Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Age models and stable isotope ratios from the Mid-Miocene

Mid-Miocene pelagic sedimentary sections can be correlated using intermediate and high resolution oxygen and carbon isotopic records of benthic foraminifera. Precision of a few tens of thousands of years is readily achievable at sites with high sedimentation rates, for example, Deep Sea Drilling Project sites 289 and 574. The mid-Miocene carbon isotope records are characterized by an interval of high d13C values between 17 and 13.5 Ma (the Monterey Excursion of Vincent and Berger 1985) upon which are superimposed a series of periodic or quasi-periodic fluctuations in d13C values. These fluctuations have a period of approximately 440 kyr, suggestive of the 413 kyr cycle predicted by Milankovitch theory. Vincent and Berger proposed that the Monterey Excursion was the result of increased organic carbon burial in continental margins sediments. The increased d13C values (called 13C maxima) superimposed on the generally high mid-Miocene signal coincide with increases in d18O values suggesting that periods of cooling and/or ice buildup were associated with exceptionally rapid burial of organic carbon and lowered atmospheric CO2 levels. It is likely that during the Monterey Excursion the ocean/atmosphere system became progressively more sensitive to small changes in insolation, ultimately leading to major cooling of deep water and expansion of continental ice. We have assigned an absolute chronology, based on biostratigraphic and magneto-biostratigraphic datum levels, to the isotope stratigraphy and have used that chronology to correlate unconformities, seismic reflectors, carbonate minima, and dissolution intervals. Intervals of sediment containing 13C maxima are usually better preserved than the overlying and underlying sediments, indicating that the d13C values of TCO2 in deep water and the corrosiveness of seawater are inversely correlated. This again suggests that the 13C maxima were associated with rapid burial of organic carbon and reduced levels of atmospheric CO2. The absolute chronology we have assigned to the isotopic record indicates that the major mid-Miocene deepwater cooling/ice volume expansion took 2 m.y. and was not abrupt as had been reported previously. The cooling appears abrupt at many sites because the interval is characterized by a number of dissolution intervals. The cooling was not monotonic, and the 2 m.y. interval included an episode of especially rapid cooling as well as a brief return to warmer conditions before the final phase of the cooling period. The increase in d18O values of benthic foraminifera between 14.9 and 12.9 Ma was greatest at deeper water sites and at sites closest to Antarctica. The data suggest that the d18O value of seawater increased by no more than about 1.1 per mil during this interval and that the remainder of the change in benthic d18O values resulted from cooling in Antarctic regions of deepwater formation. Equatorial planktonic foraminifera from sites 237 and 289 exhibit a series of 0.4 per mil steplike increases in d13C values. Only one of these increases in planktonic d13C is correlated with any of the features in the mid-Miocene benthic carbon isotope record.

Ocean temperature response to idealized Gleissberg and de Vries solar cycles in a comprehensive climate model

The ~90-year Gleissberg and ~200-year de Vries cycles have been identified as two distinctive quasi-periodic components of Holocene solar activity. Evidence exists for the impact of such multi-decadal to centennial-scale variability in total solar irradiance (TSI) on climate, but concerning the ocean, this evidence is mainly restricted to the surface response. Here we use a comprehensive global climate model to study the impact of idealized solar forcing, representing the Gleissberg and de Vries cycles, on global ocean potential temperature at different depth levels, after a recent proxy record indicates a signal of TSI anomalies in the northeastern Atlantic at mid-depth. Potential impacts of TSI anomalies on deeper oceanic levels are climatically relevant due to their possible effect on ocean circulation by altering water mass characteristics. Simulated solar anomalies are shown to penetrate the ocean down to at least deep-water levels. Despite the fact that the two forcing periods differ only by a factor of ~2, the spatial pattern of response is significantly distinctive between the experiments, suggesting different mechanisms for solar signal propagation. These are related to advection by North Atlantic Deep Water flow (200-year forcing), and barotropic adjustment in the South Atlantic in response to a latitudinal shift of the westerly wind belt (90-year forcing).

Investigations on fossil bivalves and wood from Seymour Island, Antarctica

Quasi-periodic variation in sea-surface temperature, precipitation, and sea-level pressure in the equatorial Pacific known as the El Niño - Southern Oscillation (ENSO) is an important mode of interannual variability in global climate. A collapse of the tropical Pacific onto a state resembling a so-called 'permanent El Niño', with a preferentially warmed eastern equatorial Pacific, flatter thermocline, and reduced interannual variability, in a warmer world is predicted by prevailing ENSO theory. If correct, future warming will be accompanied by a shift toward persistent conditions resembling El Niño years today, with major implications for global hydrological cycles and consequent impacts on socioeconomic and ecological systems. However, much uncertainty remains about how interannual variability will be affected. Here, we present multi-annual records of climate derived from growth increment widths in fossil bivalves and co-occurring driftwood from the Antarctic peninsula that demonstrate significant variability in the quasi-biennial and 3-6 year bands consistent with ENSO, despite early Eocene (~50 Mya) greenhouse conditions with global average temperature -10 degrees higher than today. A coupled climate model suggests an ENSO signal and teleconnections to this region during the Eocene, much like today. The presence of ENSO variation during this markedly warmer interval argues for the persistence of robust interannual variability in our future greenhouse world.

Sedimentology and geochemistry of core GIK23258-2 in the Barents Sea

At the western continental margin of the Barents Sea, 75°N, hemipelagic sediments provide a record of Holocene climate change with a time resolution of 10-70 years. Planktic foraminifera counts reveal a very early Holocene thermal optimum 10.7-7.7 kyr BP, with summer sea surface temperatures (SST) of 8°C and a much enhanced West Spitsbergen Current. There was a short cooling between 8.8 and 8.2 kyr BP. In the middle and late Holocene summer, SST dropped to 2.5°-5.0°C, indicative of reduced Atlantic heat advection, except for two short warmings near 2.2 and 1.6 kyr BP. Distinct quasi-periodic spikes of coarse sediment fraction (with large portions of lithic grains, benthic and planktic foraminifera) record cascades of cold, dense winter water down the continental slope as a result of enhanced seasonal sea ice formation and storminess on the Barents shelf over the entire Holocene. The spikes primarily cluster near recurrence intervals of 400-650 and 1000-1350 years, when traced over the entire Holocene, but follow significant 885-/840- and 505-/605-year periodicities in the early Holocene. These non-stationary periodicities mimic the Greenland-[Formula: See Text]Be variability, which is a tracer of solar forcing. Further significant Holocene periodicities of 230, (145) and 93 years come close to the deVries and Gleissberg solar cycles.

High-resolution sediment record from a submarine meandering canyon system in the eastern Atlantic

Based on a high-resolution sediment record from a submarine meandering canyon system offshore the present-day hyperarid Saharan Africa, two phases of turbidity-current activity can be distinguished during the past 13,000 years. Frequent, siliciclastic turbidity currents can be related to deglacial sea-level history, whereas rhythmically recurring fine-grained and carbonate-rich turbidity currents with recurrence times of roughly 900 years are inferred for the Holocene. Various trigger mechanisms can be considered to initiate turbidity currents, but only a few can explain a periodic turbidite activity. A comparison of Holocene turbidite recurrence times and basic cycles of 900 and 1,800 years found in various Holocene paleoclimate studies suggests that a previously unrecognized climate-related coupling may be active.

Stable carbon and oxygen isotope record od IODP Hole 306-U1313

The Mid-Pleistocene transition (MPT) was the time when quasi-periodic (? 100 kyr), high-amplitude glacial variability developed in the absence of any significant change in the character of orbital forcing, leading to the establishment of the characteristic pattern of late Pleistocene climate variability. It has long been known that the interval around 900 ka stands out as a critical point of the MPT, when major glaciations started occurring most notably in the northern hemisphere. Here we examine the record of climatic conditions during this significant interval, using high-resolution stable isotope records from benthic and planktonic foraminifera from a sediment core in the North Atlantic (Integrated Ocean Drilling Program Expedition 306, Site U1313). We have considered the time interval from late in Marine Isotope Stage (MIS) 23 to MIS 20 (910 to 790 ka). Our data indicate that interglacial MIS 21 was a climatically unstable period and was broken into four interstadial periods, which have been identified and correlated across the North Atlantic region. These extra peaks tend to contradict previous studies that interpreted the MIS 21 variability as consisting essentially of a linear response to cyclical changes in orbital parameters. Cooling events in the surface record during MIS 21 were associated with low benthic carbon isotope excursions, suggesting a coupling between surface temperature changes and the strength of the Atlantic meridional overturning circulation. Time series analysis performed on the whole interval indicates that benthic and planktonic oxygen isotopes have significant concentrations of spectral power centered on periods of 10.7 kyr and 6 kyr, which is in agreement with the second and forth harmonic of precession. The excellent correspondence between the foraminifera d18O records and insolation variations at the Equator in March and September suggests that a mechanism related to low-latitude precession variations, advected to the high latitudes by tropical convective processes, might have generated such a response. This scenario accounts for the presence of oscillations at frequencies equal to precession harmonics at Site U1313, as well as the occurrence of higher amplitude oscillations between the MIS22/21 transition and most of MIS 21, times of enhanced insolation variability.

Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Analysis of mode competition in a monolithic master- oscillator power‐amplifier emitting at 1.5 μm

The optical and radio-frequency spectra of a monolithic master-oscillator power-amplifier emitting at 1.5 ?m have been analyzed in a wide range of steady-state injection conditions. The analysis of the spectral maps reveals that, under low injection current of the master oscillator, the device operates in two essentially different operation modes depending on the current injected into the amplifier section. The regular operation mode with predominance of the master oscillator alternates with lasing of the compound cavity modes allowed by the residual reflectance of the amplifier front facet. The quasi-periodic occurrence of these two regimes as a function of the amplifier current has been consistently interpreted in terms of a thermally tuned competition between the modes of the master oscillator and the compound cavity modes.

Emission regimes in a distributed feedback tapered master-oscillator power-amplifier at 1.5 µm

Integrated master-oscillator power amplifiers driven under steady-state injection conditions are known to show a complex dynamics resulting in a variety of emission regimes. We present experimental results on the emission characteristics of a 1.5 µm distributed feedback tapered master-oscillator power-amplifier in a wide range of steady-state injection conditions, showing different dynamic behaviors. The study combines the optical and radio-frequency spectra recorded under different levels of injected current into the master oscillator and the power amplifier sections. Under low injection current of the master oscillator the correlation between the optical and radio-frequency spectral maps allows to identify operation regimes in which the device emission arises from either the master oscillator mode or from the compound cavity modes allowed by the residual reflectance of the amplifier front facet. The quasi-periodic occurrence of these emission regimes as a function of the amplifier current is interpreted in terms of a thermally tuned competition between the modes of the master oscillator and the compound cavity modes. Under high injection current of the masteroscillator, two different regimes alternate quasi-periodically as a function of the injected current in the power amplifier: a stable regime with a single mode emission at the master oscillator frequency, and an unstable and complex self-pulsating regime showing strong peaks in the radio-frequency spectra as well as multiple frequencies in the optical spectra.

Pattern formation of parametrically driven surface waves induced by vibration

Esta tesis se centra en la generación de ondas superficiales subarmónicas en fluidos sometidos a vibración forzada en el régimen gravitatorio capilar con líquidos de baja viscosidad. Tres problemas diferentes han sido estudiados: un contenedor rectangular con vibración horizontal, la misma geometría pero con una combinación de vibración vertical y horizontal y un obstáculo completamente sumergido vibrado verticalmente en un contenedor grande. Se deriva una ecuación de amplitud desde primeros principios para describir las ondas subarmónicas con forzamiento parámetrico inducido por la vibración. La ecuación es bidimensional mientras que el problema original es tridimensional y admite un forzamiento espacial no uniforme. Usando esta ecuación los tres sistemas han sido analizados, centrándose en calcular la amplitud crítica, la orientación de los patrones y el carácter temporal de los patrones espaciotemporales, que pueden ser estrictamente subarmónicos o cuasiperiodicos con una frecuencia de modulación temporal. La dependencia con los parámetros adimensionales también se considera. La teoría será comparada con los experimentos disponibles en la literatura. Abstract This thesis focus on the generation of subharmonic surface waves on fluids subject to forced vibration in the gravity-capillary regime with liquids of small viscosity. Three different problems have been considered: a rectangular container under horizontal vibration; the same geometry but under a combination of horizontal and vertical vibration; and a fully submerged vertically vibrated obstacle in a large container. An amplitude equation is derived from first principles that fairly precisely describes the subharmonic surfaces waves parametrically driven by vibration. That equation is two dimensional while the underlying problem is three-dimensional and permits spatially nonuniform forcing. Using this equation, the three systems have been analyzed, focusing on the calculation of the threshold amplitude, the pattern orientation, and the temporal character of the spatio-temporal patterns, which can be either strictly subharmonic or quasi-periodic, showing an additional modulation frequency. Dependence on the non-dimensional parameters is also considered. The theory is compared with the experiments available in the literature.

Coherent structures in statistically-stationary homogeneous shear turbulence

La región cerca de la pared de flujos turbulentos de pared ya está bien conocido debido a su bajo número de Reynolds local y la separación escala estrecha. La región lejos de la pared (capa externa) no es tan interesante tampoco, ya que las estadísticas allí se escalan bien por las unidades exteriores. La región intermedia (capa logarítmica), sin embargo, ha estado recibiendo cada vez más atención debido a su propiedad auto-similares. Además, de acuerdo a Flores et al. (2007) y Flores & Jiménez (2010), la capa logarítmica es más o menos independiente de otras capas, lo que implica que podría ser inspeccionado mediante el aislamiento de otras dos capas, lo que reduciría significativamente los costes computacionales para la simulación de flujos turbulentos de pared. Algunos intentos se trataron después por Mizuno & Jiménez (2013), quien simulan la capa logarítmica sin la región cerca de la pared con estadísticas obtenidas de acuerdo razonablemente bien con los de las simulaciones completas. Lo que más, la capa logarítmica podría ser imitado por otra turbulencia sencillo de cizallamiento de motor. Por ejemplo, Pumir (1996) encontró que la turbulencia de cizallamiento homogéneo estadísticamente estacionario (SS-HST) también irrumpe, de una manera muy similar al proceso de auto-sostenible en flujos turbulentos de pared. Según los consideraciones arriba, esta tesis trata de desvelar en qué medida es la capa logarítmica de canales similares a la turbulencia de cizalla más sencillo, SS-HST, mediante la comparación de ambos cinemática y la dinámica de las estructuras coherentes en los dos flujos. Resultados sobre el canal se muestran mediante Lozano-Durán et al. (2012) y Lozano-Durán & Jiménez (2014b). La hoja de ruta de esta tarea se divide en tres etapas. En primer lugar, SS-HST es investigada por medio de un código nuevo de simulación numérica directa, espectral en las dos direcciones horizontales y compacto-diferencias finitas en la dirección de la cizalla. Sin utiliza remallado para imponer la condición de borde cortante periódica. La influencia de la geometría de la caja computacional se explora. Ya que el HST no tiene ninguna longitud característica externa y tiende a llenar el dominio computacional, las simulaciopnes a largo plazo del HST son ’mínimos’ en el sentido de que contiene sólo unas pocas estructuras media a gran escala. Se ha encontrado que el límite principal es el ancho de la caja de la envergadura, Lz, que establece las escalas de longitud y velocidad de la turbulencia, y que las otras dos dimensiones de la caja debe ser suficientemente grande (Lx > 2LZ, Ly > Lz) para evitar que otras direcciones estando limitado también. También se encontró que las cajas de gran longitud, Lx > 2Ly, par con el paso del tiempo la condición de borde cortante periódica, y desarrollar fuertes ráfagas linealizadas no físicos. Dentro de estos límites, el flujo muestra similitudes y diferencias interesantes con otros flujos de cizalla, y, en particular, con la capa logarítmica de flujos turbulentos de pared. Ellos son exploradas con cierto detalle. Incluyen un proceso autosostenido de rayas a gran escala y con una explosión cuasi-periódica. La escala de tiempo de ruptura es de aproximadamente universales, ~20S~l(S es la velocidad de cizallamiento media), y la disponibilidad de dos sistemas de ruptura diferentes permite el crecimiento de las ráfagas a estar relacionado con algo de confianza a la cizalladura de turbulencia inicialmente isotrópico. Se concluye que la SS-HST, llevado a cabo dentro de los parámetros de cílculo apropiados, es un sistema muy prometedor para estudiar la turbulencia de cizallamiento en general. En segundo lugar, las mismas estructuras coherentes como en los canales estudiados por Lozano-Durán et al. (2012), es decir, grupos de vórticidad (fuerte disipación) y Qs (fuerte tensión de Reynolds tangencial, -uv) tridimensionales, se estudia mediante simulación numérica directa de SS-HST con relaciones de aspecto de cuadro aceptables y número de Reynolds hasta Rex ~ 250 (basado en Taylor-microescala). Se discute la influencia de la intermitencia de umbral independiente del tiempo. Estas estructuras tienen alargamientos similares en la dirección sentido de la corriente a las familias separadas en los canales hasta que son de tamaño comparable a la caja. Sus dimensiones fractales, longitudes interior y exterior como una función del volumen concuerdan bien con sus homólogos de canales. El estudio sobre sus organizaciones espaciales encontró que Qs del mismo tipo están alineados aproximadamente en la dirección del vector de velocidad en el cuadrante al que pertenecen, mientras Qs de diferentes tipos están restringidos por el hecho de que no debe haber ningún choque de velocidad, lo que hace Q2s (eyecciones, u < 0,v > 0) y Q4s (sweeps, u > 0,v < 0) emparejado en la dirección de la envergadura. Esto se verifica mediante la inspección de estructuras de velocidad, otros cuadrantes como la uw y vw en SS-HST y las familias separadas en el canal. La alineación sentido de la corriente de Qs ligada a la pared con el mismo tipo en los canales se debe a la modulación de la pared. El campo de flujo medio condicionado a pares Q2-Q4 encontró que los grupos de vórticidad están en el medio de los dos, pero prefieren los dos cizalla capas alojamiento en la parte superior e inferior de Q2s y Q4s respectivamente, lo que hace que la vorticidad envergadura dentro de las grupos de vórticidad hace no cancele. La pared amplifica la diferencia entre los tamaños de baja- y alta-velocidad rayas asociados con parejas de Q2-Q4 se adjuntan como los pares alcanzan cerca de la pared, el cual es verificado por la correlación de la velocidad del sentido de la corriente condicionado a Q2s adjuntos y Q4s con diferentes alturas. Grupos de vórticidad en SS-HST asociados con Q2s o Q4s también están flanqueadas por un contador de rotación de los vórtices sentido de la corriente en la dirección de la envergadura como en el canal. La larga ’despertar’ cónica se origina a partir de los altos grupos de vórticidad ligada a la pared han encontrado los del Álamo et al. (2006) y Flores et al. (2007), que desaparece en SS-HST, sólo es cierto para altos grupos de vórticidad ligada a la pared asociados con Q2s pero no para aquellos asociados con Q4s, cuyo campo de flujo promedio es en realidad muy similar a la de SS-HST. En tercer lugar, las evoluciones temporales de Qs y grupos de vórticidad se estudian mediante el uso de la método inventado por Lozano-Durán & Jiménez (2014b). Las estructuras se clasifican en las ramas, que se organizan más en los gráficos. Ambas resoluciones espaciales y temporales se eligen para ser capaz de capturar el longitud y el tiempo de Kolmogorov puntual más probable en el momento más extrema. Debido al efecto caja mínima, sólo hay un gráfico principal consiste en casi todas las ramas, con su volumen y el número de estructuras instantáneo seguien la energía cinética y enstrofía intermitente. La vida de las ramas, lo que tiene más sentido para las ramas primarias, pierde su significado en el SS-HST debido a las aportaciones de ramas primarias al total de Reynolds estrés o enstrofía son casi insignificantes. Esto también es cierto en la capa exterior de los canales. En cambio, la vida de los gráficos en los canales se compara con el tiempo de ruptura en SS-HST. Grupos de vórticidad están asociados con casi el mismo cuadrante en términos de sus velocidades medias durante su tiempo de vida, especialmente para los relacionados con las eyecciones y sweeps. Al igual que en los canales, las eyecciones de SS-HST se mueven hacia arriba con una velocidad promedio vertical uT (velocidad de fricción) mientras que lo contrario es cierto para los barridos. Grupos de vórticidad, por otra parte, son casi inmóvil en la dirección vertical. En la dirección de sentido de la corriente, que están advección por la velocidad media local y por lo tanto deforman por la diferencia de velocidad media. Sweeps y eyecciones se mueven más rápido y más lento que la velocidad media, respectivamente, tanto por 1.5uT. Grupos de vórticidad se mueven con la misma velocidad que la velocidad media. Se verifica que las estructuras incoherentes cerca de la pared se debe a la pared en vez de pequeño tamaño. Los resultados sugieren fuertemente que las estructuras coherentes en canales no son especialmente asociado con la pared, o incluso con un perfil de cizalladura dado. ABSTRACT Since the wall-bounded turbulence was first recognized more than one century ago, its near wall region (buffer layer) has been studied extensively and becomes relatively well understood due to the low local Reynolds number and narrow scale separation. The region just above the buffer layer, i.e., the logarithmic layer, is receiving increasingly more attention nowadays due to its self-similar property. Flores et al. (20076) and Flores & Jim´enez (2010) show that the statistics of logarithmic layer is kind of independent of other layers, implying that it might be possible to study it separately, which would reduce significantly the computational costs for simulations of the logarithmic layer. Some attempts were tried later by Mizuno & Jimenez (2013), who simulated the logarithmic layer without the buffer layer with obtained statistics agree reasonably well with those of full simulations. Besides, the logarithmic layer might be mimicked by other simpler sheardriven turbulence. For example, Pumir (1996) found that the statistically-stationary homogeneous shear turbulence (SS-HST) also bursts, in a manner strikingly similar to the self-sustaining process in wall-bounded turbulence. Based on these considerations, this thesis tries to reveal to what extent is the logarithmic layer of channels similar to the simplest shear-driven turbulence, SS-HST, by comparing both kinematics and dynamics of coherent structures in the two flows. Results about the channel are shown by Lozano-Dur´an et al. (2012) and Lozano-Dur´an & Jim´enez (20146). The roadmap of this task is divided into three stages. First, SS-HST is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, longterm simulations of HST are ‘minimal’ in the sense of containing on average only a few large-scale structures. It is found that the main limit is the spanwise box width, Lz, which sets the length and velocity scales of the turbulence, and that the two other box dimensions should be sufficiently large (Lx > 2LZ, Ly > Lz) to prevent other directions to be constrained as well. It is also found that very long boxes, Lx > 2Ly, couple with the passing period of the shear-periodic boundary condition, and develop strong unphysical linearized bursts. Within those limits, the flow shows interesting similarities and differences with other shear flows, and in particular with the logarithmic layer of wallbounded turbulence. They are explored in some detail. They include a self-sustaining process for large-scale streaks and quasi-periodic bursting. The bursting time scale is approximately universal, ~ 20S~l (S is the mean shear rate), and the availability of two different bursting systems allows the growth of the bursts to be related with some confidence to the shearing of initially isotropic turbulence. It is concluded that SS-HST, conducted within the proper computational parameters, is a very promising system to study shear turbulence in general. Second, the same coherent structures as in channels studied by Lozano-Dur´an et al. (2012), namely three-dimensional vortex clusters (strong dissipation) and Qs (strong tangential Reynolds stress, -uv), are studied by direct numerical simulation of SS-HST with acceptable box aspect ratios and Reynolds number up to Rex ~ 250 (based on Taylor-microscale). The influence of the intermittency to time-independent threshold is discussed. These structures have similar elongations in the streamwise direction to detached families in channels until they are of comparable size to the box. Their fractal dimensions, inner and outer lengths as a function of volume agree well with their counterparts in channels. The study about their spatial organizations found that Qs of the same type are aligned roughly in the direction of the velocity vector in the quadrant they belong to, while Qs of different types are restricted by the fact that there should be no velocity clash, which makes Q2s (ejections, u < 0, v > 0) and Q4s (sweeps, u > 0, v < 0) paired in the spanwise direction. This is verified by inspecting velocity structures, other quadrants such as u-w and v-w in SS-HST and also detached families in the channel. The streamwise alignment of attached Qs with the same type in channels is due to the modulation of the wall. The average flow field conditioned to Q2-Q4 pairs found that vortex clusters are in the middle of the pair, but prefer to the two shear layers lodging at the top and bottom of Q2s and Q4s respectively, which makes the spanwise vorticity inside vortex clusters does not cancel. The wall amplifies the difference between the sizes of low- and high-speed streaks associated with attached Q2-Q4 pairs as the pairs reach closer to the wall, which is verified by the correlation of streamwise velocity conditioned to attached Q2s and Q4s with different heights. Vortex clusters in SS-HST associated with Q2s or Q4s are also flanked by a counter rotating streamwise vortices in the spanwise direction as in the channel. The long conical ‘wake’ originates from tall attached vortex clusters found by del A´ lamo et al. (2006) and Flores et al. (2007b), which disappears in SS-HST, is only true for tall attached vortices associated with Q2s but not for those associated with Q4s, whose averaged flow field is actually quite similar to that in SS-HST. Third, the temporal evolutions of Qs and vortex clusters are studied by using the method invented by Lozano-Dur´an & Jim´enez (2014b). Structures are sorted into branches, which are further organized into graphs. Both spatial and temporal resolutions are chosen to be able to capture the most probable pointwise Kolmogorov length and time at the most extreme moment. Due to the minimal box effect, there is only one main graph consist by almost all the branches, with its instantaneous volume and number of structures follow the intermittent kinetic energy and enstrophy. The lifetime of branches, which makes more sense for primary branches, loses its meaning in SS-HST because the contributions of primary branches to total Reynolds stress or enstrophy are almost negligible. This is also true in the outer layer of channels. Instead, the lifetime of graphs in channels are compared with the bursting time in SS-HST. Vortex clusters are associated with almost the same quadrant in terms of their mean velocities during their life time, especially for those related with ejections and sweeps. As in channels, ejections in SS-HST move upwards with an average vertical velocity uτ (friction velocity) while the opposite is true for sweeps. Vortex clusters, on the other hand, are almost still in the vertical direction. In the streamwise direction, they are advected by the local mean velocity and thus deformed by the mean velocity difference. Sweeps and ejections move faster and slower than the mean velocity respectively, both by 1.5uτ . Vortex clusters move with the same speed as the mean velocity. It is verified that the incoherent structures near the wall is due to the wall instead of small size. The results suggest that coherent structures in channels are not particularly associated with the wall, or even with a given shear profile.

Magnetic susceptibility (MS) measurements on the Sancerre (France) drill-core

The Toarcian Oceanic Anoxic Event (T-OAE) of the early Jurassic period involves one of the largest perturbations of the carbon cycle in the past 250 Ma, recorded by a pronounced negative carbon-isotope excursion (CIE). Numerous studies have focused on potential causes of the T-OAE and CIE, but are hampered by an uncertain timescale. Here we present high-resolution (~2 kyr) magnetic susceptibility (MS) measurements from the marine marls of the Sancerre-Couy drill-core, southern Paris Basin, spanning the entire Toarcian Stage. The MS variations document a rich series of sub-Milankovitch to Milankovitch frequencies (precession, obliquity and eccentricity) with the periodic g2-g5 (405 kyr) and quasi-periodic g4-g3 (~2.4 Myr Cenozoic mean periodicity) eccentricity terms being the most prominent. The MS-related g4-g3 variation reflects third-order eustatic sequences, and constrains the sequence stratigraphic framework of the Toarcian Stage. In addition, MS variations reveal a modulation of g2-g5 by g4-g3 eccentricity related cycles, suggesting that sea-level change was the main control on the deposition of the Toarcian Sancerre marls, in tune with the astro-climatic frequencies. The stable 405 kyr cyclicity constrains a minimum duration of the Toarcian Stage to ~8.3 Myr, and the well documented CIE, associated with the T-OAE, to ~300 to 500 kyr. The 405 kyr MS timescale calibrates the periodicity of the prominent high-frequency d13C cycles that occur in the decreasing part of the CIE to 30 to 34 kyr, consistent with the Toarcian obliquity period predicted for an Earth experiencing sustained tidal dissipation.

Accelerating precursory activity within a class of earthquake analogue automata

A statistical fractal automaton model is described which displays two modes of dynamical behaviour. The first mode, termed recurrent criticality, is characterised by quasi-periodic, characteristic events that are preceded by accelerating precursory activity. The second mode is more reminiscent of SOC automata in which large events are not preceded by an acceleration in activity. Extending upon previous studies of statistical fractal automata, a redistribution law is introduced which incorporates two model parameters: a dissipation factor and a stress transfer ratio. Results from a parameter space investigation indicate that a straight line through parameter space marks a transition from recurrent criticality to unpredictable dynamics. Recurrent criticality only occurs for models within one corner of the parameter space. The location of the transition displays a simple dependence upon the fractal correlation dimension of the cell strength distribution. Analysis of stress field evolution indicates that recurrent criticality occurs in models with significant long-range stress correlations. A constant rate of activity is associated with a decorrelated stress field.