Life in the Open Ocean. Joseph J. Torres

Life in the Open Ocean - Joseph J. Torres


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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.

      (1.5)

      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.

      Drag

      Recalling the no‐slip rule for a solid body in a flow, it follows logically that a swimming individual will be creating a shear as it moves its “no‐slip” form through the water. The shear will be resisted by the viscosity of the fluid just as in our example with the flat plate, and the magnitude of that resistance will depend on how much surface is exposed to the flow. The resistance is called the friction drag, or skin friction drag, and since friction is something we have all experienced, it is a pretty easy one to comprehend. Friction drag, being in the province of viscosity, is most important at low Reynolds numbers.

      (1.6)

      which you may recognize as the “fluid equivalent” of the expression for momentum. In fact, drag is the removal of momentum from a flowing fluid.

      All swimming species experience drag as they swim. At low Reynolds numbers, usually in smaller species swimming at slower speeds, friction drag is the more important force. At higher Re, pressure drag is more important. Because drag is difficult to measure and more difficult to predict from theory, total drag is most often used to describe the drag force, without discriminating between friction and pressure drag.

      Total drag depends on three elements. The first is the dynamic pressure, as expressed earlier, which itself is a function of the velocity of the fluid and its density. The second is the size of the object in the flow since pressure is a force per unit area. The third is the shape of the object in the flow.

Schematic illustration of flow-induced differential pressure.

      The way drag force behaves with different shapes in a flow regime cannot be predicted from first principles except for the simplest shapes, such as a sphere. Instead, drag force must be measured empirically to create a fudge factor known as the drag coefficient or Cd. The drag coefficient in turn depends on the character of the flow regime itself, which is represented by the Reynolds number. So drag is represented by the equations

      (1.7)equation

      and

      (1.8)equation

      The difficulty of predicting how drag behaves for different shapes in a flow is a real problem for those interested in estimating the cost of overcoming drag to swimming species. You cannot just look up a Cd for your target species unless you happen to be very lucky. Usually you have to use the next best thing, which is a value determined for the closest shape you can find (see e.g. Batchelor 1967).

      Temperature in the ocean varies predictably in both the horizontal (latitude and longitude) and vertical (depth) planes. However, to understand why temperature varies with depth and latitude in the way that it does, we need to know a little about ocean circulation. In turn, to understand ocean circulation, we need to have a clear mental picture of the geography of the ocean basins.


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