Stokes drift in coral reefs with depth-varying permeability

In his famous paper of 1847 (Stokes GG. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8 , 441–455), Stokes introduced the drift effect of particles in a fluid that is undergoing wave motion. This effect, now known as Stokes drift, is the result of differences between the Lagrangian and Eulerian velocities of the fluid element and has been well-studied, both in the laboratory and as a mechanism of mass transport in the oceans. On a smaller scale, it is of vital importance to the hydrodynamics of coral reefs to understand drift effects arising from waves on the ocean surface, transporting nutrients and oxygen to the complex ecosystems within. A new model is proposed for a class of coral reefs in shallow seas, which have a permeable layer of depth-varying permeability. We then note that the behaviour of the waves above the reef is only affected by the permeability at the top of the porous layer, and not its properties within, which only affect flow inside the porous layer. This model is then used to describe two situations found in coral reefs; namely, algal layers overlying the reef itself and reef layers whose permeability decreases with depth. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

A free-running oscillator times and executes centriole biogenesis

The accurate timing of organelle biogenesis and the precise regulation of organelle size are crucial for cell physiology. Centriole biogenesis initiates exclusively in S-phase, when a daughter centriole emerges from the side of a pre-existing mother and grows until it reaches its mother’s size. This process is regulated by Polo-like kinase 4 (Plk4), which is recruited to centrioles in oscillatory waves in flies and human cells 1,2. The nature and function of Plk4 oscillations is, however, unknown. Here we discover that Plk4 forms an adaptive oscillator at the base of the growing centriole, whose function is to time and set the duration of centriole biogenesis in Drosophila embryos. We demonstrate that the Plk4 oscillator is free-running of, but is entrained and calibrated by, the core Cdk/Cyclin cell-cycle oscillator, explaining how centrioles can duplicate independently of the cell cycle 3–5. Mathematical modelling and further experiments indicate that the Plk4 oscillator is generated by a time-delayed negative-feedback loop in which Plk4 recruitment to, and dissociation from, the centriole is monitored via changes in the affinity-state of its centriolar receptor, Asterless. We postulate that such organelle-specific autonomous oscillators could regulate the timing and execution of organelle biogenesis more generally.

Do Brain Oscillations Orchestrate Memory?

Rhythmicity and oscillations are common features in nature, and can be seen in phenomena such as seasons, breathing, and brain activity. Despite the fact that a single neuron transmits its activity to its neighbor through a transient pulse, rhythmic activity emerges from large population-wide activity in the brain, and such rhythms are strongly coupled with the state and cognitive functions of the brain. However, it is still debated whether the oscillations of brain activity actually carry information. Here, we briefly introduce the biological findings of brain oscillations, and summarize the recent progress in understanding how oscillations mediate brain function. Finally, we examine the possible relationship between brain cognitive function and oscillation, focusing on how oscillation is related to memory, particularly with respect to state-dependent memory formation and memory retrieval under specific brain waves. We propose that oscillatory waves in the neocortex contribute to the synchronization and activation of specific memory trace ensembles in the neocortex by promoting long-range neural communication.

The Inverse KdV-Based Nonlinear Fourier Transform (KdV-NLFT): Nonlinear Superposition of Cnoidal Waves and Reconstruction of the Original Data

Since 2008, at Leichtweiß-Institute for Hydraulic Engineering and Water Resources at TU Braunschweig a KdV-based nonlinear Fourier transform is implemented and successfully applied to numerical and hydraulic model test data of solitary wave fission behind submerged reefs [1]. The KdV-NLFT is the application of the direct and inverse scattering transform for the solution of the Korteweg-deVries equation. This approach explicitly considers both solitons and oscillatory waves (cnoidal waves) as spectral basic components for the decomposition of the original data. Furthermore, the nonlinear wave-wave interactions between the nonlinear spectral basic components are explicitly considered in the analysis. The direct KdV-NLFT decomposes the original data into cnoidal waves and provides wave heights, wave numbers or frequencies, phases and the moduli which are a measure of the nonlinearity of cnoidal waves. Details of this procedure are given in Brühl & Oumeraci [2]. The interpretation of the nonlinear spectral basic components is described in Brühl & Oumeraci [3]. The inverse KdV-NLFT which is addressed here calculates the nonlinear wave-wave interactions between cnoidal waves and provides the original data by superposition of cnoidal waves and their nonlinear interactions. The practical application of the KdV-NLFT for the analysis of long-wave propagation in shallow water is presented in Brühl & Oumeraci [4].

Oscillatory Flow in a Porous Channel with Porous Medium and Small Suction

ABSTRACTThis paper deals with an analytical solution of an oscillatory flow in a channel filled with a porous medium saturated with a viscous fluid. The consideration of porosity in the channel is the basic idea of the paper. The oscillatory waves in the channel with porous medium are produced due to self-excited pressure disturbances caused by inevitable fluctuation in a suction rate at the porous walls. The ensuing steady axial velocity and the time dependent oscillatory axial velocity are found analytically using perturbation method and WKB approximation. The important physical quantities like the velocity profile, amplitude of the oscillation and penetration depth of the oscillatory velocity have been given special emphasis in this analysis. The effects of porosity of the medium on these quantities are calculated analytically and examined graphically. We find that the amplitude of oscillatory velocity and the penetration depth of the oscillatory axial velocity decrease with increasing values of inverse Darcy parameter. The oscillations in the fluid can be minimized by decreasing the permeability of the medium.