Hydrodynamic refers to the behavior of liquids in motion and the forces that arise when solid objects move through them. The term comes from Greek roots meaning “water” and “power,” and the science behind it governs everything from how fast a dolphin can swim to how blood flows through your arteries. While the basic idea sounds simple enough, the real-world consequences of hydrodynamic forces are surprisingly broad, shaping modern ship design, renewable energy technology, competitive swimming, and even how your cardiologist thinks about plaque buildup.
The Three Forces Working Against You in Water
When any object moves through water, it encounters resistance. That resistance, called drag, comes in three distinct forms, and understanding them is the starting point for nearly everything in applied hydrodynamics. The first is skin drag, sometimes called friction drag, which results from water molecules clinging to and sliding along the object’s surface. The second is form drag, also called pressure drag, which depends on the object’s shape and how cleanly water can flow around it without separating into turbulent eddies. The third is wave drag, which only matters near the water’s surface and comes from the energy spent creating waves in the object’s wake.
These three types of drag interact in ways that are not always intuitive. For a human swimmer, wave drag turns out to be a much bigger deal than researchers originally thought. Experiments using a towed mannequin showed that total drag at the water’s surface can be up to 2.4 times the drag when the same body is fully submerged, and passive wave drag alone accounts for roughly half to 60 percent of total resistance at typical swimming speeds.1PubMed. Wave drag on human swimmers That finding matters for competitive swimmers: simply gliding deeper underwater after a turn, where wave drag drops to zero, can save a meaningful amount of energy. The interplay among skin drag, form drag, and wave drag also explains why body posture and alignment matter so much in the water. A review of hydrodynamic glide efficiency in swimming found that surface characteristics affect skin drag, depth affects wave drag, and body size, shape, and alignment all influence form drag.2PubMed. Hydrodynamic glide efficiency in swimming
How Dolphins Solved a Problem That Stumped Engineers for Nearly a Century
In 1936, a British zoologist named Sir James Gray calculated how much power a dolphin would need to swim at the speeds people had observed in the wild. His math said it was impossible. A dolphin’s muscles simply could not produce enough force to overcome the drag that a rigid, dolphin-shaped body would experience at those speeds. The puzzle became known as Gray’s paradox, and it nagged at biologists and engineers for 88 years.
The core of the problem was that early models treated the dolphin’s body like a stiff torpedo, calculating drag the same way you would for a submarine hull. But dolphins are not stiff. Their bodies flex, their skin is compliant, and their swimming style concentrates thrust production at the tail flukes while the streamlined body mostly just needs to slip through the water with minimal disturbance. In thunniform swimming, the style used by dolphins and tuna, the body creates drag while the oscillating tail flukes generate thrust, and these two regions are largely separate.3Scientific Reports. Gray’s paradox: A fluid mechanical perspective
The paradox was finally resolved in 2024 with direct measurements of free-ranging dusky dolphins filmed by an uncrewed aerial vehicle. Researchers found that the drag coefficient of a swimming dolphin decreases exponentially as speed increases, cutting drag by up to 89 percent at speeds above two meters per second. On top of that, dolphins that porpoised (leaped out of the water periodically) at high speeds gained an additional 17 percent drag reduction. At the fastest recorded speed of about 6.9 meters per second, total drag was only 32 newtons with a power output nearly identical to what other mammals of similar size can sustain aerobically. The reduced drag coefficient at higher speeds indicated that the boundary layer around the dolphin’s body stayed less turbulent than expected, which is the key to the whole trick.4PubMed Central. Drag reduction and locomotory power in dolphins: Gray’s paradox revealed
Fish Tails and the Vortex Trick
Fish generate thrust in a fundamentally different way than a propeller does. Rather than spinning, a fish tail sweeps side to side, and the fluid dynamics of that sweep create something called a leading-edge vortex, a swirling pocket of low pressure that clings to the front edge of the tail fin as it moves. This vortex is not waste energy; it is the engine of thrust production, pulling the fin forward in much the same way that a vortex on the leading edge of an insect wing generates lift.
Research using physical tail models in flow tanks revealed that at the natural swimming rhythm most fish prefer, a leading-edge vortex forms, stays attached, and spirals from the tail root to the tip before connecting with a tip vortex and shedding downstream as a coherent loop. When the tail beats too quickly, the vortex detaches and the pattern breaks down.5PubMed Central. The fish tail motion forms an attached leading edge vortex Numerical simulations of carangiform swimmers (the broad category including mackerel and trout) have further mapped how factors like swimming speed, tail-beat frequency, and body flexibility interact to either sustain or disrupt this vortex, with peak thrust production tied directly to the timing and strength of the leading-edge vortex on the caudal fin.6PubMed Central. Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics
Tail shape matters too. Simulations of fish-like swimmers with different trailing-edge profiles found that expanding the trailing edge delays the shedding of the leading-edge vortex, which might sound helpful but actually increases the lateral force on the fin. That lateral force is essentially wasted energy pushing the fish sideways rather than forward.7Ocean Engineering. Effect of trailing-edge shape on the swimming performance of a fish-like swimmer under self-propulsion Evolution, it seems, has already optimized tail geometry to balance vortex retention with minimal side-to-side waste.
Penguins, Shark Skin, and Borrowed Ideas
Dolphins and fish are not the only marine animals with hydrodynamic tricks worth studying. Humboldt penguins appear to use induced turbulence in their boundary layer to reduce drag by an average of about 31 percent across a range of swimming speeds. Tests on a model penguin showed that turbulence near the body surface reduced boundary layer height and delayed flow separation, meaning water stayed attached to the body’s contour rather than peeling away and creating a turbulent wake.8Journal of Bionic Engineering. Drag reduction in a swimming Humboldt penguin, Spheniscus humboldti, when the boundary layer is turbulent This is counterintuitive: turbulence sounds like it should make things worse, but a thin turbulent boundary layer hugging the body is much less draggy than a thick separated wake behind it.
Shark skin has inspired an entire subfield of engineering. The tiny tooth-like structures covering a shark’s body, called denticles, function as riblets, and two fluid mechanisms explain how they reduce drag. First, the riblet spacing lifts streamwise vortices generated in turbulent flow away from the surface, reducing the area exposed to high shear stress. Second, the riblets restrict crossflow velocity fluctuations, limiting momentum transfer between vortices. The ideal riblet spacing balances these two effects at roughly one-third to one-half the diameter of the streamwise vortices.9Integrative and Comparative Biology. Experimental Studies of Bioinspired Shark Denticles for Drag Reduction Riblet-inspired textures have been tested on aircraft, ship hulls, and swimsuits, and while the drag reductions are modest (typically single-digit percentages), those small gains compound over long distances and high fuel costs.
Even fish mucus has taught engineers something useful. Experiments in the 1970s demonstrated that the slime coating fish produce reduces skin friction by lowering the effective viscosity of the water right at the body’s surface and thickening the laminar sublayer, the thin sheet of smooth flow closest to the skin.10Journal of Fluid Mechanics. Anomalous drag-reducing phenomenon at a water/fish-mucus or polymer interface This principle has been applied commercially using polymer additives in pipelines: injecting small amounts of long-chain polymers into crude oil pipelines can cut pumping energy considerably by mimicking that mucus effect.
Superhydrophobic Surfaces and Trapped Air
Nature offers another approach to drag reduction that engineers are actively copying: water-repellent surfaces. The lotus leaf, famous for its ability to shed water droplets, inspired research into superhydrophobic coatings. These surfaces combine microscale roughness with chemical water-repelling treatments to trap a thin layer of air between the solid surface and the flowing water. Because air has far lower viscosity than water, this trapped layer essentially lets the water slide over a cushion of gas rather than grinding directly against the hull or pipe wall.11Annual Review of Fluid Mechanics. Slip on Superhydrophobic Surfaces
The thickness of that air layer turns out to be the critical variable. Numerical simulations of channel flow over superhydrophobic surfaces showed that thicker air layers produce greater velocities at the surface interface and larger reductions in frictional drag. As the air layer grows, it more effectively cushions the moving water from the solid surface beneath, amplifying the drag-reduction effect in turbulent flow.12PubMed Central. Numerical investigation of the effect of air layer on drag reduction in channel flow over a superhydrophobic surface The engineering challenge is keeping that air layer intact under real-world conditions. Hydrostatic pressure at depth, biofouling from marine organisms, and the sheer force of high-speed flow can all collapse the air pockets. Researchers are working on more durable surface textures and re-entrant geometries that hold air more tenaciously, but making superhydrophobic coatings last on a working ship hull remains an open problem.
Ships, Hydrofoils, and Moving Cargo Efficiently
Naval architecture has been shaped by hydrodynamic principles for centuries, even before the underlying physics was formally described. One of the most visible examples is the bulbous bow, the round protrusion that juts forward below the waterline of most large commercial ships. Bulbous bows work by generating their own wave system that partially cancels the bow wave the hull creates, reducing wave-making resistance. The shape, size, and position of the bulb have to be matched to the ship’s speed and hull form, making bulbous bow design a topic of ongoing hydrodynamic optimization.13Journal of Physics: Conference Series. Bulbous Bow Shapes Effect on Ship Characteristics: A Review
Hydrofoils take a completely different approach. Instead of trying to push a hull through the water more efficiently, a hydrofoil lifts the hull out of the water entirely. Submerged wing-shaped foils generate hydrodynamic lift as the craft accelerates, raising the hull above the surface and eliminating most of the wave drag and form drag. Research on hydrofoil-assisted craft has shown that positioning the front hydrofoil optimally can significantly reduce total resistance and improve performance, because the lift force raises the center of gravity out of the water, leaving only the thin foil struts piercing the surface.14Ocean Engineering. Investigation of front hydrofoil position influence on the hydrofoil-assisted craft This is the same principle behind America’s Cup sailing yachts that appear to fly above the waves and behind high-speed passenger ferries in places like Hong Kong and the Greek islands.
Biomimetic propulsion is also being explored for unmanned underwater vehicles. Rather than traditional propellers, some experimental designs use oscillating fins modeled after fish tails. Testing of such a system found that peak net thrust occurred at specific oscillation frequencies and deflection angles, but with an inherent trade-off: pushing harder for more thrust decreases energy efficiency, mirroring what happens when a fish sprints to escape a predator versus cruising at a sustainable pace.15Scientific Reports. Biomimetic propulsion system efficiency for unmanned underwater vehicle
Harvesting Energy from Moving Water
The same hydrodynamic principles that make swimming and shipping efficient can be reversed to pull energy out of flowing water. Tidal stream turbines, wave energy converters, and river-current devices all rely on the interaction between a moving fluid and an engineered surface to generate electricity.
One of the more creative approaches involves oscillating hydrofoils rather than spinning rotors. Instead of a windmill-style turbine, these devices use wings that pitch and heave in the current, extracting energy from the oscillating lift forces. A prototype tested in a water flume achieved about 40 percent hydrodynamic efficiency, which is comparable to the best performances achievable with conventional rotor-blade turbines.16Renewable Energy. Prototype testing of a hydrokinetic turbine based on oscillating hydrofoils The advantage of oscillating hydrofoils is that they work well in shallow water where rotary turbines cannot fit, and they are less hazardous to marine life because nothing spins at high speed.
Placing tidal energy converters in the real world brings additional hydrodynamic complications. Simulations of a proposed tidal array in Sanda Sound, Scotland, found that array location matters enormously: shifting the array by less than a kilometer could roughly double the power output. But doubling the installed capacity of the array also doubled the average velocity deficit in surrounding waters and quadrupled water-level differences during peak spring tides.17Applied Energy. Hydrodynamic changes imposed by tidal energy converters on extracting energy on a real case scenario Extracting energy from a tidal channel necessarily slows the current and alters local water circulation, which can affect sediment transport, nutrient mixing, and marine habitats downstream. Responsible deployment requires careful hydrodynamic modeling not just of the device itself but of the entire local environment.
Blood Flow and Arterial Hydrodynamics
Hydrodynamics is not just an outdoor or industrial concern. Inside your body, the same principles govern how blood moves through arteries, and the consequences are directly medical. Atherosclerosis, the buildup of fatty plaque that leads to heart attacks and strokes, does not develop randomly throughout the circulatory system. It clusters at specific locations, particularly at the branching points where arteries split into two.
The reason is wall shear stress, the frictional force that flowing blood exerts on the inner lining of an artery. In straight sections of artery where flow is smooth and fast, shear stress is relatively high and uniform, which appears to be protective. But at bifurcations, the flow slows, separates, and sometimes reverses direction, creating zones of low and oscillating shear stress. These zones are where plaque preferentially accumulates. In coronary artery bifurcations, low and oscillating wall shear stress is not only linked to the initial development of atherosclerosis but may also promote re-narrowing and blood clot formation after stent implantation.18PubMed Central. Local fluid dynamics in patients with bifurcated coronary lesions undergoing percutaneous coronary interventions
Detailed simulations of the carotid artery, the major vessel supplying blood to the brain, have revealed that the actual geometry of a patient’s artery matters far more than simplified models suggest. When researchers built a simulation from a real patient’s anatomy rather than an idealized textbook shape, the flow patterns looked quite different. A strong helical flow dominated the carotid sinus (the widened section where the artery branches), driven by the natural asymmetry and curvature of the vessel. Accounting for the flexibility of the artery wall reduced the magnitude of shear stress and expanded the regions of slow or reversed flow, though the overall patterns stayed similar.19PubMed. Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation This kind of patient-specific hydrodynamic modeling is increasingly being used to plan interventions: by simulating how a stent will change the local flow dynamics before implanting it, cardiologists can choose a design and position that minimizes problematic shear patterns.
Walking on Water at the Smallest Scale
At the opposite end of the size spectrum from ships and dolphins, hydrodynamic forces explain one of nature’s most charming tricks: the water strider standing and skating on the surface of a pond. At this scale, gravity matters far less than surface tension, the cohesive force among water molecules that creates a thin elastic film at the surface. A water strider’s legs are coated with microscopic hydrophobic hairs that press into this film without breaking through, distributing the insect’s weight across enough surface area to stay dry.
But a water strider does not just float. It rows, and the propulsion mechanism is genuinely hydrodynamic. As the legs sweep backward, they create hemispherical vortices beneath the surface that push the insect forward. Kinematic analysis of these vortices showed that their translational speed is roughly determined by leg speed, and peak leg speed during a rowing stroke is about 2.5 times the mean leg speed, producing a brief burst of momentum that launches the insect across the surface.20Procedia Engineering. Modeling of the Propulsion Hydrodynamics for the Water Strider Locomotion on Water Surface Researchers studying water striders have drawn on their findings to design tiny robots that can walk on water, potential tools for environmental monitoring of ponds and wetlands. The challenge at this scale is not reducing drag but managing surface tension: break the surface film and your robot sinks.
The Equation Nobody Has Fully Solved
Behind virtually all of these applications sits one mathematical framework: the Navier-Stokes equation, first introduced by French engineer Claude-Louis Navier in 1822. The equation describes how the velocity of a fluid changes in response to pressure, viscosity, and external forces. It is the governing law for nearly every hydrodynamic phenomenon discussed above, from dolphin swimming to arterial blood flow to tidal turbine siting.
The catch is that nobody has proved whether the Navier-Stokes equation always produces smooth, well-behaved solutions, or whether it can sometimes blow up into infinities. This is not an obscure technicality. It is one of the seven Millennium Prize Problems in mathematics, with a million-dollar bounty for a proof in either direction. In practice, engineers and physicists work around the gap by solving the equation numerically, breaking a fluid domain into millions of tiny cells and computing the forces in each one. This is called computational fluid dynamics, and it is how the fish-tail vortex simulations, arterial flow models, and superhydrophobic surface studies described above all produce their results. The answers are extremely good approximations, but they remain approximations. Every hydrodynamic simulation is, at some level, a very sophisticated guess constrained by an equation whose full mathematical behavior remains an open question two centuries after it was written down.