Fig 1.
Wind field is calculated using FDM on a finite 2D grid, where wind enters in the x-direction and interacts with penguins. Penguin behavior is simulated using SPH method. Flow responds to penguin movement within the grid.
Fig 2.
(a) Smooth kernel value depends on distance from individual, and (b) only particles (open circles) within smooth length of the particle (red circle) contribute because W falls off rapidly for r ≥ h and the interactions are zero for r > 2h.
Fig 3.
Comparison of metabolic heat loss formulations.
Blue line uses (22) with A proportional to number of penguins in proximity. Red line (our model) updates Tw dynamically and A is constant. Metabolic Heat Loss is the percentage relative to the heat lost for a single individual.
Fig 4.
Relationship between exposed (wind chill) temperature (Twc) and penguin acceleration (b).
Individual penguins will move towards the huddle (+b) if Twc < LCT or away from the huddle (-b) if Twc > UCT.
Fig 5.
Flowchart for the coupled fluid-behavior model.
Wind field is computed using the FDM method (red shading) then provides wind velocity and ambient temperature data to the behavior model. Penguin behavior is then calculated using the SPH method (blue shading) and provides new positions and ambient temperatures around individual penguins back to the wind model. Unshaded portion indicates where model is coupled. Numbers in brackets correspond to the steps outline in the text.
Fig 6.
Penguin huddle formation over 2-hour simulation.
(A-1) pengion positions, (A-2) wind velocity field [m s-1], and (A-3) wind chill temperature [°C] at time to (A), (B-F) same as in (A) but for 30 min, 60 min, 75 min, 90 min and 120 min since the start of the simulation.
Table 1.
Summary of descriptive statistics.
Mean exposted temperature, range, percent of penguins in the thermo-neutral zone, and huddle density for each fo the time periods presented in Fig 6.
Fig 7.
Distribution of penguin exposed temperature at end of simulation (2 hours).
Fig 8.
Huddle density and dimensions.
Black circle shows the estimated huddle size used for density computations. Symbols indicate whether an individual was on the windward (red square), leeward (yellow diamond), side (purple triangle), or interior (blue circle) of the huddle. Symbols are same for Figs 8 and 9.
Fig 9.
Relationship between individual metabolic heat loss and its distance to huddle center.
Metabolic heat loss for penguins on windward, leeward, side, or interior of the huddle. Dashed vertical lines indicate the huddle edge.
Fig 10.
Relationship between individual penguin exposed temperature and distance to huddle center.
Exposed temperature for penguins on windward, leeward, side, or interior of the huddle. Dashed vertical lines indicate the huddle edge.
Fig 11.
Relationship between percent of huddle radius in three sizes of huddles.
(a) Penguin exposed temperature, and (b) local penguin density within the huddle for 100, 200, or 800 penguins normalized by the huddle diameter.