Probabilistic analytical modelling of predator–prey interactions in fishes

Predation is a fundamental interaction between species, yet it is largely unclear what tactics are successful for the survival or capture of prey. One challenge in this area comes with how to test theoretical ideas about strategy with experimental measurements of features such as speed, flush distance and escape angles. Tactics may be articulated with an analytical model that predicts the motion of predator or prey as they interact. However, it may be difficult to recognize how the predictions of such models relate to behavioural measurements that are inherently variable. Here, we present an alternative approach for modelling predator–prey interactions that uses deterministic dynamics, yet incorporates experimental kinematic measurements of natural variation to predict the outcome of biological events. This technique, called probabilistic analytical modelling (PAM), is illustrated by the interactions between predator and prey fish in two case studies that draw on recent experiments. In the first case, we use PAM to model the tactics of predatory bluefish ( Pomatomus saltatrix ) as they prey upon smaller fish ( Fundulus heteroclitus ). We find that bluefish perform deviated pure pursuit with a variable pursuit angle that is suboptimal for the time to capture. In the second case, we model the escape tactics of zebrafish larvae ( Danio rerio ) when approached by adult predators of the same species. Our model successfully predicts the measured patterns of survivorship using measured probability density functions as parameters. As these results demonstrate, PAM is a data-driven modelling approach that can be predictive, offers analytical transparency, and does not require numerical simulations of system dynamics. Though predator–prey interactions demonstrate the use of this technique, PAM is not limited to studying biological systems and has broad utility that may be applied towards understanding a wide variety of natural and engineered dynamical systems where data-driven modelling is beneficial.

Dynamics of large-scale circulation of turbulent thermal convection in a horizontal cylinder

A systematic study of the effects of cell geometry on the dynamics of large-scale flows in turbulent thermal convection is carried out in horizontal cylindrical cells of different lengths filled with water. Four different flow modes are identified with increasing aspect ratio $\Gamma $. For small aspect ratios ($\Gamma \leq 0.16$), the flow is highly confined in a thin disc-like cell with a quasi-two-dimensional (quasi-2D) large-scale circulation (LSC) in the circular plane of the cell. For larger aspect ratios ($\Gamma >0.16$), we observe periodic switching of the angular orientation $\theta $ of the rotation plane of LSC between the two longest diagonals of the cell. The sides of the container along which the LSC oscillates changes at a critical aspect ratio $\Gamma _{c}\simeq 0.82$. The measured switching period is equal to the LSC turnover time for $\Gamma \leq \Gamma _c$, shows a sharp increase at $\Gamma _{c}$ and decays exponentially to the LSC turnover time with increasing $\Gamma $. For $\Gamma \geq 1.3$, a periodic rocking of LSC along the long axis of the cylinder is also observed. The measured probability density function $P(\theta )$ of the LSC orientation $\theta $ peaks at the two diagonal positions, and its shape is described by a phenomenological model proposed by Brown & Ahlers (Phys. Fluids, vol. 20, 2008b, 075101; J. Fluid Mech., vol. 638, 2009, pp. 383–400). Using this model, we describe the dynamics of the LSC orientation $\theta $ by stochastic motion in a double-well potential. The potential is predicted from a model in which the sidewall shape produces an orientation-dependent pressure on the LSC. This model also captures key features of the four flow modes. The experiment reveals an interesting array of rich dynamics of LSC in the horizontal cylinders, which are very different from those observed in the upright cylindrical convection cells. The success of the model for both upright and horizontal cylinders suggests that it can be applied to different geometries.

Prediction of Cross-Shore Beach Profile Evolution in the Vicinity of Seawalls

Although there exist advanced models which predict to beach profile for natural beaches, the behavior of the beaches in front of seawalls still suffers from the lack of appropriate theoretical models and sufficient measured data. Following the results obtained from the measurements, a beach profile evolution model is developed, using the measured probability distribution of the near-bed horizontal velocities as input, to predict the short-term bed level changes in the vicinity of e partially reflective seawall. The present model introduces a new approach in which based on integrating the probability density functions of the near-bed horizontal velocities, the sediment displacements and consequently bed level changes are calculated in front of a partially reflective structure. The results obtained from the model and comparison with the experiments are promising and encouraging for further developments of the proposed model.

Biodiesel as an Alternative Fuel in Siemens Dry Low Emissions Combustors: Atmospheric and High Pressure Rig Testing

Atmospheric and high pressure rig tests were conducted to investigate the feasibility of using biodiesel as an alternative fuel to power industrial gas turbines in one of the world’s leading dry low emissions (DLE) combustion systems, the SGT-100. At the same conditions, tests were also carried out for mineral diesel to provide reference information to evaluate biodiesel as an alternative fuel. In atmospheric pressure rig tests, the likelihood of the machine lighting was identified based on the measured probability of the ignition of a single combustor. Lean ignition and extinction limits at various air temperatures were also investigated with different air assist pressures. The ignition test results reveal that reliable ignition can be achieved with biodiesel across a range of air mass flow rates and air fuel ratios (AFRs). In high pressure rig tests, emissions and combustion dynamics were measured for various combustor air inlet pressures, temperatures, combustor wall pressure drops, and flame temperatures. These high pressure rig results show that biodiesel produced less NOx than mineral diesel. The test results indicate that the Siemens DLE combustion system can be adapted to use biodiesel as an alternative fuel without major modification.

Biodiesel as an Alternative Fuel in Siemens DLE Combustors: Atmospheric and High Pressure Rig Testing

Atmospheric and high pressure rig tests were conducted to investigate the feasibility of using biodiesel as an alternative fuel to power industrial gas turbines in one of the world’s leading Dry Low Emissions (DLE) combustion systems, the SGT-100. At the same conditions, tests were also carried out for mineral diesel to provide reference information to evaluate biodiesel as an alternative fuel. In the atmospheric pressure rig tests, the likelihood of the machine lighting was identified based on the measured probability of the ignition of a single combustor. Lean ignition and extinction limits at various air temperatures were also investigated with different air assist pressures. The ignition test results reveal that reliable ignition can be achieved with biodiesel across a range of air mass flow rates and air fuel ratios. In the high pressure rig tests, emissions and combustion dynamics were measured for various combustor air inlet pressures, temperatures, combustor wall pressure drops and flame temperatures. These high pressure rig results show that biodiesel produced less NOx than mineral diesel. The test results indicate that the Siemens DLE combustion system can be adapted to use biodiesel as an alternative fuel without major modification.

CLABAUTAIR: a new algorithm for retrieving three-dimensional cloud structure from airborne microphysical measurements

A new algorithm is presented to reproduce the three-dimensional structure of clouds from airborne measurements of microphysical parameters. Data from individual flight legs are scanned for characteristic patterns, and the autocorrelation functions for several directions are used to extrapolate the observations along the flight path to a full three-dimensional distribution of the cloud field. Thereby, the mean measured profiles of microphysical parameters are imposed to the cloud field by mapping the measured probability density functions onto the model layers. The algorithm was tested by simulating flight legs through synthetic clouds (by means of Large Eddy Simulations (LES)) and applied to a stratocumulus cloud case measured during the first field experiment of the EC project INSPECTRO (INfluence of clouds on the SPECtral actinic flux in the lower TROposphere) in East Anglia, UK. The number and position of the flight tracks determine the quality of the retrieved cloud field. If they provide a representative sample of the entire field, the derived pattern closely resembles the statistical properties of the real cloud field.

CLABAUTAIR: a new algorithm for retrieving three-dimensional cloud structure from airborne microphysical measurements

A new algorithm is presented to retrieve the three-dimensional structure of clouds from airborne measurements of microphysical parameters. Data from individual flight legs are scanned for characteristic patterns, and the autocorrelation functions for several directions are used to extrapolate the observations along the flight path to a full three-dimensional distribution of the cloud field. Thereby, the mean measured profiles of microphysical parameters are imposed to the cloud field by mapping the measured probability density functions onto the model layers. The algorithm was tested by simulating flight legs through synthetic clouds (by means of Large Eddy Simulations (LES)) and applied to a stratocumulus cloud case measured during the first field experiment of the EC project INSPECTRO (INfluence of clouds on the SPECtral actinic flux in the lower TROposphere) in East Anglia, UK. The number and position of the flight tracks determine the quality of the retrieved cloud field. If they provide a representative sample of the entire field, the derived pattern closely resembles the statistical properties of the real cloud field.

Measurements and numerical simulations of snow-particle saltation

First, wind-tunnel experiments were carried out to measure the trajectories of saltating snow particles with varying friction velocity. Trajectories of saltating particles were recorded by a video system with a laser sheet and trajectory statistics, such as ejection and impact velocities and angles, were obtained for each particle. Parabolic trajectories are considerably elongated with an increase in the friction velocity; impact angle was approximately the same but ejection angle decreased with increasing friction velocity. Furthermore, it should be noted that the gradient of flux decay with height decreased with friction velocity. In the experiments, a snow-particle counter, which can sense not only the number of particles but also their diameters, was introduced. The flux distribution and the transport rate obtained as a function of the particle size gave a new insight into the relationship with the friction velocity.Trajectories of saltating grains were computed, using the measurements of the initial ejection velocities, angles and the mean velocity profile of the air. The results agreed reasonably with our measurements. Using the measured probability distribution of the ejection velocities, an ensemble of trajectories was computed and thence the vertical profiles of stream-wise fluxes. The exponential decay of the flux on height was obtained in all cases and it supports the basic validity of the model, although agreement is less than expected.