Dissertations / Theses on the topic 'Winds Antarctica Mathematical models'

Antarctic Wind Engineering deals with the effects of wind on the built environment. The assessment of wind induced forces, wind resource and wind driven snowdrifts are the main tasks for a wind engineer when participating on the design of an Antarctic building. While conventional Wind Engineering techniques are generally applicable to the Antarctic environment, there are some aspects that require further analysis due to the special characteristics of the Antarctic wind climate and its boundary layer meteorology.

The first issue in remote places like Antarctica is the lack of site wind measurements and meteorological information in general. In order to complement this shortage of information various meteorological databases have been surveyed. Global Reanalyses, produced by the European Met Office ECMWF, and RACMO/ANT mesoscale model simulations, produced by the Institute for Marine and Atmospheric Research of Utrecht University (IMAU), have been validated versus independent observations from a network of 115 automatic weather stations. The resolution of these models, of some tens of kilometers, is sufficient to characterize the wind climate in areas of smooth topography like the interior plateaus or the coastal ice shelves. In contrast, in escarpment and coastal areas, where the terrain gets rugged and katabatic winds are further intensified in confluence zones, the models lack resolution and underestimate the wind velocity.

The Antarctic atmospheric boundary layer (ABL) is characterized by the presence of strong katabatic winds that are generated by the presence of surface temperature inversions in sloping terrain. This inversion is persistent in Antarctica due to an almost continuous cooling by longwave radiation, especially during the winter night. As a result, the ABL is stably stratified most of the time and, only when the wind speed is high it becomes near neutrally stratified. This thesis also aims at making a critical review of the hypothesis underlying wind engineering models when extreme boundary layer situations are faced. It will be shown that the classical approach of assuming a neutral log-law in the surface layer can hold for studies of wind loading under strong winds but can be of limited use when detailed assessments are pursued.

The Antarctic landscape, mostly composed of very long fetches of ice covered terrain, makes it an optimum natural laboratory for the development of homogeneous boundary layers, which are a basic need for the formulation of ABL theories. Flux-profile measurements, made at Halley Research Station in the Brunt Ice Shelf by the British Antarctic Survery (BAS), have been used to analyze boundary layer similarity in view of formulating a one-dimensional ABL model. A 1D model of the neutral and stable boundary layer with a transport model for blowing snow has been implemented and verified versus test cases of the literature. A validation of quasi-stationary homogeneous profiles at different levels of stability confirms that such 1D models can be used to classify wind profiles to be used as boundary conditions for detailed 3D computational wind engineering studies.

A summary of the wind engineering activities carried out during the design of the Antarctic Research Station is provided as contextual reference and point of departure of this thesis. An elevated building on top of sloping terrain and connected to an under-snow garage constitutes a challenging environment for building design. Building aerodynamics and snowdrift management were tested in the von Karman Institute L1B wind tunnel for different building geometries and ridge integrations. Not only for safety and cost reduction but also for the integration of renewable energies, important benefits in the design of a building can be achieved if wind engineering is considered since the conceptual phase of the integrated building design process.

Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Thesis (M.S.)--Massachusetts Institute of Technology at Woods Hole Oceanographic Institution, 2006.
"September 2006." Description based on title screen as viewed on June 8, 2010. DTIC Descriptor(s): Doppler Radar, Wind Velocity, Sound Ranging, Doppler Sonar, Buoys, Measurement, Motion, Oceanographic Equipment, Theses DTIC Identifier(s): Doppler Sodar, Sodar (Sound Detection and Ranging), ASIS Includes bibliographical references (leaf 75). Also available in print.

The use of an ocean surface velocity dependent wind stress is examined in the context of a 3-layer double-gyre quasigeostrophic wind-driven ocean circulation model. The new wind stress formulation results in a large reduction of the power input by the wind into the oceanic circulation. This wind stress is proportional to a quadratic function of Ua--u o, where Ua is the wind at 10m above the ocean surface and uo is the ocean surface current. Because the winds are typically faster than the ocean currents, the impact of the ocean surface velocity on the wind stress itself is relatively small. However, the power input is found to be greatly reduced with the new formulation. This is shown by simple scaling argument and numerical simulations in a square basin. Our results suggest that the wind power input may be as much as 35% smaller than is typically assumed.
The ocean current signature is clearly visible in the scatterometer-derived wind stress fields. We argue that because the actual ocean velocity differs from the modeled ocean velocities, care must be taken in directly applying scatterometer-derived wind stress products to the ocean circulation models. This is not to say that the scatterometer-derived wind stress is not useful. Clearly the great spatial and temporal coverage make these data sets invaluable. Our point is that it is better to separate the atmospheric and oceanic contribution to the stresses.
Finally, the new wind stress decreases the sensitivity of the solution to the (poorly known) bottom friction coefficient. The dependence of the circulation strength on different values of bottom friction is examined under the standard and the new wind stress forcing for two topographic configurations. A flat bottom and a meridional ridge case are studied. In the flat bottom case, the new wind stress leads to a significant reduction of the sensitivity to the bottom friction parameter, implying that inertial runaway occurs for smaller values of bottom friction coefficient. The ridge case also gives similar results. In the case of the ridge and the new wind stress formulation, no real inertial runaway regime has been found over the range of parameters explored.

Subglacial water plays an important role in the regulation of an ice sheet's mass balance. It may be the dominant control on the velocities of ice streams and outlet glaciers on scales of months to millennia. Recent satellite observations of ice surface elevation changes have given researchers new insights into how subglacial water is stored and transported. Localized uplift and settling of the ice surface implies that lakes exist beneath the ice sheet that are being filled and drained on relatively short time scales. %At the base of an ice sheet water can be transported through a variety of drainage networks or stored in subglacial lakes. Here, a numerical investigation of the mechanisms of transport and storage of subglacial water and the associated time scales is presented. Experiments are carried out using a finite element model of coupled ice and water flow. The first experiment seeks to understand the relationship between the depth of a basal depression and the area over which the feature affects basal water flow. It is found that as the perturbation to a topographic depression's depth is increased, water is rerouted in response to the perturbation. Additionally it is found that the relationship between perturbation depth and the extent upstream to which its effects reach is nonlinear. The second experiment examines how the aspect ratio of bed features (prolate, oblate, or equidimensional) influences basal water flow. It is found that the systems that develop and their interactions are mediated by both the topography and the feedbacks taken into account by the coupling of the systems in the model. Features oriented parallel to ice and water flow are associated with distributed fan systems that develop branches which migrate laterally across the domain and interact with one another on monthly and yearly timescales. Laterally oriented features develop laterally extensive ponds. As the ratio of longitudinal to lateral dimension of the topography is increased, a combination of these two water distributions is seen.

I examine how two different realizations of bed morphology affect Thwaites Glacier response to ocean warming through the initiation of marine ice sheet instability and associated grounding line retreat. A state of the art numerical ice sheet model is used for this purpose. The bed configurations used are the 1-km resolution interpolated BEDMAP2 bed and a higher-resolution conditional simulation produced by John Goff at the University of Texas using the same underlying data. The model is forced using a slow ramp approach, where melt of ice on the floating side of the grounding line is increased over time, which gently nudges the glacier toward instability. Once an instability is initiated, the anomalous forcing is turned off, and further grounding line retreat is tracked.

Two model experiments are conducted. The first experiment examines the effect of different anomalous forcing magnitudes over the same bed. The second experiment compares the generation and progress of instabilities over different beds. Two fundamental conclusions emerge from these experiments. First, different bed geometries require different ocean forcings to generate a genuine instability, where ice dynamics lead to a positive feedback and grounding line retreat becomes unstable. Second, slightly different forcings produce different retreat rates, even after the anomalous forcing is shut off, because different forcing magnitudes produce different driving stresses at the time the instability is initiated. While variability in the retreat rate over time depends on bed topography, the rate itself is set by the magnitude of the forcing. This signals the importance of correct knowledge of both bed shape and ocean circulation under floating portions of Antarctic ice sheets. The experiments also imply that different ocean warming rates delivered by different global warming scenarios directly affects the rate of Antarctic contribution to sea level rise.

This thesis studies the scattering properties of different types of imperfections in large Arctic and Antarctic ice sheets. Such irregularities include cracks, pressure ridges and both open and refrozen leads. The scattering by a transition region between sea ice and a very thick ice shelf, for example as is found in the Ross Sea in Antarctica, is also treated. Methods of solution are based on applications of Green�s theorem to the appropriate situation, which leads to either a single integral equation or a pair of coupled integral equations to be solved at the boundary between the ice and the sea water. Those equations over a finite interval are solved using numerical quadrature, while those over semi-infinite ranges are solved using the Wiener-Hopf method. Results calculated using different techniques are able to be checked against each other, giving us great confidence in their accuracy. In particular, the scattering by three ice sheets of different thicknesses is confirmed analytically by mode-matching coupled with the residue calculus technique. The scattering by the single irregularities is investigated partly for its own sake, and partly with the aim of using it to treat the scattering when large numbers of features are included in a single ice sheet. The principal objective of doing this is to observe the change in the general amounts of reflection and transmission as the background ice thickness is changed. There is enough variation in our results for us to conclude that there is definite potential for using the change in an incident wave spectrum after passing through a given ice field to estimate the background ice thickness.

A marginal ice zone (MIZ) is characterised by distinct ice floes and its direct exposure to the open ocean. Sea ice is typically described as a continuous material but this description can be inappropriate in an MIZ due to the granular nature of the ice cover and the scale of processes acting on the ice floes. In this thesis, the kinematic behaviour of sea ice in an MIZ modelled as a granular material is investigated with an emphasis on the influence of ocean waves. The kinematic behaviour of a set of ice floes subject to ocean wave forcing was recorded in an experiment conducted in the Ross Sea. Kinematic data were recorded from each ice floe using a GPS receiver, tri-axial accelerometer, and compass. The data show (1) the influence of wave forcing and (2) collisions between neighbouring ice floes. It was also discovered that the GPS receivers were able to resolve the effects of ocean wave forcing despite their poor absolute accuracy. The number density and normalised structure factor (NSF) are introduced to describe the spatial structure of a set of ice floes. Four idealised distributions (in 1D and 2D) are analysed to gain insight into the way that different factors determine the shape of the NSF. It is shown that (1) a significant sinusoidal deviation causes a peak in the NSF, (2) ordered structure dominates low spatial frequencies, and (3) disorder dominates high spatial frequencies. A comparison of the contributions from these different factors is used to estimate the significance of a sinusoidal deviation in the positions of the ice floes. A granular model of an MIZ is developed using a novel set of equations of motion to examine the effect of ocean wave forcing. The equations of motion are derived for small ice floes and allows forcing by multiple waves. These equations predict a transient, wave-induced torque, which can be sustained by the application of a second force to the ice floe. Torque induced by the interaction of two forces on an ice floe may be a general feature of sea ice motion. The number density and NSF are used to analyse the distribution of ice floes in the granular model. At low solids-fractions the number density is correlated at the frequency of the wave forcing. As the solids-fraction is increased this correlation is destroyed by collisions between the ice floes and new correlations are created that are related to the packing structure of the ice floes. When the number density is weighted by the velocity of the ice floes, the correlations between floes are related to the convolution of the wave velocity field and the number density. These correlations may be incorporated into the thickness distribution of large-scale models using the maximum entropy method. The granular model was also examined as a percolating network of contacts and it was found that percolation was more likely to occur along the crest of a wave than in the direction of propagation.

Coastal South African cities like Port Elizabeth are said to have a strong potential for wind energy. This study aims to model wind data in order to be able assess the power potential belonging to a given site. The main challenge in modelling wind direction data is that it is categorized as circular data and therefore requires special techniques for handling that are different from usual statistical samples. Statistical tools such as descriptive measures and distribution fitting, were re-invented for directional data by researchers in this field. The von Mises distribution is a predominant distribution in circular statistics and is commonly used to describe wind directions. In this study, the circular principles described by previous researchers were developed by using the statistical software, Mathematica. Graphical methods to present the wind data were developed to give an overview of the behaviour of the winds in any given area. Data collected at Coega, an area near Port Elizabeth, South Africa, was used to illustrate the models which were established in this study. Circular distributions were fit to the directional data in order to make appropriate conclusions about the prevailing wind directions in this area.

A modeling study is undertaken to better understand the physics of katabatic flows. This study is divided into three topics; a comparison between a large eddy simulation (LES) and a mesoscale model of katabatic flows, a sensitivity study of katabatic flows to various physical parameters, and an investigation into the effect of subgrid scale terrain features on katabatic flow models. In the first topic, a comparison between LES, and a mesoscale model, ARPS, of katabatic flows is made to better quantify the accuracy of subgrid parametenzation in ARPS. It is shown that, although the modeled flows agree on a number of parameters, the LES model produces a lower and faster jet than that of ARPS, and also cools more near the surface. The momentum budgets of the two models agree well with each other. The ARPS model has a higher amount of TKE than the LES model, due to an overproduction by shear in the ARPS subgrid parameterizations. The second portion of this thesis represents a sensitivity study of katabatic flows to various physical parameters. The depth and strength of katabatic flows are shown to vary with surface heat fluxes, slope angle, and ambient stratification. Katabatic flows are shown to grow in depth and magnitude as slope angle increases, due to an increase in entrainment of overlying ambient air. The ratio of advection to mixing is shown to collapse to a near universal value regardless of surface heat fluxes. With increasing ambient stratification, entrainment in katabatic flows becomes small and the momentum equation is reduced to a two-way balance between buoyancy and drag. In this case, the heat flux of entrained air into the katabatic flow approaches that of the surface cooling, and the flow ceases to grow in the down-slope direction. Finally, predictions for bulk velocity and buoyancy strength scales are developed as a function of slope angle and surface heat fluxes. The last portion of this study focuses on the effect of subgrid scale terrain features on katabatic flows. It is shown that in areas of inadequate terrain resolution, the effect of the terrain smoothing routine in ARPS is to increase the slope height in areas of concave mountains. The concept of energy conversion in katabatic flows is introduced, and it is shown that the effect of raising terrain is to assign parcels more buoyant potential energy than they would otherwise have, and thus over-predict the magnitude of katabatic flows. Finally, an investigation into the effect of changing upper slope angle on katabatic flows over combined slopes is made. It is concluded that a combined slope cannot be predicted using a linear combination of simple slopes, since the transition portion of the slope results in a turbulent hydraulic jump with enhanced mixing. The magnitude of mixing in the turbulent hydraulic jump in combined slopes is shown to depend on the difference between upper and lower slope angle.
Graduation date: 2004

A time dependent model of the shallow, tropical convective boundary layer is developed and tested. To simplify the treatment of thermodynamic processes and return to first principles of physics, conserved quantities of entropy and total water density are used as primary model variables. In addition, a new shallow cumulus parameterization scheme is developed and is based on the use of a time dependent cloud kinetic energy equation combining local concepts of cloud processes with the use of a special buoyancy length scale. Two model simulations are performed in an attempt to assess the model's performance and the effectiveness of the parameterization scheme. Results indicate that the model does a reasonable job in both representing the equilibrium structure of a shallow convective boundary layer and in generating a realistic boundary layer structure from an initial state consisting of a shallow moist layer with dry air aloft. The cumulus parameterization scheme appears to adequately represent the transport of thermodynamic quantities associated with convective activity and the use of conserved variables provides an effective way of representing the boundary layer structure and treating the mixing processes associated with cloud processes. This work illustrates the usefulness of generalized conserved variables, particularly entropy and total water density, and indicates that the general approach of using a time dependent cloud kinetic energy equation may be effective for representing thermodynamic processes in the tropical boundary layer.
Graduation date: 1992

The Madden-Julian oscillation (MJO) and the quasi-biennial oscillation (QBO) are two key modes of variability in the tropical atmosphere. The MJO, characterized by propagating, planetary-scale signals in convection and winds, is the main source of subseasonal variability and predictability in the tropics. The QBO is a ~28-month cycle in which the tropical stratospheric zonal winds alternate between easterly and westerly regimes. Via thermal wind balance these winds induce temperature anomalies, and both wind and temperature signals reach the tropopause. Recent observational results show a remarkably strong link between the MJO and the QBO during boreal winter: the MJO is stronger and more predictable when QBO winds in the lower stratosphere are easterly than when winds are westerly. Despite its important implications for MJO theory and prediction, the physical processes driving the MJO-QBO interaction are not well-understood. In this thesis, we use a hierarchy of models – including a cloud-resolving model, a forecast model, and a global climate model – to examine whether models can reproduce the MJO-QBO link, and better understand the possible mechanisms driving the connection. Based in part on our modeling findings, we further explore observed QBO temperature signals thought to be important for the MJO-QBO link. After providing necessary background and context in the first two chapters, the third chapter looks at the MJO-QBO link in a small-domain, cloud-resolving model. The model successfully simulates convection associated with two MJO events that occurred during the DYNAMO field campaign. To examine the effect of QBO, we add various QBO temperature and wind anomalies into the model. We find that QBO temperature anomalies alone, without wind anomalies, qualitatively affect the model MJO similarly to the observed MJO-QBO connection. QBO wind anomalies have no clear effect on the modeled MJO. We note however that the MJO response is quite sensitive to the vertical structure of the QBO temperature anomalies, and for realistic temperature signals the model response is very small. In the fourth chapter, we look at the MJO-QBO link in a state-of-the-art global forecast model with a good representation of the MJO. We conduct 84 hind-cast experiments initialized on dates across winters from 1989-2017. For each of these dates, we artificially impose an easterly and a westerly QBO in the stratospheric initial conditions, and examine the resulting changes to the simulated MJO under different stratospheric states. We find that the effect of the QBO on the model MJO is of the same sign as observations, but is much smaller. A large sample size is required to capture any QBO signal, and tropospheric initial conditions seem more important than the stratosphere in determining the behavior of the simulated MJO. Despite the weak signal, we find that simulations with stronger QBO temperature anomalies have a stronger MJO response. In the fifth chapter, we conduct experiments in recent versions of a NASA general circulation model. We find that a version with a high vertical resolution generates a reasonable QBO and MJO, but has no MJO-QBO link. However, this model has weaker-than-observed QBO temperature anomalies, which may explain the lack of an MJO impact. To explore this potential bias, we impose the QBO by nudging the model stratospheric winds towards reanalysis, leading to more realistic simulation of QBO temperature anomalies. Despite this, the model still fails to show a strong MJO-QBO link across several ensemble experiments and sensitivity tests. We conclude with discussion of possible reasons why the model fails to capture the MJO-QBO connection. The sixth chapter examines QBO temperature signals in a range of observational and reanalysis datasets. In particular, we are motivated by two elements of the MJO-QBO relationship which are especially puzzling: the seasonality (i.e. that the MJO-QBO link is only significant in boreal winter) and long-term trend (i.e. that the MJO-QBO link seems to have only emerged since the 1980s). By examining QBO temperature signals around the tropopause, we highlight changes to the strength and structure of QBO temperature anomalies both in boreal winter and in recent decades. Whether these changes are linked to the MJO-QBO relationship, and what more generally might explain them, is not presently clear. Overall, we demonstrate that capturing the MJO-QBO relationship in a variety of models is a difficult task. The majority of evidence indicates that QBO-induced temperature anomalies are a plausible pathway through which the QBO might modulate the MJO, but the theoretical description of precisely how these temperature anomalies may impact convection is lacking and likely more nuanced than the literature to date suggests. Most models show only a weak modulation of the MJO associated with changes in upper-tropospheric temperatures, and even when those temperature signals are artificially enhanced, comprehensive GCMs still fail to show a significant MJO-QBO connection. Our observational study indicates that temperature anomalies associated with the QBO show striking modulations on various timescales of relevance to the MJO-QBO link, but do not conclusively demonstrate a clear connection to the MJO. This difficulty simulating a strong MJO-QBO connection suggests that models may lack a key process in driving the MJO and coupling the tropical stratosphere and troposphere. It is further possible that the observed link may be in some regards different than is currently theorized -- for example statistically not robust, due to non-stratospheric processes, or driven by some mechanism that has not been suitably explored.

Indiana University-Purdue University Indianapolis (IUPUI)
Hydraulic wind power transfer systems deliver the captured energy by the blades to the generators differently. In the conventional systems this task is carried out by a gearbox or an intermediate medium. New generation of wind power systems transfer the captured energy by means of high-pressure hydraulic fluids. A hydraulic pump is connected to the blades shaft at a high distance from the ground, in nacelle, to pressurize a hydraulic flow down to ground level equipment through hoses. Multiple wind turbines can also pressurize a flow sending to a single hose toward the generator. The pressurized flow carries a large amount of energy which will be transferred to the mechanical energy by a hydraulic motor. Finally, a generator is connected to the hydraulic motor to generate electrical power. This hydraulic system runs under two main disturbances, wind speed fluctuations and load variations. Intermittent nature of the wind applies a fluctuating torque on the hydraulic pump shaft. Also, variations of the consumed electrical power by the grid cause a considerable load disturbance on the system. This thesis studies the hydraulic wind power transfer systems. To get a better understanding, a mathematical model of the system is developed and studied utilizing the governing equations for every single hydraulic component in the system. The mathematical model embodies nonlinearities which are inherited from the hydraulic components such as check valves, proportional valves, pressure relief valves, etc. An experimental prototype of the hydraulic wind power transfer systems is designed and implemented to study the dynamic behavior and operation of the system. The provided nonlinear mathematical model is then validated by experimental result from the prototype. Moreover, this thesis develops a control system for the hydraulic wind power transfer systems. To maintain a fixed frequency electrical voltage by the system, the generator should remain at a constant rotational speed. The fluctuating wind speed from the upstream, and the load variations from the downstream apply considerable disturbances on the system. A controller is designed and implemented to regulate the flow in the proportional valve and as a consequence the generator maintains its constant speed compensating for load and wind turbine disturbances. The control system is applied to the mathematical model as well as the experimental prototype by utilizing MATLAB/Simulink and dSPACE 1104 fast prototyping hardware and the results are compared.