Читать книгу Life in the Open Ocean - Joseph J. Torres - Страница 17

Osborne Reynolds observed that a dye stream introduced into a liquid flowing through a pipe would yield a nice linear (laminar) flow or a turbulent disturbed one depending upon three characteristics of the liquid and one of the pipe. The velocity of the flow, the density of the liquid, the viscosity of the liquid, and the diameter of the pipe determined whether the flow was laminar or turbulent. Manipulating any one of the four variables was equally effective in changing the characteristics of the flow. The relationship between those variables is described in the equation for Reynolds number:

(1.3)

where U is the velocity of the flow, l is the diameter of the pipe, and ρ and μ are by now familiar as density and viscosity, respectively. You will also note that the ratio of density and viscosity gives us the inverse of the kinematic viscosity, which can then be put in the denominator:

(1.4)

A Reynolds number of 2000 marks the transition between laminar and turbulent flow. The diameter of the pipe (l) for a swimming organism becomes instead the greatest length of the organism in the direction of flow.

The Reynolds number is a dimensionless number, i.e. it has no units, and it is a very useful tool for describing the characteristics of flow around a submerged body. It is the ratio of the inertial (velocity × characteristic length × density) to the viscous (dynamic viscosity) forces mentioned earlier. In fact, the Reynolds number can be derived by dividing the formula for momentum ( ρSU ²) (inertial force) by that for viscous force (Eq. 1.1).

(1.5)

The derivation is done in slightly different ways in Vogel (1981) and in Denny (1993). I have followed Vogel’s derivation here. Both books are highly recommended for a more thorough treatment of the forces summarized here.

The useful property of Reynolds number is that you can get a good idea of the physical characteristics of a flow regime with a single number. Low Re (less than 1), such as that experienced by a protist or the moving limb of a swimming crustacean, is dominated by viscous forces. Flow will be laminar. A small swimming crustacean may have Re in the neighborhood of 100–2000 where inertial forces predominate (Torres 1984) but flow is largely laminar. In contrast, a tuna swimming at 10 m s⁻¹ with an Re of 30 000 000 (Vogel 1981) is in a highly turbulent flow regime. Most of the species of interest in this book live with Reynolds numbers in the 100s–1000s when moving and feeding.

To get an intuitive sense for the world in which pelagic species live, we need to know what forces they must generate or overcome in order to move and to breathe. Our next topic deals with two of the most important forces acting on any swimming animal: friction drag and pressure drag.