In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth,the use of sigma coordinates allows the calculation of residual velocity around the mean water surface le...In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth,the use of sigma coordinates allows the calculation of residual velocity around the mean water surface level.Theoretical analysis and generic numerical experiments were conducted to understand the physical meaning of the residual velocities at sigma layers in breadth-averaged tidal channels.For shallow water waves,the sigma layers coincide with the water wave surfaces within the water column such that the Stokes velocity and its vertical and horizontal components can be expressed in discrete forms using the sigma velocity.The residual velocity at a sigma layer is the sum of the Eulerian velocity and the vertical component of the Stokes velocity at the mean depth of the sigma layer and,therefore,can be referred to as a semi-Lagrangian residual velocity.Because the vertical component of the Stokes velocity is one order of magnitude smaller than the horizontal component,the sigma residual velocity approximates the Eulerian residual velocity.The residual transport velocity at a sigma layer is the sum of the sigma residual velocity and the horizontal component of the Stokes velocity and approximates the Lagrangian residual velocity in magnitude and direction,but the two residual velocities are not conceptually the same.展开更多
Based on their differences in physical characteristics and time-space scales,the ocean motions have been divided into four types in the present paper：turbulence,wave-like motion,eddy-like motion and circulation.Apply...Based on their differences in physical characteristics and time-space scales,the ocean motions have been divided into four types in the present paper：turbulence,wave-like motion,eddy-like motion and circulation.Applying the three-fold Reynolds averages to the governing equations with Boussinesq approximation,with the averages defined on the former three sub-systems,we derive the governing equation sets of the four sub-systems and refer to their sum as ＂the ocean dynamic system＂.In these equation sets,the interactions among different motions appear in two forms：the first one includes advection transport and shear instability generation of larger scale motions,and the second one is the mixing induced by smaller scale motions in the form of transport flux residue.The governing equation sets are the basis of analytical/numerical descriptions of various ocean processes.展开更多
基金The National Basic Research Program of China under contract No.2015CB954000the National Natural Science Foundation of China under contract No.41476004。
文摘In shallow coastal regions where water surface fluctuations are non-negligible compared to the mean water depth,the use of sigma coordinates allows the calculation of residual velocity around the mean water surface level.Theoretical analysis and generic numerical experiments were conducted to understand the physical meaning of the residual velocities at sigma layers in breadth-averaged tidal channels.For shallow water waves,the sigma layers coincide with the water wave surfaces within the water column such that the Stokes velocity and its vertical and horizontal components can be expressed in discrete forms using the sigma velocity.The residual velocity at a sigma layer is the sum of the Eulerian velocity and the vertical component of the Stokes velocity at the mean depth of the sigma layer and,therefore,can be referred to as a semi-Lagrangian residual velocity.Because the vertical component of the Stokes velocity is one order of magnitude smaller than the horizontal component,the sigma residual velocity approximates the Eulerian residual velocity.The residual transport velocity at a sigma layer is the sum of the sigma residual velocity and the horizontal component of the Stokes velocity and approximates the Lagrangian residual velocity in magnitude and direction,but the two residual velocities are not conceptually the same.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.40776020,41106032)the National Basic Research Program of China (973 Program,Grant Nos.G1999043800,2006CB403600,2010CB950404 and 2010CB950300)
文摘Based on their differences in physical characteristics and time-space scales,the ocean motions have been divided into four types in the present paper：turbulence,wave-like motion,eddy-like motion and circulation.Applying the three-fold Reynolds averages to the governing equations with Boussinesq approximation,with the averages defined on the former three sub-systems,we derive the governing equation sets of the four sub-systems and refer to their sum as ＂the ocean dynamic system＂.In these equation sets,the interactions among different motions appear in two forms：the first one includes advection transport and shear instability generation of larger scale motions,and the second one is the mixing induced by smaller scale motions in the form of transport flux residue.The governing equation sets are the basis of analytical/numerical descriptions of various ocean processes.
