of depth (Denny 1993).
Salinity alters the density of water considerably more than does temperature or pressure. The difference in density between freshwater and seawater is substantial. Salinity itself is the amount of dissolved material expressed in g per kg of seawater. The material consists mainly of salts; the principal salt is sodium chloride. The nicely intuitive definition of salinity as g per kg, or parts per thousand, has been replaced in some circles by the introduction of practical salinity. Practical salinity (Sp; UNESCO 1983) is the ratio of the electrical conductivity of a seawater sample and to a standard solution of potassium chloride. Since it is a ratio, practical salinity has no units. It is very close to actual salinity, though. To get back to actual salinity in g per kg from practical salinity, you use the following equation: S = 1.00510 Sp (Bearman 1989).
The fact that water is far denser than air has its good points and bad points from the perspective of a swimming animal. On the plus side, it means that much less structural investment is required to support the weight of an organism in water than on land. A popular analogy compares a tree and a kelp of equal height above the substrate. Clearly, the kelp has far less energy invested in its 0.05 m diameter stipe than the tree has in its 0.5 m trunk. The principle works equally well for a jellyfish elegantly trailing its tentacles in the ocean or piled up in a soggy mass on the beach.
The aquatic medium provides buoyant support according to the difference in density between the body and the medium in which it is immersed. The weight of an object in water is described by the equation
where ρ (rho) is the density of the object, ρ w is the density of water, g is the acceleration of gravity (9.8 m s−2), and V is the volume of the object in question. The expression ( ρ − ρ w) is the effective density or ρ e of our submerged body and determines whether it will float, remain suspended, or sink. Its effective weight in water is thus g· ρ e V, and it follows logically that a body will weigh more in air than in water, usually by 5‐ to 50‐fold (Denny 1993). Do not be guilty of synonymizing weight and mass. Mass is a scalar quantity measured in kilograms; weight is a force that is measured in newtons. You will notice that the mass of an object in water does not change, but its weight does.
Seawater at a salinity of 35‰ has a density of 1024 kg m−3, meaning that marine species enjoy more buoyant support from their medium than do their freshwater counterparts. Knowing what we know about relative weights in air and water, neutral buoyancy for marine species will be achieved with a density equal to that of seawater. Let us compare the density of some common biological materials. Mollusk shells at 2700 kg m−3 are quite dense, providing protection and support for the soft tissues beneath but also assuring that they are most useful in bottom‐dwelling species. Cow bones are also quite dense, 2060 kg m−3, providing the skeletal support needed by a heavy animal in air. Neither structure is appropriate for a species concerned with remaining suspended in mid‐water, so the likelihood of cows invading the marine environment remains low. In contrast, muscle is 1050–1080 kg m−3, only about 5% higher than the density of seawater. Fats are slightly less dense than seawater, 915–945 kg m−3 so they provide a source of static lift for marine species. It is instructive to note that small changes in an animal’s density can confer big advantages to its weight in water but would do little to affect its weight in air. The energetic advantages of neutral buoyancy have done much to influence how pelagic species are put together. In succeeding chapters, we shall explore buoyancies and mechanisms for achieving neutral buoyancy in open‐ocean taxa.
Viscosity
The first characteristic of fluids that must be appreciated for an understanding of viscosity is the “no‐slip condition” with respect to solids. That is, at the interface between a solid and a fluid flowing over it, the velocity of the fluid is zero. A zero‐velocity boundary layer is created, whose thickness depends on the velocity of the fluid flow. At the solid–fluid boundary, fluids stick to solids absolutely. Any object in a flow thus creates a shear, as the fluid particles at the no‐slip boundary must be moving at a different velocity than those at a distance from the body in the flow.
Figure 1.2 Dynamic viscosity ( μ ). A fluid’s “stickiness” or resistance to shear. Expressed mathematically as μ = Fl/US.
The resistance to shear is the dynamic viscosity of the fluid, and it is best described using the classical “flat plate” analogy. Imagine two plates of negligible thickness oriented parallel to one another and with a fluid between them (Figure 1.2). The bottom plate is stationary, and the movable plate is pushed forward with a force that results in a constant velocity. Since the fluid at the boundary of each plate has zero velocity due to the no‐slip rule, the fluid between them is deformed or sheared, and a uniform velocity gradient develops between them in response to the constant pushing. The force needed to maintain the constant velocity depends upon the velocity itself, upon the area of the plate because the amount of fluid that needs to be moved is a function of the size of plate, and upon the viscosity of the fluid, or how easily the fluid is deformed. The resulting equation is:
where U is velocity, S is the area of the plate, μ is viscosity, and l is the distance between the plates. Think of the flat plates as the bottom and top card in a deck of playing cards. The fluid is all the cards between them, and the stickiness between the cards determines how easy it is to deform the deck. Viscosity is that stickiness. The viscosity (dynamic viscosity) is an important property of fluids because it determines how easy it is to move them and to move through them.
A second type of viscosity is quite important in understanding flow around and through objects: the kinematic viscosity or υ. It is the ratio of dynamic viscosity ( μ ) to density ( ρ ):
(1.2)
Kinematic viscosity is considerably less easy to grasp on an intuitive level, but it relates two important properties of a fluid that will be significant to us in examining the locomotion of open‐ocean fauna. Viscosity and density have much to do with patterns of flow around an organism. On the one hand, viscosity measures how adjacent particles retard a fellow fluid particle’s movement when it encounters a body in a flow. On the other, density is a measure of how likely it is that a fluid particle will keep moving. The ratio of the two forces, inertial and viscous, is the subject of our next topic, the Reynolds number.
Reynolds Number
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