Stabilisation and drag reduction of pipe flows by flattening the base profile

Recent experimental observations (Kuehnen et al., 2018) have shown that flattening a turbulent streamwise velocity profile in pipe flow destabilises the turbulence so that the flow relaminarises. We show that a similar phenomenon exists for laminar pipe flow profiles in the sense that the nonlinear stability of the laminar state is enhanced as the profile becomes more flattened. Significant drag reduction is also observed for the turbulent flow when triggered by sufficiently large disturbances. The flattening is produced by an artificial body force designed to mimick a baffle used in the experiments of Kuehnen et al. (2018) and the nonlinear stability measured by the size of the energy of the initial perturbations needed to trigger transition. In order to make the latter computation more efficient, we examine how indicative the minimal seed for transition is in measuring transition thresholds. We first show that the minimal seed is relatively robust to base profile changes and spectral filtering. We then compare the (unforced) transition behaviour of the minimal seed with several forms of randomised initial conditions in the range of Reynolds numbers Re=2400 to 10000 and find that the energy of the minimal seed after the Orr and oblique phases of its evolution is close to that of a localised random disturbance. In this sense, the minimal seed at the end of the oblique phase can be regarded as a good proxy for typical disturbances (here taken to be the localised random ones) and is thus used as initial condition in the simulations with the body force. The enhanced nonlinear stability and drag reduction predicted in the present study are an encouraging first step in modelling the experiments of Kuehnen et al. and should motivate future developments to fully exploit the benefits of this promising direction for flow control

Designing a minimal baffle to destabilise turbulence in pipe flows

Motivated by the results of recent experiments (K\"uhnen et al., Flow Turb. Combust., vol. 100, 2018, pp. 919-943), we consider the problem of designing a baffle (an obstacle to the flow) to relaminarise turbulence in pipe flows. Modelling the baffle as a spatial distribution of linear drag $\mathbf{f}(\mathbf{x},t)=-\chi(\mathbf{x})\mathbf{u}_{tot}(\mathbf{x},t)$ within the flow ($\mathbf{u}_{tot}$ is the total velocity field and $\chi \ge 0$ a scalar field), two different optimisation problems are considered to design $\chi$ at a Reynolds number $Re=3000$. In the first, the smallest baffle defined in terms of a $L_1$ norm of $\chi$ is sought which minimises the viscous dissipation rate of the flow. In the second, a baffle which minimises the total energy consumption of the flow is treated. Both problems indicate that the baffle should be axisymmetric and radially localised near the pipe wall, but struggle to predict the optimal streamwise extent. A manual search finds an optimal baffle one radius long which is then used to study how the amplitude for relaminarisation varies with $Re$ up to $15\,000$. Large stress reduction is found at the pipe wall, but at the expense of an increased pressure drop across the baffle. Estimates are then made of the break even point downstream of the baffle where the stress reduction at the wall due to the relaminarised flow compensates for the extra drag produced by the baffle.EPSR

The rise of fully turbulent flow

Over a century of research into the origin of turbulence in wallbounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date. Combining experiments, theory and computer simulations here we uncover the bifurcation scenario organising the route to fully turbulent pipe flow and explain the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.Comment: 31 pages, 9 figure

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

Opposite polarities of ENSO drive distinct patterns of coral bleaching potentials in the southeast Indian Ocean.

Episodic anomalously warm sea surface temperature (SST) extremes, or marine heatwaves (MHWs), amplify ocean warming effects and may lead to severe impacts on marine ecosystems. MHW-induced coral bleaching events have been observed frequently in recent decades in the southeast Indian Ocean (SEIO), a region traditionally regarded to have resilience to global warming. In this study, we assess the contribution of El Niño-Southern Oscillation (ENSO) to MHWs across the mostly understudied reefs in the SEIO. We find that in extended summer months, the MHWs at tropical and subtropical reefs (divided at ~20°S) are driven by opposite ENSO polarities: MHWs are more likely to occur at the tropical reefs during eastern Pacific El Niño, driven by enhanced solar radiation and weaker Australian Monsoon, some likely alleviated by positive Indian Ocean Dipole events, and at the subtropical reefs during central Pacific La Niña, mainly caused by increased horizontal heat transport, and in some cases reinforced by local air-sea interactions. Madden-Julian Oscillations (MJO) also modulate the MHW occurrences. Projected future increases in ENSO and MJO intensity with greenhouse warming will enhance thermal stress across the SEIO. Implementing forecasting systems of MHWs can be used to anticipate future coral bleaching patterns and prepare management responses

Additive Pressures of Elevated Sea Surface Temperatures and Herbicides on Symbiont-Bearing Foraminifera

Elevated ocean temperatures and agrochemical pollution individually threaten inshore coral reefs, but these pressures are likely to occur simultaneously. Experiments were conducted to evaluate the combined effects of elevated temperature and the photosystem II (PSII) inhibiting herbicide diuron on several types of symbiotic algae (diatom, dinoflagellate or rhodophyte) of benthic foraminifera in hospite. Diuron was shown to evoke a direct effect on photosynthetic efficiency (reduced effective PSII quantum yield ΔF/F′m), while elevated temperatures (>30°C, only 2°C above current average summer temperatures) were observed to impact photosynthesis more indirectly by causing reductions in maximum PSII quantum yield (Fv/Fm), interpreted as photodamage. Additionally, elevated temperatures were shown to cause bleaching through loss of chlorophyll a in foraminifera hosting either diatoms or dinoflagellates. A significant linear correlation was found between reduced Fv/Fm and loss of chlorophyll a. In most cases, symbionts within foraminifera proved more sensitive to thermal stress in the presence of diuron (≥1 µg L−1). The mixture toxicity model of Independent Action (IA) described the combined effects of temperature and diuron on the photosystem of species hosting diatoms or dinoflagellates convincingly and in agreement with probabilistic statistics, so a response additive joint action can be assumed. We thus demonstrate that improving water quality can improve resilience of symbiotic phototrophs to projected increases in ocean temperatures. As IA described the observed combined effects from elevated temperature and diuron stress it may therefore be employed for prediction of untested mixtures and for assessing the efficacy of management measures

An extreme climatic event alters marine ecosystem structure in a global biodiversity hotspot

Extreme climatic events, such as heat waves, are predicted to increase in frequency and magnitude as a consequence of global warming but their ecological effects are poorly understood, particularly in marine ecosystems1, 2, 3. In early 2011, the marine ecosystems along the west coast of Australia—a global hotspot of biodiversity and endemism4, 5—experienced the highest-magnitude warming event on record. Sea temperatures soared to unprecedented levels and warming anomalies of 2–4?°C persisted for more than ten weeks along >2,000?km of coastline. We show that biodiversity patterns of temperate seaweeds, sessile invertebrates and demersal fish were significantly different after the warming event, which led to a reduction in the abundance of habitat-forming seaweeds and a subsequent shift in community structure towards a depauperate state and a tropicalization of fish communities. We conclude that extreme climatic events are key drivers of biodiversity patterns and that the frequency and intensity of such episodes have major implications for predictive models of species distribution and ecosystem structure, which are largely based on gradual warming trends