Water waves over a muddy seabed - Fields Institute · Water waves over a muddy seabed Chiang C....
Transcript of Water waves over a muddy seabed - Fields Institute · Water waves over a muddy seabed Chiang C....
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Water waves over a muddy seabed
Chiang C. Mei, MIT
WithZhenhua Huang, NTU, Singapore M.Krotov, MITErell-Isis Garnier, MITTFunded by US Office of Naval Research
April,May, 2013 ROC, Toronro 1
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Allepey, S. India (Mathew, Baba & Kurian, 1995)
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India, Mathew,
Baba, Kurian
JCR 1995
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5 6 7 8
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1989
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Alleppey, S. India (Mathew et al 1995)
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Past works
• Field survey: – Surinum: Wells & Colemen 1981
– India: Mathew, Baba & Kurian, 1995
• Math models:
• Newtonian mud: Dalrymple & Liu 刘立方 , Liu & Chan
– Bingham plastic: Mei and Liu 刘格非 , Coussot
– Simple Kelvin-Voigt viscoelastic: McPherson, Jiang & Mehta, Ng 吴朝 安
– Plasto-viscoelastic: Shibayama
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Lianyun gang
Hangzhou bay
Field mud samples
连云港
杭州湾
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Fluid-mud rheologyNot Newtonian, Not Bingham plastic, but
Viscoelastic
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Part I: Horizontal seabed, intermediate wave length
(Mei, Krotov & Huang, 2010, JFM)
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Shallow mud layer
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Scales
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Water layer
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Water at Leading orderHomogeneous BVP on the fast scale
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Leading order mud motion
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Stokes boundary layer
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Solvability of order 1
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Interface displacement
Hangzhou Bay for
d/h=0.03--0.2
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Interface displacement
Lianyun Harborfor
d/h=0.03—0.2
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Damping coefficient
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Part II
Shallow water long waves on a sloping beach
Garnier, Huang & Mei, J. Fluid Mech. 2013,(718), 371-397.
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Boussinesq approximation
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Shallow water, very shallow mud:
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Fluid mud from Hangzhou Bay and Lianyun Harbor (Huang & Huhe
1992)
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Lianyun Harbor
Hangzhou Bay
Lianyun Harbor
Hangzhou Bay
ROC, Toronro
Hangzhou Bay Hangzhou Bay
Lianyun HarborLianyun Harbor
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Water layer:Long wave equations
(dimensionless and Boussinesq)
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Crudest approximation
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Harmonic generation in shallow water
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frequency
Wave number
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(a) A = 5 cm: H = 30 cm, T = 1:90 s,L = 3:23 m (Ur = 0:45);
(b) A = 5 cm: H = 20 cm, T = 2:75 s, L= 3:86 m (Ur = 2:35)
Barbara Karakiewicz, 1972
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Periodic surface waves
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Mud motion at leading order
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Mud Harmonics
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Wave harmonics
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Hangzhou Bay Lianyun Harbor
d=0.5 m
d=0.75 m
d=1.0 m
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Surface wave harmonics
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Hangzhou Bay Lianyun Harbor
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Interface harmonics
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Near the shoreline
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Steady displacement (cf: Acoustic streaming)
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Mean mud displacement
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Profile of mud surface displacement
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angzhou Bay
Ianyun Harbor
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Work needed
• Short-range:– Measurement of fluid mud rheology with a
dynamic rheometer (RMS 605?)
– Laboratory experiments on a sloping beach
• Fundamental:– Transition between consolidated and fluidized
mud
– Transition between fluid mud and clear water (lutocline)
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Thank youMerci, GraciasVielen Dankありがとうございます。
谢, 감사합니다多 ,Спасибо ευχαριστὠ