On the stationarity of linearly forced turbulence in finite domains

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the `linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.Comment: 15 pages, 7 figures, changes in the discussion at the end of section VI, formula (60) correcte

The Static Failure of Adhesively Bonded Metal Laminate Structures: A Cohesive Zone Approach

Data on distribution, ecology, biomass, recruitment, growth, mortality and productivity of the West African bloody cockle Anadara senilis were collected at the Banc d'Aguuin, Mauritania, in early 1985 and 1986. Ash-free dry weight appeared to be correlated best with shell height. A. senilis was abundant on the tidal flats of landlocked coastal bays, but nearly absent on the tidal flats bordering the open sea. The average biomass for the entire area of tidal flats was estimated at 5.5 g·m−2 ash-free dry weight. The A. senilis population appeared to consist mainly of 10 to 20-year-old individuals, showing a very slow growth and a production: biomass ratio of about 0.02 y−1. Recruitment appeared negligible and mortality was estimated to be about 10% per year. Oystercatchers (Haematopus ostralegus), the gastropod Cymbium cymbium and unknown fish species were responsible for a large share of this. The distinction of annual growth marks permitted the assessment of year-class strength, which appeared to be correlated with the average discharge of the river Senegal. This may be explained by assuming that year-class strength and river discharge both are correlated with rainfall at the Banc d'Arguin.