Water waves over a muddy seabed - Fields Institute · Water waves over a muddy seabed Chiang C....

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

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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

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

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

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

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

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Hangzhou Bay Hangzhou Bay

Lianyun HarborLianyun Harbor

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

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

Surface wave harmonics

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Hangzhou Bay Lianyun Harbor

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

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