Two problems in mesoscale wave dynamics are addressed: (i) wave-turbulence interaction in a breaking mountain wave and (ii) gravity wave generation associated with coastal heating gradients. The mean and turbulent structures in a breaking mountain wave are considered using an ensemble of high-resolution (essentially LES) wave-breaking calculations. A turbulent kinetic energy budget for the wave shows that the turbulence production is almost entirely due to the mean shear. Most of the production is at the top of the leeside shooting ow, where the mean- ow Richardson number is persistently less than 0:25. Computation of the turbulent heat and momentum uxes shows that the dissipation of mean- ow wave energy is due primarily to the momentum uxes. The resulting drag on the leeside shooting ow leads to a loss of mean ow Bernoulli function as well as a cross-stream PV ux. The dependence of both the resolved-scale and subgrid turbulent uxes on the grid spacings is examined by computing a series of ensembles with varying grid spacings. The subgrid parameterization is shown to produce an overestimate of the PV ux at low grid resolution. The generation of gravity waves by coastal heating gradients is explored using linear theory calculations and idealized numerical modeling. The linear theory for ow without terrain shows that the solution depends on two parameters: a nondimensional coastal width L and a nondimensional wind speed U. For U 6= 0 the solution is composed of three distinct wave branches. Two of these branches correspond to the no-wind solution of Rotunno, except with Doppler shifting and dispersion. The third branch exists only for U 6= 0 and is shown to be broadly similar to ow past a steady heat source or a topographic obstacle. The relative importance of this third branch is determined largely by the parameter combination U=L. The e ect of terrain is explored in the linear context using an idealized linear model and associated diagnostic computations. These results are then extended to the nonlinear problem using idealized nonlinear model runs.

No description available.

In the ewe, one to three antral follicles emerge or grow from a pool of small antral follicles (1 to 3 mm in diameter) every 3 to 5 days and reach diameters of ¡Ý5 mm before regression or ovulation. Each follicular wave is triggered by a peak in serum concentrations of FSH. It is not clear what characteristics of an FSH peak cause follicular wave emergence and what aspects of development of a follicular wave are regulated by its preceding FSH peak.<p> In Experiment 1, we found that the amplitude of FSH peaks decreased, while basal serum FSH concentrations increased across the inter-ovulatory interval (P < 0.05). However, there were no associated changes in the growth, static or regression phases of follicular waves or the number and size of follicles in a wave. In Experiment 2, using computer-assisted quantitative echotextural analysis, we found that the numerical pixel value (NPV) for the wall of anovulatory follicles emerging in the third wave of the cycle was significantly higher than for waves 1 and 2 at the time of wave emergence but it decreased as follicles reached maximum follicular diameter (P < 0.05). A tendency for a similar pattern for the wall of follicles in the last wave of the cycle was also observed (P = 0.07).<p> In Experiment 3, treatment with ovine FSH (oFSH) increased the amplitude of an FSH peak by 5 to 6 fold. This treatment increased estradiol production (P < 0.05) but had little effect on other characteristics of the subsequent follicular wave. Daily injections of oFSH (Experiment 4) for four days, resulted in the occurrence of 4 discrete peaks in serum FSH concentrations. Each injection of oFSH resulted in the emergence of a new follicular wave.<p> In Experiment 5, six cyclic ewes received oFSH (0.1 ¦Ìg/kg, sc) every 6 h for 42 h, to try to give a gradual increase in the leading slope of an FSH peak. Serum FSH concentrations increased in oFSH treated ewes (P < 0.05) resulting in an additional peak between two endogenously driven FSH peaks and therefore, did not give the planned gradual leading slope to an FSH peak. Ovine FSH treatment occurred in the early growth phase of wave 1 of the inter-ovulatory interval and increased the growth rate of growing follicles in that wave, compared to control ewes (P < 0.05). This apparently induced dominance in follicles in wave 1, causing them to suppress wave emergence in response to the injected FSH. In Experiment 6, oFSH was infused constantly (1.98 ¦Ìg/ewe/h, iv, n = 6) for 60 h. Infusion of oFSH maintained serum FSH concentrations at a level similar to the zenith of a peak. This resulted in a superstimulatory effect with a peak in the mean number of large follicles on Day 2 after the start of FSH infusion (P < 0.001).<p> A hormonal milieu similar to low serum progesterone concentrations was created by treatment of ewes with prostaglandin and medroxyprogesterone acetate (MAP) sponges (Experiment 7). This treatment delayed regression of the penultimate follicular wave of a cycle. However, the delayed follicular atresia was accompanied by a greater degree of apoptosis in somatic cells of follicles growing in the penultimate wave compared to those in the final wave of the cycle, when collected one day before expected ovulation.<p> In conclusion, trends in basal serum concentrations of FSH and peaks in serum FSH concentrations, across the estrous cycle, are associated with changes in the image attributes of follicles emerging later in the estrous cycle, perhaps reflecting a greater readiness of those follicles for ovulation and formation of CL. The ovine ovary can respond to discrete peaks in serum FSH concentrations with the emergence of new follicular waves on a daily basis. This led us to conclude that follicular dominance is not evident in the ewe and peaks in serum FSH concentrations are likely to be driven by some endogenous rhythm that is unrelated to ovarian follicular secretory products. However, direct dominance can be induced by giving supplemented FSH during the growth phase of a follicle. Extended exposure of ovine ovaries to the serum concentrations of FSH found at the zenith of a peak overrides the mechanisms that recruit follicles into a wave and induces a superovulatory response in cyclic ewes. Finally, an increase in the incidence of apoptosis occurs in antral follicles in sheep that have an extended lifespan, prior to any morphological changes detectable by ultrasonography. This would seem to cause decreased follicular viability and lowered fertility of the oocytes that the follicles contain.

In the ewe, one to three antral follicles emerge or grow from a pool of small antral follicles (1 to 3 mm in diameter) every 3 to 5 days and reach diameters of ¡Ý5 mm before regression or ovulation. Each follicular wave is triggered by a peak in serum concentrations of FSH. It is not clear what characteristics of an FSH peak cause follicular wave emergence and what aspects of development of a follicular wave are regulated by its preceding FSH peak.<p> In Experiment 1, we found that the amplitude of FSH peaks decreased, while basal serum FSH concentrations increased across the inter-ovulatory interval (P < 0.05). However, there were no associated changes in the growth, static or regression phases of follicular waves or the number and size of follicles in a wave. In Experiment 2, using computer-assisted quantitative echotextural analysis, we found that the numerical pixel value (NPV) for the wall of anovulatory follicles emerging in the third wave of the cycle was significantly higher than for waves 1 and 2 at the time of wave emergence but it decreased as follicles reached maximum follicular diameter (P < 0.05). A tendency for a similar pattern for the wall of follicles in the last wave of the cycle was also observed (P = 0.07).<p> In Experiment 3, treatment with ovine FSH (oFSH) increased the amplitude of an FSH peak by 5 to 6 fold. This treatment increased estradiol production (P < 0.05) but had little effect on other characteristics of the subsequent follicular wave. Daily injections of oFSH (Experiment 4) for four days, resulted in the occurrence of 4 discrete peaks in serum FSH concentrations. Each injection of oFSH resulted in the emergence of a new follicular wave.<p> In Experiment 5, six cyclic ewes received oFSH (0.1 ¦Ìg/kg, sc) every 6 h for 42 h, to try to give a gradual increase in the leading slope of an FSH peak. Serum FSH concentrations increased in oFSH treated ewes (P < 0.05) resulting in an additional peak between two endogenously driven FSH peaks and therefore, did not give the planned gradual leading slope to an FSH peak. Ovine FSH treatment occurred in the early growth phase of wave 1 of the inter-ovulatory interval and increased the growth rate of growing follicles in that wave, compared to control ewes (P < 0.05). This apparently induced dominance in follicles in wave 1, causing them to suppress wave emergence in response to the injected FSH. In Experiment 6, oFSH was infused constantly (1.98 ¦Ìg/ewe/h, iv, n = 6) for 60 h. Infusion of oFSH maintained serum FSH concentrations at a level similar to the zenith of a peak. This resulted in a superstimulatory effect with a peak in the mean number of large follicles on Day 2 after the start of FSH infusion (P < 0.001).<p> A hormonal milieu similar to low serum progesterone concentrations was created by treatment of ewes with prostaglandin and medroxyprogesterone acetate (MAP) sponges (Experiment 7). This treatment delayed regression of the penultimate follicular wave of a cycle. However, the delayed follicular atresia was accompanied by a greater degree of apoptosis in somatic cells of follicles growing in the penultimate wave compared to those in the final wave of the cycle, when collected one day before expected ovulation.<p> In conclusion, trends in basal serum concentrations of FSH and peaks in serum FSH concentrations, across the estrous cycle, are associated with changes in the image attributes of follicles emerging later in the estrous cycle, perhaps reflecting a greater readiness of those follicles for ovulation and formation of CL. The ovine ovary can respond to discrete peaks in serum FSH concentrations with the emergence of new follicular waves on a daily basis. This led us to conclude that follicular dominance is not evident in the ewe and peaks in serum FSH concentrations are likely to be driven by some endogenous rhythm that is unrelated to ovarian follicular secretory products. However, direct dominance can be induced by giving supplemented FSH during the growth phase of a follicle. Extended exposure of ovine ovaries to the serum concentrations of FSH found at the zenith of a peak overrides the mechanisms that recruit follicles into a wave and induces a superovulatory response in cyclic ewes. Finally, an increase in the incidence of apoptosis occurs in antral follicles in sheep that have an extended lifespan, prior to any morphological changes detectable by ultrasonography. This would seem to cause decreased follicular viability and lowered fertility of the oocytes that the follicles contain.

Coastal regions are vulnerable to various natural processes, ranging from normal waves to extreme events. Given the flourishing development and large population along coastlines, various measures have been taken to mitigate the water-induced damage. Nature-based coastal protection, especially vegetation, has attracted unprecedented studies over the past two decades. To enhance understanding of this subject, this dissertation evaluates the impact of patchy vegetation on wave and runup dynamics along coastlines. Selecting from a prototype in Dalehite Cove, Galveston Bay, TX, results from a Boussinesq model (COULWAVE) showed patchy vegetation reduced up to 75% mean shoreward current in the mound-channel wetland systems. These vegetation patches also reduced the primary circulation around mounds, with a power-form relation between circulation size and various parameters (i.e., bathymetry, incident wave and vegetated roughness). Substituting spectral waves for regular waves in the similar wetlands, more energy was transferred into the higher frequencies. The impact of patchy vegetation on wave energy was frequency- and space-dependent, with increased energy observed in specific harmonics and locations. Comparison with unvegetated horizontal bathymetry demonstrated that mound-channel bathymetry was the dominant factor in transferring and dissipating wave energy, while vegetation patches added a fair contribution. As for extreme events, such as tsunamis, laboratory experiments and numerical simulations were conducted to assess the effectiveness of patchy vegetation with various roughness levels, spacings and sizes. Overall, vegetation patches reduced the most destructive loads onshore by up to 80%. Within-patch roughness variation only caused uncertainty on the hydrodynamics around the seaward patches, while the mitigation of extreme loads was not undermined. A logarithmic relation was observed between the protected area from extreme loads and the vegetated coverage. These findings will fill the knowledge gap of hydrodynamics in the presence patchy vegetation, and improve the engineering practice of coastal protection using nature-based infrastructure. / Ph. D.

Pulse detonation combustion has been of interest for many years since it offers several advantages over standard deflagrative combustion. In theory, detonative combustion is a better use of fuel compared to deflagrative combustion since less entropy is generated during a detonation. As a result, detonation offers higher pressure and temperature gain across the wave front compared to the comparable deflagration. Since a detonation is a supersonic event which uses a shock to compress and dissociate reactants, a Pulse Detonation Combustor (PDC) is a relatively simple device that does not necessarily require a large compressor section at the inlet. Despite these benefits, using a turbine to extract work from a PDC is a problem littered with technical challenges. A PDC necessarily operates cyclically, producing highly transient pressure and temperature fields. This cyclic operation presents concerns with regards to turbine reliability and effective work extraction. The research presented here investigated the implementation of a pulse detonation diffuser, a device intended to temporally and spatially distribute the energy produced during a detonation pulse. This device would be an inert extension from a baseline PDC, manipulating the decaying detonation front while minimizing entropy production. A diffuser will seek to elongate, steady, attenuate, and maintain the quality of energy contained in the exhaust of a detonation pulse. These functions intend to reduce stresses introduced to a turbine and aid in effective work extraction. The goal of this research was to design, implement, and evaluate such a diffuser using the using conventional analysis and simulated and physical experimentation. Diffuser concepts using various wave dynamic mechanisms were generated. Analytical models were developed to estimate basic timing and wave attenuation parameters for a given design. These models served to inform the detail design process, providing an idea for geometric scale for a diffuser. Designs were simulated in ANSYS Fluent. The simulated performance of each diffuser was measured using metrics quantifying the wave attenuation, pulse elongation, pulse steadying, and entropy generation for each design. The most promising diffuser was fabricated and tested using a detonation tube. Diffuser performance was compared against analytical and computational models using dynamic pressure transducer diagnostics. / Master of Science

In this thesis, a general methodology for generating representative load cycles for arbitrary monohull surface vessels is developed. The proposed methodology takes a hull geometry and propeller placement, vessel loading condition, vessel mission, and weather data (wind, waves, currents) and, from that, generates the propeller states (torque, speed, power) and steering gear states (torque, speed, power) necessary to accomplish the given mission. The propeller states, together with the steering gear states, thus define the load cycle corresponding to the given inputs (vessel, mission, weather). Some key aspects of the proposed methodology include the use of a surge-sway-yaw model for vessel dynamics as well as the use of surrogate geometries for both the hull and propeller(s). What results is a methodology that is lean (that is, it requires only sparse input), fast, easy to generalize, and reasonably accurate. The proposed methodology is validated by way of two separate case studies, case A and case B (both involving distinct car-deck ferries), with case A being a more ideal case, and case B being a less ideal case given the methodology proposed. In both cases, the load cycle generation process completed in greater than real time, achieving time ratios (simulated time to execution time) of 3.3:1 and 12.8:1 for cases A and B respectively. The generated propeller and steering gear states were then compared to data collected either at sea or from the vessels' documentation. For case A, the propeller speed, torque, and power values generated were all accurate to within +/- 3%, +/- 7%, and +/- 10% of the true values, respectively, while cruising, and accurate to within +/- 14%, +/- 36%, and +/- 42% of the true values, respectively, while maneuvering. In addition, the steering gear powers generated in case A were consistent with the capabilities of the equipment actually installed on board. For case B, the propeller speed, torque, and power values generated were all accurate to within +/- 2%, +/- 8%, and +/- 9% of the true values, respectively, while cruising, and accurate to within +/- 28%, +/- 45%, and +/- 66% of the true values, respectively, while maneuvering. In case B, however, the steering gear powers generated were questionable. Considering the results of the validation, together with the rapid process runtimes achieved and sparse inputs given, one may conclude that the methodology proposed in this thesis shows promise in terms of being able to generate representative load cycles for arbitrary monohull surface vessels. / Graduate

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. There is growing consensus that these arrhythmias are associated with the formation of spiral and scroll waves of electrical activation in mammalian cardiac tissue; whereas single spiral and scroll waves are believed to be associated with VT, their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem in-so-far-as to develop an understanding of the electrophysiological basis of VT and VF. In this thesis, we provide a brief overview of recent numerical studies of spiral- and scroll-wave dynamics in mathematical models of mammalian cardiac tissue. In addition to giving a description of how spiral and scroll waves can be initiated in such models, how they evolve, how they interact with conduction and ionic inhomogeneities, how their dynamics is influenced by the size and geometry of the heart, we also discuss how active Purkinje networks and passive fibroblast clusters modify the electrical activity of cardiomyocytes, and the relevance of such studies to defibrillation. In Chapter 2 we present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional (3D) TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inho-mogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inho-mogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study. In Chapter 3 we present a comprehensive numerical study of plane and scroll waves of electrical activation in two state-of-the-art ionic models for rabbit and pig cardiac tissue. We use anatomically realistic, 3D simulation domains, account for muscle-fiber rotation, and show how to include conduction and ionic inhomogeneities in these models; we consider both localized and randomly distributed inhomogeneities. Our study allows us to compare scroll-wave dynamics, with and without inhomogeneities, in these rabbit-and pig-heart models at a level that has not been attempted hitherto. We begin with a comparison of single-cell action potentials (APs) and ionic currents in the Bers-Puglisi (BP) and modified-Luo-Rudy I (mLRI) models for rabbit- and pig-myocytes, respec-tively. We then show how, for plane-wave propagation in rabbit- and pig-heart models, the conduction velocity CV and wavelength λ depend on the distance of the plane of measurement from the plane containing the heart apex. Without inhomogeneities, and in the parameter r´egime in which these models display scroll waves, the rabbit-heart model supports a single scroll wave, which rotates periodically, whereas the pig-heart model supports two scroll waves, which rotate periodically, but with a slight difference in phase; this is partly because the rabbit-heart model is smaller in size, than the pig-heart one. With randomly-distributed inhomogeneities, we find that the rabbit-heart model loses its ability to support electrical activity, even at inhomogeneity concentra-tions as low as 5%. In the pig-heart model, we obtain rich, scroll-wave dynamics in the presence of localized or distributed inhomogeneities, both of conduction and ionic types; often, but not always, scroll waves get anchored to localized inhomogeneities; and distributed inhomogeneities can lead to scroll-wave break up. In Chapter 4, we present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibrob-lasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to Nf fibroblasts via a gap-junctional conductance Ggap, reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a ran-dom distribution of fibroblasts in a myocyte background reveal that, as the percentage Pf of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperi-odic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilib-rium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis. In Chapter 5 we present a detailed numerical study of the electrophysiological in-teractions between a random Purkinje network and simulated human endocardial tissue, (a) in the presence of, and (b) in the absence of existing electrical excitation in the system. We study the dependence of the activation-onset-time (ta) on the strength of coupling (Dmp) between the myocyte layer and the Purkinje network, in the absence of any external stimulus. Since the connection between the endocardial layer and the Purkinje network occurs only at discrete points, we also study the dependence of ta on the number of Purkinje-myocyte junctions (PMJs) at fixed values of Dmp, in the ab-sence of any applied excitation. We study signal propagation in the system; our results demonstrate the situations of (a) conduction block from the Purkinje layer to the endo-cardial layer, (b) anterograde propagation of the excitation from the Purkinje layer to the endocardium, (c) retrograde propagation of the excitation from the endocardium to the Purkinje layer and (d) development of reentrant circuits in the Purkinje layer that lead to formation of ectopic foci at select PMJs. We extend our study to explore the effects of Purkinje-myocyte coupling on spiral wave dynamics, whereby, we find that such coupling can lead to the distortion and breakage of the parent rotor into multiple rotors within the system; with or without internal coherence. We note that retrograde propa-gation leads to the development of reentrant circuits in the Purkinje network that help to initiate and stabilize ectopic foci. However, in some cases, Purkinje-myocyte coupling can also lead to the suppression of spiral waves. Finally we conduct four representative simulations to study the effects of transmural heterogeneity, fiber rotation and coupling with a non-penetrating Purkinje network on a three dimensional slab of cardiac tissue. Lastly, In Chapter 6, we study reentry associated with inexcitable obstacles in the ionically-realistic TNNP model for human ventricular tissue, under the influence of high-frequency stimulation. When a train of plane waves successively impinge upon an obstacle, the obstacle splits these waves as they tend to propagate past it; the emergent broken waves can either travel towards each other, bridging the gap introduced by the obstacle at the time of splitting, or, they can travel away from each other, resulting in the growth of the gap. The second possibility eventually results in the formation of spiral waves. This phenomenon depends on frequency of the waves. At high frequency, the excitability of the tissue decreases and the broken waves have a tendency to move apart. Hence high-frequency stimulation increases the chances of reentry in cardiac tissue. We correlate the critical period of pacing that leads to reentry in the presence of an inexcitable obstacle, with the period of spiral waves, formed in the homogeneous domain, and study how the critical period of pacing depends on the parameters of the model.

Stationary wave theory elucidates the dynamics of the time mean zonally asymmetric component of the atmospheric circulation and separates it from the dynamics of the zonal mean climatological flow. This thesis focuses on the dynamics of stationary wave nonlinearity and its applications in stationary wave modelling and the stationary wave response to climate change. Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the observed zonally asymmetric atmospheric general circulation. Stationary wave nonlinearity is examined in quasi-geostrophic barotropic dynamics in both the presence and absence of transient waves. Stationary wave nonlinearity is shown to account for most of the difference between the linear and full nonlinear stationary waves, particularly if the zonal-mean flow adjustment to the stationary waves is taken into account. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A time-integration type nonlinear stationary wave modelling technique is tested in this simple barotropic setting and is shown to be able to predict stationary wave nonlinearity and capture the basic features of the full nonlinear stationary wave. A baroclinic nonlinear stationary wave model is then developed using this technique and is applied to the problem of the stationary wave response to climate change. Previous stationary wave modelling has largely focused on the tropospheric circulation, but the stationary wave field extends into the stratosphere and plays an important dynamical role there. This stationary wave model is able to represent the stratospheric stationary wave field and is used to analyze the Northern Hemisphere stationary wave response to climate change simulated by the Canadian Middle Atmosphere Model (CMAM). In the CMAM simulation changes to the zonal mean basic state alone can explain much of the stationary wave response, which is largely controlled by changes of the zonal mean circulation in the Northern Hemisphere subtropical upper troposphere. However, details of the stratospheric wave driving response are also sensitive to other aspects of the zonal-mean response and to the heating response. Many climate change related effects appear to contribute robustly to an increased wave activity flux into the stratosphere.

Stationary wave theory elucidates the dynamics of the time mean zonally asymmetric component of the atmospheric circulation and separates it from the dynamics of the zonal mean climatological flow. This thesis focuses on the dynamics of stationary wave nonlinearity and its applications in stationary wave modelling and the stationary wave response to climate change. Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the observed zonally asymmetric atmospheric general circulation. Stationary wave nonlinearity is examined in quasi-geostrophic barotropic dynamics in both the presence and absence of transient waves. Stationary wave nonlinearity is shown to account for most of the difference between the linear and full nonlinear stationary waves, particularly if the zonal-mean flow adjustment to the stationary waves is taken into account. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A time-integration type nonlinear stationary wave modelling technique is tested in this simple barotropic setting and is shown to be able to predict stationary wave nonlinearity and capture the basic features of the full nonlinear stationary wave. A baroclinic nonlinear stationary wave model is then developed using this technique and is applied to the problem of the stationary wave response to climate change. Previous stationary wave modelling has largely focused on the tropospheric circulation, but the stationary wave field extends into the stratosphere and plays an important dynamical role there. This stationary wave model is able to represent the stratospheric stationary wave field and is used to analyze the Northern Hemisphere stationary wave response to climate change simulated by the Canadian Middle Atmosphere Model (CMAM). In the CMAM simulation changes to the zonal mean basic state alone can explain much of the stationary wave response, which is largely controlled by changes of the zonal mean circulation in the Northern Hemisphere subtropical upper troposphere. However, details of the stratospheric wave driving response are also sensitive to other aspects of the zonal-mean response and to the heating response. Many climate change related effects appear to contribute robustly to an increased wave activity flux into the stratosphere.