Re: the Kelvin Wake again

[Leigh Palmer <palmer@SFU.CA>]

At 2:55 AM -0700 5/30/00, Mark Sylvester wrote:
> At 15.01 29/05/00 -0700, Leigh Palmer wrote:
> > I said:
> >
> > > Kelvin wakes pertain only to displacement boats.
> > > Boats that are hydroplaning (such as some of the
> > > speedboats you see) don't leave Kelvin wakes.
> >
> > On second thought, planing boats probably do leave
> > Kelvin wakes, but they are likely of very small
> > amplitude and they may be swamped by the turbulent
> > wake of such a boat. The stern wake of a ferry is
> > not a Kelvin wake either. Look at the bow wakes of
> > the displacement craft, from ducks through tugs
> > pulling barges. You'll see lots of Kelvin wakes,
> > all opening at 39 degrees.
>
> Does the turbulent wake *look* different, apart from having a variable
> angle?

Certainly. The turbulent wake has a turbulent surface;
it "breaks" or is "foamy". The Kelvin wake is a laminar
phenomenon that propagates as a coherent wave from a
boat moving with constant velocity. (An accelerating or
decelerating boat won't leave a 39 degree Kelvin wake
either, of course.) I recall seeing an aerial photograph
of Kelvin wakes from large ships that extended for
several kilometers.

I think that a large part of your impression that there
are many different angles of Kelvin wakes is due to the
variety of presentations to your line of sight. It is
highly unlikely that you are viewing these wakes from
other than a low angle with respect to the surface. The
constancy of the angle is only evident when it is viewed
from overhead.


> I visualize the kelvin wake as comprising in each line of the v many
> separate wavecrests, each at an angle to the line of the v:
>
>                 /\
>                /  \
>                /  \
>               /    \
>               /    \
>              /      \
>              /      \
>             /        \
>
> This is typical of what is observed.

That's the correct animal, alright.

> I also recall a speedboat wake as being just a continuous line in each v -
> must check if this is observed.

I expect it is incoherent and will not propagate for
long distances. The Kelvin wake of a planing speedboat
probably persists long after the turbulent wake has
dissipated.

> Conjecture: could the separate wavecrests of the kelvin wake have an
> opening angle that depends on the speed of the vessel, even though the
> overall wake line has a constant opening angle?

My guess (I don't recall this result) is that Kelvin
wakes are similar to one another; the relative angle is
constant. Of course Kelvin wakes generated by faster
boats propagate faster than Kelvin wakes generated by
slower boats, and they have greater characteristic
lengths (the wavelet length and the width of the wake).

Leigh

I have now looked up the result in a book. The opening
angle of the wavelet fronts is 109.5 degrees, independent
of boat velocity. The book, "Bores, Breakers, Waves, and
Wakes" by R. A. R. Tricker, first published in 1964 by
Mills & Boon Limited, London, has a very clear derivation
which should be quite accessible to brighter IB students.
The downside is that the book itself is not very
accessible. I couldn't find it at six booksellers' web
sites that I tried.