Numerical Simulation Of ‘Dead Water' Resistance In A Two-Layer Fluid

Scientific researches have shown that the seawater universally exhibit a marked stratified characteristic in the vertical distribution because of the changing of temperature and salinity.In these stratified ocean zones there are usually strong internal waves.Especially in polar regions,the fresh water layer formed by glacier melting is usually much shallow,where when a boat is sailing,there is an extra resistance due to the wave generating at the pycnocline,which makes the boat slow down suddenly.This phenomenon is known as ‘dead water'.Obviously the study for the effect of “dead water” is of great significance for ship's sailing.Based on the linear potential theory,a mathematical model is established for a structure moving at a two-layer fluid,by the high-order boundary element method.The flow satisfies 3D Laplace equation in the upper and lower domain simultaneously.The non-penetrating rigid condition(double-body assumption)is applied on the free surface,and the linearized dynamic and kinematic boundary conditions are applied on the internal surface.The artificial shore is added to eliminate the waves far away.In this way a linear boundary value problem is established.A Rankine source and its mirror image of free surface or seabed are introduced as Green function in the upper domain or lower domain respectively.Thus boundary integral equations in the upper and lower domain are obtained by applying the second Green identity.Furthermore,the upper and lower domain equations are coupled into a new one by using the pressure continuity condition at the inner interface and the velocity continuity condition.The new equation is solved in the time domain.In each time step,the fourth-order Adam-Bashford-Moulton scheme is used to update the internal surface and velocity potential ? of the internal interface at current time.In order to reach the stable state more quickly,a ramping function is introduced within a period of initial time.The convergence of the numerical model is verified firstly.Then the dead water resistance of three groups of box structure with different drafts at different towing speeds are calculated and compared with the experimental results to verify the correctness of the numerical method.On this basis,the characteristics and changing rules of structure resistance under different drafts,widths and water depths of lower layer are calculated and discussed.The numerical results show that the resistance of the structure always increases first and then decreases with the increasing of towing speed,and there is a maximum value at a certain speed.Finally,the wave-making characteristics of the internal interface are studied when the structure size or the water depth of lower layer changes,and the wave-making rules on the internal surface is analyzed.The results show that the internal surface wave-making always increases first and then decreases with the increasing towing speed,and the strongest wave-making always corresponds to the maximum structure resistance.When the towing speed is small,transverse waves and divergent waves are generated behind the first wave peak on the internal surface.While when the towing speed is large,only divergent waves remain behind the first wave peak.In addition,by the reference of ship wave-making theory in single layer fluid,the relationship between structure resistance and wave-making on internal surface in a two-layer fluid is discussed.