Characteristic Quantity Research Of Turbulent Bottom Boundary Layer With Different Eddy Viscosities

The physical properties and dynamic processes of the oscillatory bottom boundarylayer that is a typical and important boundary layer are very complicated. Thehydrodynamic properties of turbulent bottom boundary layer are important researchand application value in marine engineering, marine biology and so on. However, theestablishment of the theory model of the ocean bottom boundary layer and itsanalytical solution are seldom. Observation experiment and theoretical research of theocean bottom boundary layer have also been the research hot spot for the physicaloceanography, marine environmental engineering and biology. In this paper, the mainwork is structured following: on the one hand, discusses the effective viscosityreduction behavior model of solid suspension in ocean bottom boundary layer; On theother hand, establish two different new forms of turbulent viscosity and research thedynamic of the turbulent bottom boundary layer theoretically. This paper is organizedinto three parts as follows.In the first part of the paper the transformation field method is used to model thereduction behaviour of effective viscosity of solid suspensions theoretically byenlarging the particle size at a given high concentration of particles based on theStokes equation. Under a simple shearing flow, the effective viscosity of solidsuspensions can be reduced by controlling the inclusion particle size or the number ofinclusion particles in a unit volume. With a lot of samples of random cubic particles ina unit cell, our statistical results show that at the same higher concentration, theeffective viscosity of solid suspensions can be reduced by increasing the particle sizeor reducing the number of inclusion particles in a unit volume. This work disclosesthe viscosity reduction mechanism of increasing particle size, which is observedexperimentally.In the second part of the paper the analytical solutions of the velocity distributionwithin the turbulent bottom boundary layer are deduced by supposed a new eddyviscosity of cubic polynomial form az2(1z/d). Based on the simplifiedNavier-Stokes equations, the property of the hypergeometric function is used to thismodel. Moreover, other dynamic parameters of bottom boundary layer are alsoobtained, such as the bottom shear stress, the Ekman transport, Ekman pumping and the velocity fields near the bottom. Thus the dynamic characteristics of well-mixedturbulent bottom boundary are discussed theoretically. Furthermore, numerical resultsshow that the total velocity profile, Ekman velocity and shear stress are sensitivenessto the ratio of the tidal frequency and the Coriolis parameter, but have been lessinfluenced on the roughness heights at the top of the bottom boundary layer.In the third part of the paper, we give another eddy viscosity of cubic polynomialform az (1z/d)2, and derive an analytical solution of velocity for turbulentrough bottom boundary layer. Furthermore, numerical results show that the velocityprofile in the bottom boundary layer is influenced strongly by the ratio of the tidalfrequency and the Coriolis parameter but is not sensitive to the roughness heights atthe top of the bottom boundary layer. Comparing with measured data of a tidal currentwithin bottom boundary layer, it indicates that the analytical model agrees well withobservation of the tidal current velocity magnitude.In this paper, we research theoretically the effective viscosity reduction behaviourof solid suspension and eddy viscosity parametric forms. They are important meansand methods in researching dynamic influence factors of bottom boundary layer.