On the basis of a three-dimensional weakly nonliear theory of Lagrangian residual current in the Baroclinic shallow seas, a diagnostic numerical calculation of wind-driven, thermohaline and tide-induced Lagrangian res...On the basis of a three-dimensional weakly nonliear theory of Lagrangian residual current in the Baroclinic shallow seas, a diagnostic numerical calculation of wind-driven, thermohaline and tide-induced Lagrangian residual current in the Bohai Sea is made. The model involves the Richardson number in the eddy viscosity coefficient, wind, thcrmolialine and tidal effects in the focing terms. The runoff of the Huanghe River and a part of the Huanghai Warm Water coming from the Huanghai Sea through the Bohai Sea Strait is also considered. The velocity-splitting method is adopted. The wind-driven circu lation, thermohaline circulation and the tide-induced Lagrangian residual circulation are also obtained individually and analysed. The dynamics of the three main eddies in the Lagrangian mean circulation is discussed. Finally, the numerical result is partly verified with the observed data.展开更多
The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodi...The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.展开更多
An improved method for computing the three-dimensional(3 D)first-order Lagrangian residual velocity(uL)is estab-lished.The method computes tidal body force using the harmonic constants of the zeroth-order tidal curren...An improved method for computing the three-dimensional(3 D)first-order Lagrangian residual velocity(uL)is estab-lished.The method computes tidal body force using the harmonic constants of the zeroth-order tidal current.Compared with using the tidal-averaging method to compute the tidal body force,the proposed method filters out the clutter other than the single-frequency tidal input from the open boundary and obtains uL that is more consistent with the analytic solution.Based on the new method,uL is calculated for a wide bay with a longitudinal topography.The strength and pattern of uL are mostly determined by the parts of the tidal body force related to the vertical mixing of the Stokes’drift and the Coriolis effect,with a minor contribution from the advection effect.The geometrical shape of the bay can influence uL through the topographic gradient.The magnitude of uL increases with the increases in tidal energy input and vertical eddy viscosity and decreases in terms of the bottom friction coefficient.展开更多
Based on an inverted one-and-one-half inviscid reduced gravity shallow water model with bottom topography representing an abyssal layer under a stagnant upper layer on the equatorial β-Plane, a set of field equations...Based on an inverted one-and-one-half inviscid reduced gravity shallow water model with bottom topography representing an abyssal layer under a stagnant upper layer on the equatorial β-Plane, a set of field equations governing the wave-induced Lagrangian residual currents is developed. The equations show that the wave-induced Lagrangian residual ot satisfies generalized geostrophic dynamics. The relation of meridional residual current to vertical residual current resulted from the varied bottom is similar to the Sverdrup transport relation. The tranport process of potential vorticity for zeroth order approximation is determined by the advection whose velocity is equal to that of the weve-induced Lagrangian residual current.A Kelvin wave solution and the reated solution of Kelvin wave-induced Lagrangian residual current for the case of slowly varying topography are obtained anaytically. The wave solution shows that a shoaling eastward bottom can decrease the propagation speed of the Kelvin wave and cause it to take a longer time to transmit the energy from the west to the central and easterm parts of the basin, and can also shorten the wavelength and enhance the wave amplitude. The wave-induced residual current solution reveals that the existence of a sloping bottom can result in a onier meridional component of wave-induced mesidual current and that Kelvin wave-induced Lagrangian currents’s responses to bottom variation are greater than those of Kelvin wave orbital currents.展开更多
The study in this paper is focusing on trajectories of particles in the irrotational progressive water waves coexisting with uniform current. The parametric equations of particle trajectories over a range of levels in...The study in this paper is focusing on trajectories of particles in the irrotational progressive water waves coexisting with uniform current. The parametric equations of particle trajectories over a range of levels in a Lagrangian type of description are developed analytically via the Euler-Lagrange transformation. The Lagrangian wave period of particle motion differing from the Eulerian wave period and the mass transport can also be obtained directly. The third-order solution of particle trajectory exhibits that they do not move in closed orbital motion but represent a net movement that decreases exponentially with the water depth. Uniform current is found to have significant effect on the trajectories and drift velocity of gravity waves. Overall, the influence of increased uniform current is to increase the relative horizontal distance traveled by a particle, as well as the magnitude of the time-averaged drift velocity on the free surface. For adverse current cases, a reverse behavior is found. The obtained third-order solutions satisfy the irrotational condition contrasted to the Gerstner waves and are verified by reducing to those of two-dimensional gravity waves in Lagrangian coordinates.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘On the basis of a three-dimensional weakly nonliear theory of Lagrangian residual current in the Baroclinic shallow seas, a diagnostic numerical calculation of wind-driven, thermohaline and tide-induced Lagrangian residual current in the Bohai Sea is made. The model involves the Richardson number in the eddy viscosity coefficient, wind, thcrmolialine and tidal effects in the focing terms. The runoff of the Huanghe River and a part of the Huanghai Warm Water coming from the Huanghai Sea through the Bohai Sea Strait is also considered. The velocity-splitting method is adopted. The wind-driven circu lation, thermohaline circulation and the tide-induced Lagrangian residual circulation are also obtained individually and analysed. The dynamics of the three main eddies in the Lagrangian mean circulation is discussed. Finally, the numerical result is partly verified with the observed data.
基金National Science Council in Taiwan 97-2221-E-230-023
文摘The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.
基金supported by the National Natural Science Foundation of China (No. 41676003)the NSFC Shandong Joint Fund for Marine Science Research Centers (No. U1606402)
文摘An improved method for computing the three-dimensional(3 D)first-order Lagrangian residual velocity(uL)is estab-lished.The method computes tidal body force using the harmonic constants of the zeroth-order tidal current.Compared with using the tidal-averaging method to compute the tidal body force,the proposed method filters out the clutter other than the single-frequency tidal input from the open boundary and obtains uL that is more consistent with the analytic solution.Based on the new method,uL is calculated for a wide bay with a longitudinal topography.The strength and pattern of uL are mostly determined by the parts of the tidal body force related to the vertical mixing of the Stokes’drift and the Coriolis effect,with a minor contribution from the advection effect.The geometrical shape of the bay can influence uL through the topographic gradient.The magnitude of uL increases with the increases in tidal energy input and vertical eddy viscosity and decreases in terms of the bottom friction coefficient.
文摘Based on an inverted one-and-one-half inviscid reduced gravity shallow water model with bottom topography representing an abyssal layer under a stagnant upper layer on the equatorial β-Plane, a set of field equations governing the wave-induced Lagrangian residual currents is developed. The equations show that the wave-induced Lagrangian residual ot satisfies generalized geostrophic dynamics. The relation of meridional residual current to vertical residual current resulted from the varied bottom is similar to the Sverdrup transport relation. The tranport process of potential vorticity for zeroth order approximation is determined by the advection whose velocity is equal to that of the weve-induced Lagrangian residual current.A Kelvin wave solution and the reated solution of Kelvin wave-induced Lagrangian residual current for the case of slowly varying topography are obtained anaytically. The wave solution shows that a shoaling eastward bottom can decrease the propagation speed of the Kelvin wave and cause it to take a longer time to transmit the energy from the west to the central and easterm parts of the basin, and can also shorten the wavelength and enhance the wave amplitude. The wave-induced residual current solution reveals that the existence of a sloping bottom can result in a onier meridional component of wave-induced mesidual current and that Kelvin wave-induced Lagrangian currents’s responses to bottom variation are greater than those of Kelvin wave orbital currents.
基金supported by science council of Taiwan with grant no.NSC-97-2221-E-230-023
文摘The study in this paper is focusing on trajectories of particles in the irrotational progressive water waves coexisting with uniform current. The parametric equations of particle trajectories over a range of levels in a Lagrangian type of description are developed analytically via the Euler-Lagrange transformation. The Lagrangian wave period of particle motion differing from the Eulerian wave period and the mass transport can also be obtained directly. The third-order solution of particle trajectory exhibits that they do not move in closed orbital motion but represent a net movement that decreases exponentially with the water depth. Uniform current is found to have significant effect on the trajectories and drift velocity of gravity waves. Overall, the influence of increased uniform current is to increase the relative horizontal distance traveled by a particle, as well as the magnitude of the time-averaged drift velocity on the free surface. For adverse current cases, a reverse behavior is found. The obtained third-order solutions satisfy the irrotational condition contrasted to the Gerstner waves and are verified by reducing to those of two-dimensional gravity waves in Lagrangian coordinates.
