Standing Waves, Holes, and Hydraulic Jumps

Standing Wave (Hydraulic Jump) during a Flood, El Paso, Texas

Standing Wave (Hydraulic Jump) during a Flood, El Paso, Texas

Surface waters store energy through elevation and velocity. Potential energy from elevation is proportional to the height whereas kinetic energy increases as the velocity of the water squared squared (velocity times velocity). Pressure energy is proportinal to the depth below the water surface. As water moves down a stream, the total energy level always drops, but the proportion composed of elevation, velocity, and pressure energy continuously changes in a facinating array of patterns. As the water churns through a rocky area, turbulence leads to a constant stirring. Water moves from the surface to the bottom of the stream while the energy converts from elevation to pressure. The water in pools has most of the energy in elevation and pressure; in rapids the energy is predominantly in the velocity. Watch carefully when rapidly flowing water enters a pool, or where a rock or log slows the flow. As the water slows, energy must be conserved. Some of the velocity energy is converted to elevational energy causing the water level to actually rise – the water actually flows uphill. This phenomenon is called a hydraulic jump. Standing waves and holes are types of hydraulic jumps.

Hydraulic Jump at Redstone Park, Gila Wilderness, New Mexico

A more techincal explaination for this is as follows. For short stretches of a river it is reasonable to assume, approximately, that the energy level of the river is constant. In fact, some energy is always converted into heat, but for short stretches of the stream the amount is small in relation to the total energy. The total energy being the addition of the potential energy (varies with depth) and kinetic energy (depends on velocity squared). Solving the equations for the possible water velocities at the same energy level gives two possible solutions: a) deep water with slow flow, or b) shallow water with very rapid flow. These two states are called subcritical and supercritical (shooting) flow. An interesting phenomenon occurs in the transition from supercritical to subcritical flow. This occurs, for example, when very rapid water flow is slowed by reaching a pool, or being backed up by a large rock or boulder. Since only two velocities are possible, the water “jumps” from the rapid and shallow supercritical state to slow flowing deep subcritical stage. This is called a hydraulic jump and is visible as a standing wave in the river or steam. Hydraulic jumps can occur an any scale from the smallest brook to large rivers passing through rapids. Try turning on the water in a large (preferably flatt bottomed) sink while leaving the drain open. Adjust the tap until you see a circular ring form in the bottom. Initially the water just below the spigot is supercritical. As it flows outward in a primarily circular direction the velocity gradually slows leading to a “jump” from supercritical to subcritical flow. The hydraulic jump is visible as a circular ridge visible on the bottom of the sink.

The very same physics are present in river rapids. A “hole” is formed in river rapids when the water first accelerates while dropping in elevation (transition from subcritical to supercritical flow) when flowing over a rock, followed by a deacceleration caused by moving into a deeper, slower moving section of the river. The scary downstream edge of the “hole” is a hydraulic jump.

The schizophrenic nature of water flow, and much of the fun of river running, comes from the physics of energy – the hydraulic jump. In a hydraulic jump a large portion of the energy the water has picked up in the steep portion of the river is lost as turbulence. Hydraulic jumps are present in streams at all scales from rivulets to large rivers. The main requirement is sufficient elevation drop to accelerate the water to the supercritical/ shooting flow state followed by something that slows the water back down (backwater, pool, rock, log). Depending upon the geometry of the river the hydraulic jumps form standing waves and/or holes.

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