In this thesis direct numerical simulations are used to investigate two phenomenain shear flows: laminar-turbulent transition over a flat plate and periodicvortex shedding induced by a jet in cross flow. The emphasis is on understanding and controlling the flow dynamics using tools from dynamical systems and control theory. In particular, the global behavior of complex flows is describedand low-dimensional models suitable for control design are developed; this isdone by decomposing the flow into global modes determined from spectral analysisof various linear operators associated with the Navier–Stokes equations.Two distinct self-sustained global oscillations, associated with the sheddingof vortices, are identified from direct numerical simulations of the jet incrossflow. The investigation is split into a linear stability analysis of the steadyflow and a nonlinear analysis of the unsteady flow. The eigenmodes of theNavier–Stokes equations, linearized about an unstable steady solution revealthe presence of elliptic, Kelvin-Helmholtz and von K´arm´an type instabilities.The unsteady nonlinear dynamics is decomposed into a sequence of Koopmanmodes, determined from the spectral analysis of the Koopman operator. Thesemodes represent spatial structures with periodic behavior in time. A shearlayermode and a wall mode are identified, corresponding to high-frequency andlow-frequency self-sustained oscillations in the jet in crossflow, respectively.The knowledge of global modes is also useful for transition control, wherethe objective is to reduce the growth of small-amplitude disturbances to delaythe transition to turbulence. Using a particular basis of global modes, knownas balanced modes, low-dimensional models that capture the behavior betweenactuator and sensor signals in a flat-plate boundary layer are constructed andused to design optimal feedback controllers. It is shown that by using controltheory in combination with sensing/actuation in small, localized, regionsnear the rigid wall, the energy of disturbances may be reduced by an order of magnitude.

Direct numerical simulations of the receptivity and instability of boundary layers on flat and curved surfaces are herein reported. Various flow models are considered with the aim to capture aspects of flows over straight and swept wings such as wall curvature, pressure variations, leading-edge effects, streamline curvature and crossflow. The first model problem presented, the flow over a swept flat plate, features a crossflow inside the boundary layer. The layer is unstable to steady and traveling crossflow vortices which are nearly aligned with the free stream. Wall roughness and free-stream vortical modes efficiently excite these crossflow modes, and the associated receptivity mechanisms are linear in an environment of low-amplitude perturbations. Receptivity coefficients for roughness elements with various length scales and for free-stream vortical modes with different wavenumbers and frequencies are reported. Key to the receptivity to free-stream vorticity is the upstream excitation of streamwise streaks evolving into crossflow modes. This mechanism is also active in the presence of free-stream turbulence. The second flow model is that of a Görtler boundary layer. This flow type forms on surfaces with concave curvature, e.g. the lower side of a turbine blade. The dominant instability, driven by a vertically varying centrifugal force, appears as pairs of steady, streamwise counter-rotating vortical rolls and streamwise streaks. The Görtler boundary layer is in particular receptive to free-stream vortical modes with zero and low frequencies. The associated mechanism builds on the excitation of upstream disturbance streaks from which the Görtler modes emerge, similar to the mechanism in swept-plate flows. The receptivity to free-stream vorticity can both be linear and nonlinear. In the presence of free-stream turbulence, nonlinear receptivity is more likely to trigger steady Görtler vortices than linear receptivity unless the frequencies of the free-stream fluctuations are very low. The third set of simulations considers the boundary layer on a flat plate with an elliptic leading edge. This study aims to identify the effect of the leading edge on the boundary-layer receptivity to impinging free-stream vortical modes. Three types of modes with streamwise, vertical and spanwise vorticity are considered. The two former types trigger streamwise disturbance streaks while the latter type excites Tollmien-Schlichting wave packets in the shear layer. Simulations with two leading edges of different bluntness demonstrate that the leading-edge shape hardly influences the receptivity to streamwise vortices, whereas it significantly enhances the receptivity to vertical and spanwise vortices. It is shown that the receptivity mechanism to vertical free-stream vorticity involves vortex stretching and tilting - physical processes which are clearly enhanced by blunt leading edges. The last flow configuration studied models an infinite wing at 45 degrees sweep. This model is the least idealized with respect to applications in aerospace engineering. The set-up mimics the wind-tunnel experiments carried out by Saric and coworkers at the Arizona State University in the 1990s. The numerical method is verified by simulating the excitation of steady crossflow vortices through micron-sized roughness as realized in the experiments. Moreover, the receptivity to free-stream vortical disturbances is investigated and it is shown that the boundary layer is most receptive, if the free-stream modes are closely aligned with the most unstable crossflow mode / QC 20101025

Understanding spatial and temporal variations in strain accumulation and release along plate boundaries is a fundamental problem in tectonics. Short-term and long-term slip rates are expected to be equal if the regional stress field remains unchanged over time, yet discrepancies between modern geodetic (decadal time scale) slip rates and long-term geologic (10^3 to 10^6 years) slip rates have been observed on parts of the Pacific-North American plate boundary system. Contemporary geodetic slip rates are observed to be ~2 times greater than late Pleistocene geologic slip rates across the southern Walker Lane. I use a combination of GPS geodesy, detailed field geologic mapping, high-resolution LiDAR geodetic imaging, and terrestrial cosmogenic nuclide geochronology to investigate the observed discrepancy between long- and short-term slip rates. I find that the present day slip rate derived from GPS geodesy across the Walker Lane at ~37.5°N is 10.6 ± 0.5 mm/yr. GPS data suggest that much of the observed discrepancy occurs west of the White Mountains fault zone. New dextral slip rates on the White Mountains fault zone of 1.1 ± 0.1 mm/yr since 755 ka, 1.9 +0.5/-0.4 mm/yr since 75-115 ka, 1.9 +0.5/-0.4 mm/yr since 38.4 ± 9.0 ka, and 1.8 +2.8/-0.7 mm/yr since 6.2 ± 3.8 ka are significantly faster than previous estimates and suggest that slip rates there have remained constant since the middle Pleistocene. On the Lone Mountain fault I calculate slip rates of 0.8 ± 0.1 mm/yr since 14.6 ± 1.0 ka and 0.7 ± 0.1 mm/yr since 8.0 ± 0.5 ka, which suggest that extension in the Silver Peak-Lone Mountain extensional complex has increased dramatically since the late Pleistocene.

Transition delay in boundary-layer flows is achieved via reactive control of flow instabilities, i.e. Tollmien-Schlichting (TS) waves. Adaptive and model-based control techniques are investigated by means of direct numerical simulations (DNS) and experiments. The action of actuators localised in the wall region is prescribed based on localised measurement of the disturbance field; in particular, plasma actuators and surface hot-wire sensors are considered. Performances and limitations of this control approach are evaluated both for two-dimensional (2D) and three-dimensional (3D) disturbance scenarios. The focus is on the robustness properties of the investigated control techniques; it is highlighted that static model-based control, such as the linear-quadratic- Gaussian (LQG) regulator, is very sensitive to model-inaccuracies. The reason for this behaviour is found in the feed-forward nature of the adopted sensor/actuator scheme; hence, a second, downstream sensor is introduced and actively used to recover robustness via an adaptive filtered-x least-mean-squares (fxLMS) algorithm. Furthermore, the model of the flow required by the control algorithm is reduced to a time delay. This technique, called delayed-x least-mean-squares (dxLMS) algorithm, allows taking a step towards a self-tuning controller; by introducing a third sensor it is possible to compute on-line the suitable time-delay model with no previous knowledge of the controlled system. This self-tuning approach is successfully tested by in-flight experiments on a motor-glider. Lastly, the transition delay capabilities of the investigated control con- figuration are confirmed in a complex disturbance environment. The flow is perturbed with random localised disturbances inside the boundary layer and the laminar-to-turbulence transition is delayed via a multi-input-multi-output (MIMO) version of the fxLMS algorithm. A positive theoretical net-energy- saving is observed for disturbance amplitudes up to 2% of the free-stream velocity at the actuation location, reaching values around 1000 times the input power for the lower disturbance amplitudes that have been investigated. / I den här avhandlingen har reglertekniska metoder tillämpats för att försena omslaget från ett laminärt till ett turbulent gränsskikt genom att dämpa tillväxten av små instabiliteter, så kallade Tollmien-Schlichting vågor. Adaptiva och modellbaserade metoder för reglering av strömning har undersökts med hjälp av numeriska beräkningar av Navier-Stokes ekvationer, vindtunnelexperiment och även genom direkt tillämpning på flygplan. Plasmaaktuatorer och varmtrådsgivare vidhäftade på ytan av plattan eller vingen har använts i experimenten och modellerats i beräkningarna. Prestanda och begränsningar av den valda kontrollstrategin har utvärderats för både tvådimensionella och tredimensionella gränsskiktsinstabiliteter. Fokus har varit på metodernas robusthet, där vi visar att statiska metoder som linjär-kvadratiska regulatorer (LQG) är mycket känsliga för avvikelser från den nominella modellen. Detta beror främst på att regulatorer agerar i förkompenseringsläge (”feed-foward”) på grund av strömningens karaktär och placeringen av givare och aktuatorer. För att minska känsligheten mot avvikelser och därmed öka robustheten har en givare införts nedströms och en adaptiv fXLMS algoritm (filtered-x least-mean-squares) har tillämpats.                  Vidare har modelleringen av fXLMS-algoritmen förenklats genom att ersätta överföringsfunktionen mellan aktuatorer och givare med en lämplig tidsfördröjning.  Denna  metod som kallas för dxLMS (delayed-x least-mean-squares) kräver att ytterligare en givare införs långt uppströms för att kunna uppskatta hastigheten på de propagerande instabilitetsvågorna. Denna teknik har tillämpats framgångsrikt för reglering av gränsskiktet på vingen av ett segelflygplan. Slutligen har de reglertekniska metoderna testas för komplexa slumpmässiga tredimensionella störningar som genererats uppströms lokalt i gränsskiktet. Vi visar att en signifikant försening av laminärt-turbulentomslag äger rum med hjälp av en fXLMS algoritm. En analys av energibudgeten visar att för ideala aktuatorer och givare kan den sparade energiåtgången på grund av minskad väggfriktion vara upp till 1000 gånger större än den energi som använts för reglering.