102

Wea

ther

– A

pril

2011

, Vol

. 66,

No.

4

Win

d ag

ains

t tid

e

Figure 3. Waves in shallowing waters – abeam.

c gd= (A.3)

For a swell entering a tidal stream, we take the deep water case for simplicity, although similar results can be obtained in the general case of shallow water. The speed of the waves relative to the water is then given by Equation (A.2) both outside and within the current. Inserting Equation (A.2) into Equation (1) gives a quadratic to which the solution is:

cc

uco o

= + +⎡

⎣⎢⎢

⎤

⎦⎥⎥

12

1 14 (A.4)

In this equation, a positive sign is taken in front of the square root as only this solu-tion is physically valid, with the phase speed decreasing as the wave enters an opposing current.

If the opposing current is great enough so

that u > co/4, then the phase speed becomes

imaginary and the wave is infinitely steep. When the wavelength becomes shorter

as swell enters an opposing current, then in order to conserve energy the wave height must increase. If Ho is the initial wave height and H is the wave height in the current:

HH a a ao o

=+ +

⎛⎝⎜

⎞⎠⎟

λλ

21

21

2

( ) ( )

a u co= +1 4where (A.5)

AcknowledgementsI would like to thank Mike Brettle for first bringing Unna’s paper to my attention and for useful discussions, and also two anony-mous referees who greatly improved the final version of this paper.

ReferencesLewis D. 1972. We, the navigators. University of Hawaii Press: Honolulu, HI. pp. 110–113.Unna PJH. 1942. Waves and tidal streams. Nature 149: 219–220.White BS, Fornberg B. 1998. On the change of freak waves at sea. J. Fluid Mech. 355: 113–138.

Correspondence to: Alan Lapworth,Met Office, Field Site, Cardington Airfield,Shortstown, Bedfordshire, MK42 0SY, UK

ajlp@waitrose.com

© British Crown Copyright, 2011, published with the permission of the Controller of HMSO and the Queen’s Printer for Scotland

DOI: 10.1002/wea.606

Readers’ forum

Readers are invited to contribute short questions on any meteorological topic. We will endeavour to obtain answers to all submitted questions.

Did a drifting iceberg contribute to our record-breaking December?I was very interested to read the item refer-ring to the huge iceberg which had broken away from the Greenland icecap on 5 August (Weather News, 2010). This was said to be the largest iceberg to have broken free since 1962.

Is it a coincidence that this was followed by the coldest December in living memory – and is it possible that these truly massive icebergs could reduce the temperature of the North Atlantic (and perhaps affect the Gulf Stream) sufficiently to affect our winter weather?

David PageBromley, Kent

Reply by Jeff Ridley, Met Office Hadley CentreThe ‘giant’ iceberg which broke off from Petermann glacier (North Greenland) has travelled through the Nares Strait and now (February 2011), having broken into two, is off the coast of Baffin Island. It has been stuck in sea ice for its entire journey and will not have influenced regional weather, having not melted significantly. It will have had some influence on local waters as its motion will result in a stirring of the water

column, but it is located well away from any region of ocean overturning and cannot have contributed to  the  weather  condi-tions in December 2010 in northern Europe or America.  It is expected to leave the sea-ice  cover this summer,  and will drift out of the Labrador Sea into the North Atlantic, where it will start to melt. The iceberg does not represent a significant fraction of the annual freshwater  output from Greenland to the Atlantic, most of which is surface melt water (65%)  along with  tens of thousands of smaller icebergs.

Correspondence to: Jeff Ridley,Met Office Hadley Centre, FitzRoy Road,

Exeter EX1 3PB, UK jeff.ridley@metoffice.gov.uk

DOI: 10.1002/wea.792

ReferenceWeather News. 2010. Huge iceberg enters North Atlantic. Weather 65: 258.