplifies to a simple integral equation. The proposed method is tested on a range of analytical and experimental benchmark test cases and the results confirm that, it is possible to reconstruct the channel bed topography from a known free surface velocity distribution of one-dimensional open channel flows. Following the analysis of the case of one-dimensional shallow water flows, a numerical technique for reconstructing the channel bed topography from known free surface elevation data for steep open channel flows is developed using a modified set of equations for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. The governing equations are recast into a single first-order partial differential equation which describes the inverse problem. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other. In the framework of full two-dimensional shallow water equations, an easy-to-implement and fast to solve direct numerical technique is developed to solve the inverse problem of shallow open channel flows. The main underlying idea is analogous to the idea implemented for the case of one-dimensional reconstruction. The technique described is a “one-shot technique” in the sense that the solution of the partial differential equation provides the solution to the inverse problem directly. The idea is tested on a set of artificial data obtained by first solving the forward problem. Glaciers are very important as an indicator of future climate change or to trace past climate. They respond quickly compared to the Antarctica and Greenland ice sheets which make them ideal to predict climate changes. Glacier bedrock topography is an important parameter in glacier flow modelling to accurately capture its flow dynamics. Thus, a mathematical technique to infer this parameter from measured free surface data is invaluable. Analogous to the approaches implemented for open channel flows, easy-to-implement direct numerical and analytical algorithms are developed to infer the bedrock topography from the knowledge of the free surface elevation in one space dimension. The numerical and analytical methods are both based on the Shallow Ice Approximation and require the time series of the ablation/accumulation rate distribution. Moreover, the analytical method requires the knowledge of a non-zero glacier thickness at an arbitrary location. Numerical benchmark test cases are used to verify the suitability and applicability of the algorithms.

Abstract not available

The dynamics captured in the ocean surface current data provided by satellite altimetry has been a subject of debate since the past decade. In particular, the contribution of surface and interior dynamics to altimetry remains unclear. One avenue to settling this issue is to compare the turbulence (for example, the nature of spectra and interscale fluxes) captured by altimetry to theories of two-dimensional, surface and interior quasigeostrophic turbulence. In this thesis, we focus on mesoscales (i.e., scales of the order of few hundred kms) that are well resolved by altimetry data. Aspects of two dimensional, three dimensional, geotropic and surface quasigeostrophic turbulence are revisited and compared with the observations. Specifically, we compute kinetic energy (KE) spectra and fluxes in five geographical regions (all over the globe) using 21 years of 0.25◦resolution daily data as provided by the AVISO project. We report a strong forward cascade of KE at small scales (accompanied by a spectral scaling of the form k−3) and a robust inverse cascade at larger scales. Further, we show that the small diver-gent part in horizontal velocity data drives the strong forward flux of KE. Indeed, on considering only the non-divergent part of the flow, in accord with incompressible two-dimensional turbulence, the inverse cascade is unaffected, but the forward transfer becomes very weak and the spectral slopes over this range of scales tend to a relatively steeper k−3.5scaling. We note that our results do not agree with interior first bar clinic mode quasigeostrophic (incorrect strength of forward flux) or surface-quasigeostrophic (incorrect spectral slopes) turbulence. Rather, the results are compatible with rotating shallow water and rotating stratified Boussinesq models in which condition of geostrophic balance is dominant but the divergence of horizontal velocity field is not exactly zero. Having seen the “mean” picture of fluxes and spectra from altimetry, in the second part of the thesis we investigate the variability of these entities. In particular, we employ Empirical Or-thogonal Function (EOF) analysis and focus on the variability in the spectral flux. Remarkably, over the entire globe, irrespective of the region under consideration, we see that the first two EOFs explain a large part of the variability in flux anomalies. The geometry of these modes is distinct, the first represents a single signed transfer across scales (i.e. large to small or small to large depending on the sign of the associated principal component), while the second is a mixed mode in that it exhibits a forward/inverse transfer at large/small scales.

This thesis addresses the problem of registering one point set with respect to another. This problem arises in the context of the use of CMM/Scanners to inspect objects especially with freeform surfaces. The tolerance verification process now requires the comparison of measured points with the nominal geometry. This entails placement of the measured point set in the same reference frame as the nominal model. This problem is referred to as the registration or localization problem. In the most general form the tolerance verification task involves registering multiple point sets corresponding to multi-step scan of an object with respect to the nominal CAD model. This problem is addressed in three phases. This thesis presents a novel approach to automated inspection by matching point sets based on the Iterative Closest Point (ICP) algorithm. The Modified ICP (MICP) algorithm presented in the thesis improves upon the existing methods through the use of a localized region based triangulation technique to obtain correspondences for all the inspection points and achieves dramatic reduction in computational effort. The use of point sets to represent the nominal surface and shapes enables handling different systems and formats. Next, the thesis addresses the important problem of establishing registration between point sets in different reference frames when the initial relative pose between them is significantly large. A novel initial pose invariant methodology has been developed. Finally, the above approach is extended to registration of multiview inspection data sets based on acquisition of transformation information of each inspection view using the virtual gauging concept. This thesis describes implementation to address each of these problems in the area of automated registration and verification leading towards automatic inspection.