Penguin huddling: a continuum model #

Sam Harris, Robb McDonald

15:50 Monday in 3Q16.

Part of the Mathematical ecology session.

Abstract #

Penguins huddling in a cold wind are represented by a two-dimensional, continuum model. The huddle boundary evolves due to three effects: heat loss to the huddle exterior; the reorganisation of penguins to regulate heat production within the huddle; the conservation of huddle size. The huddle propagates slowly compared to the advective timescale of the wind, thus exterior temperature is governed by the steady advection-diffusion equation and interior temperature by a Poisson equation. The wind velocity is the gradient of a harmonic, scalar field and the conformal invariance of the exterior governing equations motivates the use of a conformal mapping approach in the numerical method. The Poisson equation is not conformally invariant, however, so the interior temperature gradient is found numerically using the AAA-least squares algorithm. The results show that, irrespective of the starting shape, penguin huddles evolve into an egg-like steady shape dependent on the wind strength, parameterised by the Péclet number Pe, and a parameter β which effectively measures the strength of the interior self-generation of heat by the penguins. The numerical method developed is applicable to a further five free boundary problems.