Two Hydraulic Conditions

[msquared48]

The first condition:

I was driving down the street during a rainstorm the other day and noted, in the wheelway of the road, that the water was running in waves down the road, the space between the waves dependent on the slope. The greater the slope, the shorter the distance vbetween the waves. This phenomenon appears to be the opposite of a hydraulic jump. Anyone know what it is called, and if there are any equations that relate the spacing of the waves?

The second condition:

We all know the effect of the Coriolis force on water going down a bathtub drain. Well, I have noted that the rotation slows, stops and reverses direction in the last half-inch or so of depth. In the diffeq's for this occurrence, anyone know the part of the equation that would demonstrate this occurrence. Also, at what depth should this phenomenon occur?

Neither circumstance pertains to any project other than idle curiosity.

Mike McCann
MMC Engineering

 

[cvg]

well, you have given very little information to go on - you should have gotten measurements of the longitudinal and cross slopes, depth of the gutter and estimated flow rate and rainfall intensity along with some idea of the n value and amount of sediment. But two theories for the waves come to mind. 1) standing wave - which is found in supercritical flow and 2) sediment transported by the flow forms dunes which travel down the gutter. flow over the dunes would appear as waves. I have also noticed that heavy rain generally falls in "sheets". This might tend to create the appearance of waves as it collects and runs off the pavement.

 

[msquared48]

cvg:

No, these were not waves caused by debris. These waves were moving down the slope of the road channel at a spacing specific to the slope of the road and the shape of the channel - essentially moving standing waves. They were also not impacted by wind driven rain in sheets as that was not occuring. The rain was steady with little wind. I see this all the time.

Mike McCann
MMC Engineering

 

[MiketheEngineer]

My guess is that the road "friction" at the higher velocities (higher slopes) is causing the wave patterns. Just a guess.

NEVER have noted the Coriolis effect you mentioned. Maybe I just haven't stuck my head far enough down the drain. Stuck my head in worse places.... I do know if you go to Australia - it goes the other way!??

 

[cvg]

while I doubt it could be standing waves which occur in highly supercritical flow, it does resemble the phenomena. I believe I have also seen it. With very shallow sheet flow, surface tension can play a larger role than with normal depths which are mostly affected by gravity. It may be that flow is transitioning between shallow depth surface tension controlled flow and deeper flow controlled by gravity. Shallow flow builds, moving slowly until sufficient water gathers / mounds such that it overcomes surface tension and begins to flow faster. However, with increasing velocity, the flow depth decreases until such point as surface tension again takes over. Thus causing a rippling effect.

 

[Ron]

Mike...the first condition is probably related to corrugation of the asphalt in the wheel path. Velocity is too slow and change not abrupt enough to create a hydraulic jump, but this is a precursor.

 

[msquared48]

Ron - Corrugation in the AC paving? I know what you mean, but no, as the "waves" if you will are moving downhill and there are no corrugations, which would be fixed on the road surface anyway.

I realize that in Florida with all that sunshine and very little topography, you probably have never seen this. You really need to expand your horizons and get out a little man!

Looked at your bathtub draining lately?

Mike McCann
MMC Engineering

 

[bimr]

Regarding "We all know the effect of the Coriolis force on water going down a bathtub drain."

No we don't. It's a myth. You must have missed that lecture in phyics class.

The formation of a vortex over the drain is explained by the conservation of angular momentum. As the radius of rotation decreases as water approaches the drain, the rate of rotation increases, for the same reason that an ice skater's rate of spin increases as the skater arms are pulled in. Any rotation around the plug hole that is initially present accelerates as water moves inward.

The Coriolis effect is significantly smaller than various other influences on drain direction, such as any residual rotation of the water and the geometry of the container.

The idea that toilets and bathtubs drain differently in the Northern and Southern Hemispheres is a myth.

http://www.snopes.com/science/coriolis.asp

Regarding "Well, I have noted that the rotation slows, stops and reverses direction in the last half-inch or so of depth."

When the water level becomes sufficiently low, the entire column of the water quickly converges.

http://geosci.uchicago.edu/~nnn/LAB/DEMOS/sink.html

 

[Ron]

Mike...we don't take baths here either!

 

[beej67]

I agree with Bimr regarding Coriolis.

I've noticed the same wave action thing in parking lots. Here's a guess, which may or may not be right -

What you've got on your road, is a boundary layer. Here's the math:

http://en.wikipedia.org/wiki/Boundary_layer

http://en.wikipedia.org/wiki/Blasius_boundary_layer

There's a viscous portion and an inviscid portion in the boundary layer, with the viscous portion being near the pavement. Viscous forces become less important the further you get away from the road, and the velocity profile flattens out to reach a sort of peak. I would bet that the depth in the trough of your waves is the viscous portion, and the waves themselves are up in the inviscid portion, sort of boiling along on top of the layer where viscous forces dominate.

I would further guess, that when the road gets steeper, the velocity profile increases, which shrinks the viscous portion and puts more of the flow up in the inviscid portion, so you'd need more 'waves' to carry the flow in. Next time you see it, stick a rule down in the flow and measure the depths of the troughs between waves. I bet they're thinner on the steeper section of road.

All speculation of course. I'd love to here if someone has a firmer answer.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[bimr]

Ripples appear on water when the wind blows, but will die quickly if the wind stops. The force that allows the ripples to propagate is surface tension.

Note that water does not travel along with the waves, only along with the current, the two being mutually exclusive.

The depth of the water is dependent on the slope. As the slope increases, the depth of flow decreases (Mannings equation).

Shallower water decreases the wavespeed, so the wavelength becomes shorter and the peak heights increase.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/watwav2.html#c1