Tag: strouhal number

The Eerie Singing of the Golden Gate Bridge
Recent changes to the Golden Gate Bridge’s guardrails have created a new soundscape in the Bay Area. Under high winds, the bridge gives off an eerie, otherworldly wail that can be heard even miles away. The new guardrails are substantially thinner than the previous ones, which reduces the wind load the bridge has to endure. But that thinner profile is also what causes the noise, through a well-known phenomena known as vortex shedding.
Animation of vortex shedding behind a cylinder. (Image credit: Wikimedia)
As air moves past a non-streamlined body, like a cylinder, it forms counter-rotating vortices that peel off the body at a set frequency. Fluid dynamicists use a non-dimensional number, the Strouhal number, to characterize this vortex shedding. For a simple shape like a cylinder, the Strouhal number is relatively constant, so I decided to do a quick and dirty calculation to examine the wind velocities responsible for the sound. (See also my analysis of Star Trek Voyager’s opening sequence.)
I began by collecting several videos with samples of the bridge’s singing (1, 2, 3). Then I used Adobe Audition to analyze the frequency content of the bridge noise. Below is a sample snapshot from a video taken on the bridge’s bike path, right next to the guardrail. The analysis shows three broad, but distinct peaks: a primary peak at 430 Hz, a small harmonic of that frequency at 860 Hz, and a separate, secondary peak centered at 1070 Hz. The broadness of the peaks, along with the competition between the primary and secondary peaks, is probably responsible for the disconcerting, discordant nature of the sound.
Frequency analysis of the Golden Gate Bridge’s “singing”, taken from a section of this video. (Image credit: N. Sharp)
Of the other videos I analyzed, a second video from near the bridge also showed the 430 Hz peak, while a video from further away had a dominant frequency of 517 Hz. There’s a lot of uncertainty introduced in not knowing exactly when each video was filmed, but given the agreement between videos 2 and 3, I suspect that video 1’s higher frequency may be caused by interference and modulation as the sound travels.
With the major frequency in hand, I estimated the size of the new guardrail wires as 10mm in diameter. After some tweaking to adjust the Reynolds number and Strouhal numbers, that gave me an estimated wind speed of 21 meters per second, or about 47 miles per hour. That’s right in line with the 43 miles per hour discussed by the news anchors.
What if the guardrails are a little thinner? If the wires are about 7.5 mm in diameter, then it only takes winds at about 15 meters per second (34 miles per hour) to create that 430 Hz note.
Keep in mind that this analysis doesn’t predict the minimum wind speed needed to create the audible noise; all I’m able to do is a back-of-the-envelope calculation of what the likely wind speed was when a video was recorded. Nevertheless, I hope you’ll find it interesting! (Video credit: KPIX CBS News; image credits: vortex shedding – Wikimedia, frequency analysis – N. Sharp; submitted by Christina T.)
June 9, 2020
Optimal Swimming
What do trout, sharks, and whales have in common? All are fast swimmers and share remarkable similarities in their swimming dynamics despite different sizes, shapes, and environments. A new study analyzing aquatic locomotion examines the characteristics of these swimmers. The researchers found that a typical parameter for studying swimming fish – the Strouhal number, which relates swimming speed, body length, and tail-beat frequency – only tells part of the story. When cruising at minimum power input, a fish cannot choose its Strouhal number – that characteristic is completely determined by the fish’s shape, which determines its drag.
Instead, researchers found that a second additional number – the ratio of the tail-beat amplitude to the body length – was also needed to describe optimal swimming. Taken together, their model predicts that optimal swimming performance lies within a narrow range of the two numbers. And when the researchers examined cruising behaviors of a diverse variety of fish and whales, they found that they did indeed swim in the ranges predicted by the model. Now that we better understand characteristics of efficient swimming, engineers can use the model to guide designs of new biologically-inspired robot swimmers. (Image credit: N. Sharp, source; research credit: M. Saadat et al.)
August 28, 2017
Is the Star Trek Voyager Opening Sequence Physically Realistic?
Today’s post is largely brought to you by the fact that I have been sick the past four days and my fiance and I have been bingeing on Star Trek Voyager. At some point, we began wondering about the sequence from 0:30-0:49 in which Voyager flies through a nebula and leaves a wake of von Karman vortices. Would a starship really leave that kind of wake in a nebula?
My first question was whether the nebula could be treated as a continuous fluid instead of a collection of particles. This is part of the continuum assumption that allows physicists to treat fluid properties like density, temperature, and velocity as well-defined quantities at all points. The continuum assumption is acceptable in flows where the Knudsen number is small. The Knudsen number is the ratio of the mean free path length to a characteristic flow length, in this case, Voyager’s size. The mean free path length is the average distance a particle travels before colliding with another particle. Nebulae are much less dense than our atmosphere, so the mean free path length is larger (~ 2 cm by my calculation) but still much smaller than Voyager’s length of 344 m. So it is reasonable to treat the nebula as a fluid.
As long as the nebula is acting like a fluid, it’s not unreasonable to see alternating vortices shed from Voyager. But are the vortices we see realistic relative to Voyager’s size and speed? Physicists use the dimensionless Strouhal number to describe oscillatory flows and vortex shedding. It’s a ratio of the vortex shedding frequency times the characteristic length to the flow’s velocity. We already know Voyager’s size, so we just need an estimate of its velocity and the number of vortices shed per second. I visually estimated these as 500 m/s and 2.5 vortices/second, respectively. That gives a Strouhal number of 0.28, very close to the value of 0.2 typically measured in the wake of a cylinder, the classical case for a von Karman vortex street.
So far Voyager’s wake is looking quite reasonable indeed. But what about its speed relative to the nebula’s speed of sound? If Voyager is moving faster than the local speed of sound, we might still see vortex shedding in the wake, but there would also be a bow shock off the ship’s leading edge. To answer this question, we need to know Voyager’s Mach number, its speed relative to the local speed of sound. After some digging through papers on nebulae, I found an equation to estimate speed of sound in a nebula (Eq 9 of Jin and Sui 2010) using the specific gas constant and temperature. Because nebulae are primarily composed of hydrogen, I approximated the nebula’s gas constant with hydrogen’s value and chose a representative temperature of 500 K (also based on Jin and Sui 2010). This gave a local speed of sound of 940 m/s, and set Voyager’s Mach number at 0.53, inside the subsonic range and well away from any shock wave formation.
Of course, these are all rough estimates and back-of-the-envelope fluid dynamics calculations, but my end conclusion is that Voyager’s vortex shedding wake through the nebula is realistic after all! (Video credit: Paramount; topic also requested by heuste11)
January 6, 2014
Vortex Street Sim
This numerical simulation shows a von Karman vortex street in the wake of a bluff body. As flow moves over the object, vortices are periodically shed off the object’s upper and lower surfaces at a steady frequency related to the velocity of the flow. The simulation takes place in a channel; note how the thickness of the boundary layers on the walls increases with downstream distance, forcing a slight constriction on the vortex street in the freestream.
October 10, 2011
Vortex Street
A flow visualization behind a cylinder shows the formation of a von Karman vortex street. The frequency of vortex shedding in the wake is directly related to the speed of the airflow–the higher the velocity, the faster vortices will shed from the cylinder. This relationship is expressed in the Strouhal number, which remains constant for any cylinder. (via freshphotons)
December 28, 2010