ALBERT

Description: We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an areawise significance test for continuous wavelet spectra to overcome the difficulties of multiple testing; it uses basic properties of continuous wavelet transform to decide whether a pointwise significant result is a real feature of the process or indistinguishable from typical stochastic fluctuations. This test is compared to the conventional one in terms of sensitivity and specificity. A software package for continuous wavelet spectral analysis and synthesis is presented.

Description: The first detailed quantitative observations of the two-dimensional collapse of a granular column along a horizontal channel are presented for a variety of materials. Together with the complementary study for the axisymmetric situation, we conclude that for granular collapses the generally accepted approaches, that are highly dependent on frictional parameters, do not describe the main flow phenomena. The motion divides in two main flow regimes at a∼1.8, where the aspect ratio a=hi∕di and hi and di are the initial height and width of the column. We describe the details of collapse by emphasizing the sequential occurrence of a main spreading followed by a final avalanching phase. For the low a regime, a〈1.8, we derive descriptions of the final geometry by direct physical arguments. For the large a regime, a〉1.8, we determine that nearly all details of the collapse, including the position of the flow front as a function of time, the emplacement time, the self-similar final profiles, and especially their maximum vertical and horizontal extension, are established during the spreading phase and can be expressed in terms of the initial geometrical parameters but are independent of basal and internal friction parameters.

Description: Results of an experimental study of a Hopf bifurcation with broken translation symmetry that organizes chaotic homoclinic dynamics from a T2 torus in a fluid flow as a direct consequence of physical boundaries are presented. It is shown that the central features of the theory of Hopf bifurcation in O(2)-symmetric systems where the translation symmetry is broken are robust and are appropriate to describe the appearance of modulated waves, homoclinic bifurcation, Takens-Bogdanov point, and chaotic dynamics in a fluid flow experiment.

Description: Experimental evidence for standing waves resulting from a supercritical Hopf bifurcation that appears as the first pattern-forming instability in counterrotating Taylor-Couette flow is presented. Depending on the aspect ratio two different types of standing waves, denoted as SW0 and SWp, could be observed. Both modes have an azimuthal wave number m51 but differ in symmetry. While for SWp , a spatiotemporal glide-reflection symmetry could be found, SW0 is purely spatial reflection symmetric. The transition between the two modes is found to be organized in a cusp bifurcation unfolded by variations of the aspect ratio. The ‘‘classical’’ spiral vortex flow appears in this control parameter regime only as a result of a secondary steady bifurcation from SW0. This transition is found to be either subcritical or supercritical. The experimentally observed bifurcation structure has been predicted by theory of Hopf bifurcation to spiral vortex flow in finite counterrotating Taylor-Couette systems.

Description: Earth's climate can be understood as a dynamical system that changes due to external forcing and internal couplings. Essential climate variables, such as surface air temperature, describe this dynamics. Our current interglacial, the Holocene (11 700 yr ago to today), has been characterized by small variations in global mean temperature prior to anthropogenic warming. However, the mechanisms and spatiotemporal patterns of fluctuations around this mean, called temperature variability, are poorly understood despite their socioeconomic relevance for climate change mitigation and adaptation. Here we examine discrepancies between temperature variability from model simulations and paleoclimate reconstructions by categorizing the scaling behavior of local and global surface air temperature on the timescale of years to centuries. To this end, we contrast power spectral densities (PSD) and their power-law scaling using simulated and observation-based temperature series of the last 6000 yr. We further introduce the spectral gain to disentangle the externally forced and internally generated variability as a function of timescale. It is based on our estimate of the joint PSD of radiative forcing, which exhibits a scale break around the period of 7 yr. We find that local temperature series from paleoclimate reconstructions show a different scaling behavior than simulated ones, with a tendency towards stronger persistence (i.e., correlation between successive values within a time series) on periods of 10 to 200 yr. Conversely, the PSD and spectral gain of global mean temperature are consistent across data sets. Our results point to the limitation of climate models to fully represent local temperature statistics over decades to centuries. By highlighting the key characteristics of temperature variability, we pave a way to better constrain possible changes in temperature variability with global warming and assess future climate risks.

Description: Despite the well-known limitations of linear stability theory in describing nonlinear and turbulent flows, it has been found to accurately capture the transitions between certain nonlinear flow behavior. Specifically, the transition in heat flux scaling in rotating convective flows can be well predicted by applying a linear stability analysis to simple profiles of a convective boundary layer. This fact motivates the present study of the linear mechanisms involved in the stability properties of simple convective setups subject to rotation. We look at an idealized two-layer setup and gradually add complexity by including rotation, a bounded domain, and viscosity. The two-layer setup has the advantage of allowing for the use of wave interaction theory, traditionally applied to understand stratified and homogeneous shear flow instabilities, in order to quantify the various physical mechanisms leading to the growth of convective instabilities. We quantitatively show that the physical mechanisms involved in the stabilization of convection by rotation take two different forms acting within the stratified interfacial region, and in the homogeneous mixed layers. The latter of these we associate with the tendency of a rotating flow to develop Taylor columns (TCs). This TC mechanism can lead to both a stabilization or destabilization of the instability and varies depending on the parameters of the problem. A simple criterion is found for classifying the influence of these physical mechanisms.