Theoretical Solutions Of Propagation Of Internal Waves And Generation Of Internal Tides Over Some Kinds Of Topographies

The ocean circulation is controlled by diapycnal mixing which consists of mechanical mixing and convective mixing. The intensity of mechanical mixing depends on the amount of mechanical energy offered by external processes, among which wind stress and tidal generation force are major sources. Internal waves are a kind of bridge relating the diapycnal mechanical mixing to external sources of mechanical energy: first, internal waves are driven by wind stress and barotropic tide so that large amount of mechanical energy are transported to abyssal ocean with propagation of internal waves; second, the mechanical energy can directly be cascaded to mixing through instability and breaking of internal waves. So it is important and essential to further investigate the generation of internal tides and the propagation of internal waves over bottom topographies.A sets of transforms are introduced in this dissertation, by using of which some kinds of topographies, such as continental slope and ridge, can be converted into flat bottom. The processing simplifies the generation of internal tides and reflection of internal waves over those kinds of topographies.Propagation of internal waves over linear slope, convex slope and concave slope are discussed by using of the transforms introduced in this dissertation. The transforms let the reflected waves from those topographies can be expressed in analytical forms. It is found that: (1) for linear slope, redistribution of incoming energy flux in modenumber space depends on both the modenumber of incident waves and the ratio of the slope of incident wave ray to slope of topography; both the transmitted and reflected energy flux(only for supercritical linear slope) focus near one or two modenumbers; for supercritical linear slope, the energy flux scattering to higher modenumbers becomes larger and the energy flux to lower modenumbers becomes smaller as the slope of incident wave ray comes near to slope of topography; (2) for convex slope, energy flux is redistributed in wide-range modenumbers and also show peaks on lower-modenubers and higher-modenumbers; (3) for concave slope, energy flux is also redistributed in wide-range modenumbers, but does not show peaks on higher-modenumbers as supercritical linear slope and convex slope do; (4) the total energy flux scattering to higher modenumbers is approximately equal tothe total energy flux to lower modenumbers for internal waves propagating over both convex slope and concave slope, which means the concave slope is the same efficient to convex slope in scattering energy flux to higher modenumbers; (5) for convex slope, the wave ray reflected from near-critical topography can extend to deep ocean and shallow shelf, while for concave slope, the wave ray reflected from near-critical topography can only extend to limited distance, then meet the topography and be reflected again; generally the shear of the internal waves reflected twice from concave slope is not enhanced while the enhanced shear does also appear before second reflection takes place, the enhanced shear can bring about intense mixing, so internal waves reflected from concave slope can also produce marked mixing near critical slope.Internal tides generated over some kinds of topographies (such as continental slope and shelf, ridge topography) are investigated by using of the transforms introduced in this dissertation. Due to nonlinear bottom boundary condition, the generation of internal tides over finite topography can only be deal with by using of ray-tracing method beforetime. The transforms introduced in this dissertation make it possible use eigenvalue method to investigate the generation of internal tides over finite topographies. One dimensional equation can be obtained through extending the stream function and forcing term into fourier series, and this equation can be solved by assuming the traveling-wave solution. Besides converting the topographies to flat bottom, the transforms also change the distribution of forcing. For subcritical topography, the inten...