Oblique surface waves incident on a fixed vertical porous membrane of various geometric configurations is analyzed here.The mixed boundary value problem is modified into easily resolvable problems by using a connectio...Oblique surface waves incident on a fixed vertical porous membrane of various geometric configurations is analyzed here.The mixed boundary value problem is modified into easily resolvable problems by using a connection.These problems are reduced to that of solving a couple of integral equations.These integral equations are solved by a one-term or a two-term Galerkin method.The method involves a basis functions consists of simple polynomials multiplied with a suitable weight functions induced by the barrier.Coefficient of reflection and total wave energy are numerically evaluated and analyzed against various wave parameters.Enhanced reflection is found for all the four barrier configurations.展开更多
At 12:15 on January 15,2022(Beijing time),a massive eruption of the Hunga Tonga-Hunga Ha'apai volcano produced violent atmospheric fluctuations,which in turn generated a global tsunami through an abrupt air pressu...At 12:15 on January 15,2022(Beijing time),a massive eruption of the Hunga Tonga-Hunga Ha'apai volcano produced violent atmospheric fluctuations,which in turn generated a global tsunami through an abrupt air pressure shock upon the sea surface.Two main components of tsunami waves,phase-locked waves and free gravity waves,were identified by significant differences in propagating speeds across the deep ocean.The phase-locked wave propagated through the ocean basin synchronously with the atmospheric Lamb wave at an average speed of approximately 306 m/s,followed by the free gravity wave at a slower speed.The locked wave reached the coast of eastern Taiwan Island at about 20:00 on January 15,in coincidence with the Lamb wave arrival.However,on the coast of Chinese mainland,tidal gauges did not record tsunami signals until at least 2 h after the Lamb wave arrivals.Theoretical analyses and numerical experiments both suggested that as a result of the incoming wave shoaling above the vast continental shelf of Chinese mainland,the locked wave was no longer trapped by the air pressure shock and gradually transformed into freely-propagating shallow water waves by slowing down its propagation.Due to the longlasting planetary atmospheric fluctuations circling the earth many times,the sea level oscillations continuously propagated onto the Chinese shelf,which resulted in the tsunami waves excited along the Chinese coasts for at least 36 h.The maximum wave amplitude recorded on the coast of eastern Taiwan Island was 44 cm at Wushi,while on the coasts of eastern and southern Chinese mainland,the maximum amplitudes were 22 cm at Shipu and 13 cm at Zhuhai.Fourier and wavelet analyses were performed to identify the major components of the tsunami waves on the Chinese coasts.The results indicated that eastern Taiwan Island was impacted mainly by the waves with periods of approximately 10-40 min.Chinese mainland was hit by the evolved shallow water waves and subsequent free waves,with periods of approximately 40-100 and 16-20 min,respectively.展开更多
The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “...The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “total generalized momentum” conservation of the gravity free system can be kept when the gravity is small in comparison with the total enery.展开更多
文摘Oblique surface waves incident on a fixed vertical porous membrane of various geometric configurations is analyzed here.The mixed boundary value problem is modified into easily resolvable problems by using a connection.These problems are reduced to that of solving a couple of integral equations.These integral equations are solved by a one-term or a two-term Galerkin method.The method involves a basis functions consists of simple polynomials multiplied with a suitable weight functions induced by the barrier.Coefficient of reflection and total wave energy are numerically evaluated and analyzed against various wave parameters.Enhanced reflection is found for all the four barrier configurations.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFC3003800)the Asian Cooperation Fund Project(Grand No.99950410)。
文摘At 12:15 on January 15,2022(Beijing time),a massive eruption of the Hunga Tonga-Hunga Ha'apai volcano produced violent atmospheric fluctuations,which in turn generated a global tsunami through an abrupt air pressure shock upon the sea surface.Two main components of tsunami waves,phase-locked waves and free gravity waves,were identified by significant differences in propagating speeds across the deep ocean.The phase-locked wave propagated through the ocean basin synchronously with the atmospheric Lamb wave at an average speed of approximately 306 m/s,followed by the free gravity wave at a slower speed.The locked wave reached the coast of eastern Taiwan Island at about 20:00 on January 15,in coincidence with the Lamb wave arrival.However,on the coast of Chinese mainland,tidal gauges did not record tsunami signals until at least 2 h after the Lamb wave arrivals.Theoretical analyses and numerical experiments both suggested that as a result of the incoming wave shoaling above the vast continental shelf of Chinese mainland,the locked wave was no longer trapped by the air pressure shock and gradually transformed into freely-propagating shallow water waves by slowing down its propagation.Due to the longlasting planetary atmospheric fluctuations circling the earth many times,the sea level oscillations continuously propagated onto the Chinese shelf,which resulted in the tsunami waves excited along the Chinese coasts for at least 36 h.The maximum wave amplitude recorded on the coast of eastern Taiwan Island was 44 cm at Wushi,while on the coasts of eastern and southern Chinese mainland,the maximum amplitudes were 22 cm at Shipu and 13 cm at Zhuhai.Fourier and wavelet analyses were performed to identify the major components of the tsunami waves on the Chinese coasts.The results indicated that eastern Taiwan Island was impacted mainly by the waves with periods of approximately 10-40 min.Chinese mainland was hit by the evolved shallow water waves and subsequent free waves,with periods of approximately 40-100 and 16-20 min,respectively.
文摘The KAM theory can be used properly to describe the motion of the double pendulum if the gravity is treated as a perturbation. The existence of the KAM invariant closed curves represents that some characters of the “total generalized momentum” conservation of the gravity free system can be kept when the gravity is small in comparison with the total enery.
