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Vortex shedding occurs due to the detachment of flow. The typical example is for the oscillating wake behind a cylinder, and has a frequency related to the size of the object.

I want to know, if a long object such as a submarine/train is travelling through a fluid, will (small) detachment of the flow at the front of the object cause vortices to to exist and travel along the body before detaching again at the end of the object?

i.e. whether these vortices have fixed frequency relative to the geometry, to distinguish them from general boundary layer turbulence.

enter image description here

I have performed a literature search, and cannot find the answer to this question. Only the repeated comment that "turbulent behaviour at larger scales is a strong function of the flow geometry and gross flow parameters"$^1$. I have also looked at the question of "wall-pressure fluctuations over a forward facing step"$^2$, but the results are typically presented in terms of coherence and frequency domain cross correlation (e.g. Corcos model$^3$) and don't answer my time-dependent question.

Furthermore, this$^4$ paper shows performs a numerical simulation which would seem to show that the answer is yes, however the relationship between the shedding frequency in this type of geometry is unclear to me.

enter image description here

  1. Robinson, Stephen K. "Coherent motions in the turbulent boundary layer." Annual Review of Fluid Mechanics 23.1 (1991): 601-639.

  2. Largeau, J. F., and V. Moriniere. "Wall pressure fluctuations and topology in separated flows over a forward-facing step." Experiments in fluids 42.1 (2007): 21-40.

  3. Corcos, G. M. "Resolution of pressure in turbulence." The Journal of the Acoustical Society of America 35.2 (2005): 192-199.

  4. Bruneau, Charles-Henri, Patrick Gilliéron, and Iraj Mortazavi. "Passive control around the two-dimensional square back Ahmed body using porous devices." Journal of Fluids Engineering 130.6 (2008): 061101.

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At low Renyolds number, the vortex shedding described in the question does not occur, based upon the following simulation videos:

http://www.youtube.com/watch?v=ElmTA0t3bEc

http://www.youtube.com/watch?v=8o-JC3R9YBY

http://www.youtube.com/watch?v=sN9LP5dNWhc

However, for higher Renyolds number see Nakamura et al. "Experiments on vortex shedding from flat plates with square leading and trailing edges" J. Fluid Mech. (1991) vol. 222, pages 437-447 . Probes are placed along the side of and spaced from the plate to analyze frequency and vorticies can be seen in photographs (Figs. 6a and 6b) alongside the plate.

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  • $\begingroup$ Excellent paper. Do you have an answer as to whether there is any well known/empirical formulas to predict the frequency of the vortices passing over the surface edge? i.e. analogous to $f=\text{St } V/D$ ? $\endgroup$
    – xyz
    Commented Apr 8, 2014 at 17:46
  • $\begingroup$ Sorry, I don't have such a formula. $\endgroup$
    – DavePhD
    Commented Apr 8, 2014 at 17:49
  • $\begingroup$ @James actually, the paper at page 439 does use an analogous formula, where D is replaced with c (chord length, the length of the plate), but considers St the dependent variable. The reference compares wake vs. side wavelength (section 3.4) and phase velocity (Fig. 8). It seems that frequency is roughly the same at the side as in the wake. $\endgroup$
    – DavePhD
    Commented Apr 8, 2014 at 19:14
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You seem to be looking for boundary layer separation, which occurs for sufficiently large Reynolds number. See Batchelor's Introduction to fluid dynamics, sections 5.8 to 5.10.

See also:

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

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

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  • $\begingroup$ You can have large Reynolds number flows in which the boundary layer is not separated. Generally large Reynolds numbers are associated with turbulent boundary layers. The pressure gradient is the relevant parameter to boundary layer separation. $\endgroup$
    – OSE
    Commented Apr 8, 2014 at 14:46

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