Hydrodynamics: Fluid Motion

Water is nearly 800 times denser than air. For swimming creatures, this fact wields a double-edged sword. On the plus side, water is more buoyant than air, requiring much less energy to prevent falling through it (what we terrestrial types call 'sinking'). Buoyancy also frees aquatic organisms from the need to support the body against collapsing under the force of gravity, which explains why the largest marine animals dwarf the largest found on land. On the minus side, water's density requires much more effort to move it out of the way. Water is also about 55 times more viscous (resistant to flow) than air. As a result, water does not move easily around a moving body.

Drag is an unavoidable consequence of living in a material world, and may be defined as resistance to moving through a fluid. A layer of fluid - called the boundary layer - 'sticks' to and is carried along with the surface of a moving body creating drag. Drag increases with speed, fluid density, and object size. In aquatic animals, boundary layer drag is ultimately due to the stickiness of water: not only does a swimming organism have to carry a mass of water along with it, but - more significantly - this mass of water adheres to the inert surrounding water, further increasing drag.

The key to understanding drag is the distinction between turbulent versus laminar flow. Turbulence is a form of fluid flow in which the molecules of the fluid move over a surface in irregular paths, resulting in the exchange of momentum from one portion of the fluid to another. Laminar means 'in layers', referring to fluid flow in which the molecules of a fluid move over a surface in discrete layers without fluctuations, so that successive particles passing the same point have the same velocity. In energy terms, a smooth laminar flow is more efficient than - and thus preferable to - a turbulent flow.

The simplest way to achieve minimum drag is through streamlining. A streamlined shape is longest in the direction of travel and tapered on both ends. But optimizing laminar flow is not as simple as one might imagine. Theoretically, the optimal shape has its maximum diameter at the anterior third of the object, with ratio of length to width of 4.5. Among fishes, many of the tunas come closest to this hydrodynamic ideal. Such specifications work fine for rigid-hulled craft such as submarines, but for flexible-bodied swimming creatures the situation is rather more complex. For a flexible form, the optimal hydrodynamic shape also features reversal of planes, in which the plane of the flattened forward portion is at right angles to the plane of the flattened rearward portion.

The essence of lift is suction. Bernoulli's Principle states that a foil with a curved upper surface moving through a fluid medium causes the fluid to move faster over the upper surface than the lower; this greater speed creates a negative pressure ('suction') above the foil. The plane of a foil relative to the long axis of the body to which it is attached is called the angle of attack. The greater the angle of attack, the more both lift and drag (which operate at right angles to one another) increase. Stalling occurs when laminar flow separates from the surface of a foil. The speed at which this occurs is called the stalling speed and varies with the size and shape of foil.

Planing surfaces allow control of yaw, pitch, and roll, but also increase drag. Turbulent flow at the distal tips of wings or fins - called wing- or fin-tip vortices - increases drag with increasing speed. Larger foils can carry greater weights, but also experience greater drag. A foil's ratio of length to width is termed its aspect ratio; a foil with a high aspect ratio affords a lot of lift relative to drag - which allows a shallower gliding angle and a higher stalling speed than low aspect ratio foils. In the case of an oscillating foil, in the form of a caudal fin or pair of flukes, a high aspect ratio tail provides maximum thrust with minimum drag.

Thrust results when a propeller or tail pushes fluid backward; the fluid pushes the body forward with the same force. In practice, velocity is dependent upon forward thrust minus rearward drag. The more drag can be reduced, the faster and more efficiently a body can move through a fluid. The course of a body through a fluid can be adjusted by changing either body shape or lift and drag characteristics of foils. Changing body shape by bending to the left or right will change course in the respective direction. Changing lift and drag characteristics of foils is rather more complex. Basically, for bodies with moveable foils, dipping the foil(s) on a given side increases drag locally, causing the body to pivot around the foil offering greater resistance to movement. By adjusting the lift and drag characteristics of foils, a moving body can achieve fine control over its course through a fluid.

 

ReefQuest Centre for Shark Research
Text and illustrations R. Aidan Martin
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