Vorticity–Stream Function Formulation for Turbulent Oscillatory Boundary Layer over the Sea Bottom

Author(s):  
Giovanna Vittori ◽  
Pilar Díaz-Carrasco ◽  
Paolo Blondeaux
2013 ◽  
Vol 40 (3) ◽  
pp. 403-425 ◽  
Author(s):  
Mosharf Hossain ◽  
Nepal Roy ◽  
Anwar Hossain

An analysis is performed to study the shear stress, the couple-stress and heat transfer characteristics of a laminar mixed convection boundary layer flow of a micropolar fluid past an isothermal permeable plate. The governing nonsimilar boundary layer equations are analyzed using the (i) series solution for small ?, (ii) asymptotic solution for large ? and (iii) primitive-variable formulation and the stream function formulation are being used for all ?. The effects of the material parameters, such as, the vortex viscosity parameter, K, and the transpiration parameter, s, on the shear stress, the couple-stress and heat transfer have been investigated. The agreement between the solutions obtained from the stream-function formulation and the primitive-variable formulation is found to be excellent.


2013 ◽  
Vol 718 ◽  
pp. 371-397 ◽  
Author(s):  
Erell-Isis Garnier ◽  
Zhenhua Huang ◽  
Chiang C. Mei

AbstractWe analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.


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