Dynamics of bubbles under stochastic pressure forcing.

Several studies have investigated the dynamics of a single spherical bubble at rest under a nonstationary pressure forcing. However, attention has almost always been focused on periodic pressure oscillations, neglecting the case of stochastic forcing. This fact is quite surprising, as random pressure fluctuations are widespread in many applications involving bubbles (e.g., hydrodynamic cavitation in turbulent flows or bubble dynamics in acoustic cavitation), and noise, in general, is known to induce a variety of counterintuitive phenomena in nonlinear dynamical systems such as bubble oscillators. To shed light on this unexplored topic, here we study bubble dynamics as described by the Keller-Miksis equation, under a pressure forcing described by a Gaussian colored noise modeled as an Ornstein-Uhlenbeck process. Results indicate that, depending on noise intensity, bubbles display two peculiar behaviors: when intensity is low, the fluctuating pressure forcing mainly excites the free oscillations of the bubble, and the bubble's radius undergoes small amplitude oscillations with a rather regular periodicity. Differently, high noise intensity induces chaotic bubble dynamics, whereby nonlinear effects are exacerbated and the bubble behaves as an amplifier of the external random forcing.

Impact of seasonal forcing on reactive ecological systems.

Our focus is on the short-term dynamics of reactive ecological systems which are stable in the long term. In these systems, perturbations can exhibit significant transient amplifications before asymptotically decaying. This peculiar behavior has attracted increasing attention. However, reactive systems have so far been investigated assuming that external environmental characteristics remain constant, although environmental conditions (e.g., temperature, moisture, water availability, etc.) can undergo substantial changes due to seasonal cycles. In order to fill this gap, we propose applying the adjoint non-modal analysis to study the impact of seasonal variations of environmental conditions on reactive systems. This tool allows the transient dynamics of a perturbation affecting non-autonomous ecological systems to be described. To show the potential of this approach, a seasonally forced prey-predator model with a Holling II type functional response is studied as an exemplifying case. We demonstrate that seasonalities can greatly affect the transient dynamics of the system.

River bedform inception by flow unsteadiness: A modal and nonmodal analysis.

River bedforms arise as a result of morphological instabilities of the stream-sediment interface. Dunes and antidunes constitute the most typical patterns, and their occurrence and dynamics are relevant for a number of engineering and environmental applications. Although flow variability is a typical feature of all rivers, the bedform-triggering morphological instabilities have generally been studied under the assumption of a constant flow rate. In order to partially address this shortcoming, we here discuss the influence of (periodic) flow unsteadiness on bedform inception. To this end, our recent one-dimensional validated model coupling Dressler's equations with a refined mechanistic sediment transport formulation is adopted, and both the asymptotic and transient dynamics are investigated by modal and nonmodal analyses.