Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for Mediu...Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for MediumRange Weather Forecasts(ECMWF)ERA5 datasets and observational data.The results revealed that the typhoon generated intense cyclones and huge typhoon waves with a maximum wind speed of 45 m/s,a minimum pressure of955 h Pa,and a maximum significant wave height of 12 m.The Stokes drift caused by typhoon waves exceeded 0.6m/s,the Stokes depth scale exceeded 18 m,and the maximum Stokes transport reached 6 m^(2)/s.The spatial distribution of 10-m wind speed,typhoon wave height,Stokes drift,Stokes depth,and Stokes transport during the typhoon was highly correlated with the typhoon track.The distribution along the typhoon track showed significant zonal asymmetry,with greater intensity on the right side of the typhoon track than on the left side.These findings provide important insights into the impact of typhoons on ocean waves and Stokes drift,thus improving our understanding of the interactions between typhoons and the ocean environment.This study also investigated the contribution of Stokes transport to the total net transport during typhoons using Ekman-Stokes Numbers as a comparative measure.The results indicated that the ratio of Stokes transport to the total net transport reached up to 50%within the typhoon radius,while it was approximately 30%outside the radius.Strong Stokes transport induced by typhoon waves led to divergence in the transport direction,which resulted in upwelling of the lower ocean as a compensation current.Thus,Stokes transport played a crucial role in the vertical mixing of the ocean during typhoons.The findings suggested that Stokes transport should be paid more attention to,particularly in high latitude ocean regions,where strong winds can amplify its effects.展开更多
The effect of Stokes drift production(SDP),which includes Coriolis-Stokes forcing,Langmuir circulation,and Craik-Lei-bovich vortexes,on the upper ocean during typhoon passage in the Bohai Sea(BS),China,is investigated...The effect of Stokes drift production(SDP),which includes Coriolis-Stokes forcing,Langmuir circulation,and Craik-Lei-bovich vortexes,on the upper ocean during typhoon passage in the Bohai Sea(BS),China,is investigated by using a coupled wave-current model.The role of SDP in turbulent mixing and the further dynamics during the entire typhoon period are comprehensively stud-ied.Experimental results show that SDP greatly increases turbulent mixing at all depths under typhoon conditions by up to seven times that under normal weather conditions.SDP generally strengthens sea surface cooling by more than 0.4℃,with the maximum reduction in sea surface temperature(SST)at the during-typhoon stage exceeding 2℃,which is approximately seven times larger than that under normal weather conditions.The SDP-induced decrease in current speed can exceed 0.2ms^(-1),and the change in current direction is generally opposite the wind direction.These results suggest that Stokes drift depresses the effect of strong winds on currents by intensifying turbulent mixing.Mixed layer depth(MLD)is distinctly increased by O(1)during typhoons due to SDP and can deepen by more than 5m.In addition,the continuous effects of SDP on SST,current,and MLD at the after-typhoon stage indi-cate a hysteretic response between SDP and typhoon actions.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear sta...The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow. The oscillations of two plates can have different velocity amplitudes, initial phases, and frequencies. The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed. The growth rates of two most unstable modes when δ < 0.12 are almost equal, and δ = δ*/h*, where δ*and h*are the Stokes-layer thickness and the half height of the channel, respectively. However, their vorticities are different. The vorticity of the most unstable mode is symmetric, while the other is asymmetric. The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ < 0.68, and have a stabilizing effect when δ > 0.68. However, the interactions always have a stabilizing effect on the other unstable mode. It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong. We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile. The effects of inconsistent velocity-amplitude, initial phase, and frequency of the oscillations on the stability are analyzed. The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency. The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.展开更多
This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through...This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.展开更多
基金financially supported by the National Key Research and Development Program of China(Grant No.2021YFB2601100)the National Natural Science Foundation of China(Grant No.52171246)+4 种基金The Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering(Grant No.2019491911)the Open Research Foundation of the State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology(Grant No.LP2005)the Science and Technology Innovation Program of Hunan Province(Grant No.2023RC3136)the Natural Science Foundation of Hunan Province(Grant No.2022JJ20041)Educational Science Foundation of Hunan Province(Grant No.23A0265)。
文摘Ocean waves and Stokes drift are generated by typhoons.This study investigated the characteristics of ocean waves and wave-induced Stokes drift and their effects during Typhoon Mangkhut using European Centre for MediumRange Weather Forecasts(ECMWF)ERA5 datasets and observational data.The results revealed that the typhoon generated intense cyclones and huge typhoon waves with a maximum wind speed of 45 m/s,a minimum pressure of955 h Pa,and a maximum significant wave height of 12 m.The Stokes drift caused by typhoon waves exceeded 0.6m/s,the Stokes depth scale exceeded 18 m,and the maximum Stokes transport reached 6 m^(2)/s.The spatial distribution of 10-m wind speed,typhoon wave height,Stokes drift,Stokes depth,and Stokes transport during the typhoon was highly correlated with the typhoon track.The distribution along the typhoon track showed significant zonal asymmetry,with greater intensity on the right side of the typhoon track than on the left side.These findings provide important insights into the impact of typhoons on ocean waves and Stokes drift,thus improving our understanding of the interactions between typhoons and the ocean environment.This study also investigated the contribution of Stokes transport to the total net transport during typhoons using Ekman-Stokes Numbers as a comparative measure.The results indicated that the ratio of Stokes transport to the total net transport reached up to 50%within the typhoon radius,while it was approximately 30%outside the radius.Strong Stokes transport induced by typhoon waves led to divergence in the transport direction,which resulted in upwelling of the lower ocean as a compensation current.Thus,Stokes transport played a crucial role in the vertical mixing of the ocean during typhoons.The findings suggested that Stokes transport should be paid more attention to,particularly in high latitude ocean regions,where strong winds can amplify its effects.
基金supported by the National Natural Science Foundation of China(No.42176020)the National Key Research and Development Program(No.2022 YFC3105002).
文摘The effect of Stokes drift production(SDP),which includes Coriolis-Stokes forcing,Langmuir circulation,and Craik-Lei-bovich vortexes,on the upper ocean during typhoon passage in the Bohai Sea(BS),China,is investigated by using a coupled wave-current model.The role of SDP in turbulent mixing and the further dynamics during the entire typhoon period are comprehensively stud-ied.Experimental results show that SDP greatly increases turbulent mixing at all depths under typhoon conditions by up to seven times that under normal weather conditions.SDP generally strengthens sea surface cooling by more than 0.4℃,with the maximum reduction in sea surface temperature(SST)at the during-typhoon stage exceeding 2℃,which is approximately seven times larger than that under normal weather conditions.The SDP-induced decrease in current speed can exceed 0.2ms^(-1),and the change in current direction is generally opposite the wind direction.These results suggest that Stokes drift depresses the effect of strong winds on currents by intensifying turbulent mixing.Mixed layer depth(MLD)is distinctly increased by O(1)during typhoons due to SDP and can deepen by more than 5m.In addition,the continuous effects of SDP on SST,current,and MLD at the after-typhoon stage indi-cate a hysteretic response between SDP and typhoon actions.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
基金Project supported by the National Natural Science Foundation of China (No. 11402211)。
文摘The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow. The oscillations of two plates can have different velocity amplitudes, initial phases, and frequencies. The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed. The growth rates of two most unstable modes when δ < 0.12 are almost equal, and δ = δ*/h*, where δ*and h*are the Stokes-layer thickness and the half height of the channel, respectively. However, their vorticities are different. The vorticity of the most unstable mode is symmetric, while the other is asymmetric. The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ < 0.68, and have a stabilizing effect when δ > 0.68. However, the interactions always have a stabilizing effect on the other unstable mode. It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong. We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile. The effects of inconsistent velocity-amplitude, initial phase, and frequency of the oscillations on the stability are analyzed. The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency. The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.
文摘This article gives a general model using specific periodic special functions, that is, degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of arbitrary r balls of the 3-Torus. The continuity equation is satisfied together with spatially periodic boundary conditions. The yicomponent forcing terms consist of a function F as part of its expression that is arbitrarily small in an r ball where it is associated with a singular forcing expression both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3(vifor all velocity components) only governing PDE resulting. The extension of three restricted subspaces in each of the principal directions in the Cartesian plane is shown as the Cartesian product ℋ=Jx,t×Jy,t×Jz,t. On each of these subspaces vi,i=1,2,3is continuous and there exists a linear independent subspace associated with the argument of the W function. Here the 3-Torus is built up from each compact segment of length 2R on each of the axes on the 3 principal directions x, y, and z. The form of the scaled velocities for non zero scaled δis related to the definition of the W function such that e−W(ξ)=W(ξ)ξwhere ξdepends on t and proportional to δ→0for infinite time t. The ratio Wξis equal to 1, making the limit δ→0finite and well defined. Considering r balls where the function F=(x−ai)2+(y−bi)2+(z−ci)2−ηset equal to −1e+rwhere r>0. is such that the forcing is singular at every distance r of centres of cubes each containing an r-ball. At the centre of the balls, the forcing is infinite. The main idea is that a system of singular initial value problems with infinite forcing is to be solved for where the velocities are shown to be locally Hölder continuous. It is proven that the limit of these singular problems shifts the finite time blowup time ti∗for first and higher derivatives to t=∞thereby indicating that there is no finite time blowup. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. Among the references, it has been shown that mathematical tools can be applied to study the asymptotic properties of solutions.
