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Head and Neck Cancer: United Kingdom National Multidisciplinary Guidelines, Sixth Edition
- Jarrod J Homer, Stuart C Winter, Elizabeth C Abbey, Hiba Aga, Reshma Agrawal, Derfel ap Dafydd, Takhar Arunjit, Patrick Axon, Eleanor Aynsley, Izhar N Bagwan, Arun Batra, Donna Begg, Jonathan M Bernstein, Guy Betts, Colin Bicknell, Brian Bisase, Grainne C Brady, Peter Brennan, Aina Brunet, Val Bryant, Linda Cantwell, Ashish Chandra, Preetha Chengot, Melvin L K Chua, Peter Clarke, Gemma Clunie, Margaret Coffey, Clare Conlon, David I Conway, Florence Cook, Matthew R Cooper, Declan Costello, Ben Cosway, Neil J A Cozens, Grant Creaney, Daljit K Gahir, Stephen Damato, Joe Davies, Katharine S Davies, Alina D Dragan, Yong Du, Mark R D Edmond, Stefano Fedele, Harriet Finze, Jason C Fleming, Bernadette H Foran, Beth Fordham, Mohammed M A S Foridi, Lesley Freeman, Katherine E Frew, Pallavi Gaitonde, Victoria Gallyer, Fraser W Gibb, Sinclair M Gore, Mark Gormley, Roganie Govender, J Greedy, Teresa Guerrero Urbano, Dorothy Gujral, David W Hamilton, John C Hardman, Kevin Harrington, Samantha Holmes, Jarrod J Homer, Deborah Howland, Gerald Humphris, Keith D Hunter, Kate Ingarfield, Richard Irving, Kristina Isand, Yatin Jain, Sachin Jauhar, Sarra Jawad, Glyndwr W Jenkins, Anastasios Kanatas, Stephen Keohane, Cyrus J Kerawala, William Keys, Emma V King, Anthony Kong, Fiona Lalloo, Kirsten Laws, Samuel C Leong, Shane Lester, Miles Levy, Ken Lingley, Gitta Madani, Navin Mani, Paolo L Matteucci, Catriona R Mayland, James McCaul, Lorna K McCaul, Pádraig McDonnell, Andrew McPartlin, Valeria Mercadante, Zoe Merchant, Radu Mihai, Mufaddal T Moonim, John Moore, Paul Nankivell, Sonali Natu, A Nelson, Pablo Nenclares, Kate Newbold, Carrie Newland, Ailsa J Nicol, Iain J Nixon, Rupert Obholzer, James T O'Hara, S Orr, Vinidh Paleri, James Palmer, Rachel S Parry, Claire Paterson, Gillian Patterson, Joanne M Patterson, Miranda Payne, L Pearson, David N Poller, Jonathan Pollock, Stephen Ross Porter, Matthew Potter, Robin J D Prestwich, Ruth Price, Mani Ragbir, Meena S Ranka, Max Robinson, Justin W G Roe, Tom Roques, Aleix Rovira, Sajid Sainuddin, I J Salmon, Ann Sandison, Andy Scarsbrook, Andrew G Schache, A Scott, Diane Sellstrom, Cherith J Semple, Jagrit Shah, Praveen Sharma, Richard J Shaw, Somiah Siddiq, Priyamal Silva, Ricard Simo, Rabin P Singh, Maria Smith, Rebekah Smith, Toby Oliver Smith, Sanjai Sood, Francis W Stafford, Neil Steven, Kay Stewart, Lisa Stoner, Steve Sweeney, Andrew Sykes, Carly L Taylor, Selvam Thavaraj, David J Thomson, Jane Thornton, Neil S Tolley, Nancy Turnbull, Sriram Vaidyanathan, Leandros Vassiliou, John Waas, Kelly Wade-McBane, Donna Wakefield, Amy Ward, Laura Warner, Laura-Jayne Watson, H Watts, Christina Wilson, Stuart C Winter, Winson Wong, Chui-Yan Yip, Kent Yip
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- Journal:
- The Journal of Laryngology & Otology / Volume 138 / Issue S1 / April 2024
- Published online by Cambridge University Press:
- 14 March 2024, pp. S1-S224
- Print publication:
- April 2024
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A generalized vortex ring model
- FELIX KAPLANSKI, SERGEI S SAZHIN, YASUHIDE FUKUMOTO, STEVEN BEGG, MORGAN HEIKAL
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- Journal:
- Journal of Fluid Mechanics / Volume 622 / 10 March 2009
- Published online by Cambridge University Press:
- 10 March 2009, pp. 233-258
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A conventional laminar vortex ring model is generalized by assuming that the time dependence of the vortex ring thickness ℓ is given by the relation ℓ = atb, where a is a positive number and 1/4 ≤ b ≤ 1/2. In the case in which , where ν is the laminar kinematic viscosity, and b = 1/2, the predictions of the generalized model are identical with the predictions of the conventional laminar model. In the case of b = 1/4 some of its predictions are similar to the turbulent vortex ring models, assuming that the time-dependent effective turbulent viscosity ν∗ is equal to ℓℓ′. This generalization is performed both in the case of a fixed vortex ring radius R0 and increasing vortex ring radius. In the latter case, the so-called second Saffman's formula is modified. In the case of fixed R0, the predicted vorticity distribution for short times shows a close agreement with a Gaussian form for all b and compares favourably with available experimental data. The time evolution of the location of the region of maximal vorticity and the region in which the velocity of the fluid in the frame of reference moving with the vortex ring centroid is equal to zero is analysed. It is noted that the locations of both regions depend upon b, the latter region being always further away from the vortex axis than the first one. It is shown that the axial velocities of the fluid in the first region are always greater than the axial velocities in the second region. Both velocities depend strongly upon b. Although the radial component of velocity in both of these regions is equal to zero, the location of both of these regions changes with time. This leads to the introduction of an effective radial velocity component; the latter case depends upon b. The predictions of the model are compared with the results of experimental measurements of vortex ring parameters reported in the literature.