VISCOSITY IN SEAKEEPING

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

Ideal free flows of optimal foragers: Vertical migrations in the ocean

We consider the collective motion of animals in time-varying environments, using as a case diel vertical migration in the ocean. The animals are distributed in space such that each animal moves optimally, seeking regions which offer high growth rates and low mortalities, subject to costs on excessive movements as well as being in regions with high densities of conspecifics. The model applies to repeated scenarios such as diel or seasonal patterns, where the animals are aware of both current and future environmental conditions. We show that this problem can be viewed as a differential game of mean field type, and that the evolutionary stable solution, i.e. the Nash equilibrium, is characterized by partial differential equations, which govern the distributions and migration velocities of animals. These equations have similarities to equations that appear in the fluid dynamics, specifically the Euler equations for compressible inviscid fluids. If the environment is constant, the ideal free distribution emerges as an equilibrium. We illustrate the theory with a numerical example of vertical animal movements in the ocean, where animals are attracted to nutrient-rich surface waters while repulsed from light during daytime due to the presence of visual predators, aiming to reduce both proximity to conspecifics and swimming efforts. For this case, we show that optimal movements are diel vertical migrations in qualitative agreement with observations.

Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution

In 1895, Korteweg and de Vries (Philos Mag 20:20, 1895) studied an equation describing the motion of waves using the assumptions of long wavelength and small amplitude. Two implicit assumptions which they also made were irrotational and inviscid fluids. Comparing experiment and observation seems to suggest that these two assumptions are well justified. This paper removes the assumption of irrotationality in the case of electrohydrodynamics with an assumption of globally constant vorticity in the fluid. A study of the effect of vorticity on wave profiles and amplitudes is made revealing some unusual features. The velocity potential is an important variable in irrotational flow; the vertical component of velocity takes place of this variable in our analysis. This allows the bypassing of the Burns condition and also demonstrates that waves exist even for negative values of the vorticity. The linear and weakly nonlinear models are derived.

Anisotropic regularity of linearized compressible vortex sheets

We consider supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients, Morando et al. recently derived a pseudo-differential equation that describes the time evolution of the discontinuity front of the vortex sheet. In agreement with the classical stability analysis, the problem is weakly stable if [Formula: see text], and the well-posedness holds in standard weighted Sobolev spaces. Our aim in this paper is to improve this result, by showing the existence in functional spaces with additional weighted anisotropic regularity in the frequency space.