In this study we concentrate on the perturbations of pressure and density caused by thermohaline and expect to discuss the instability of the primitive equations of stratified flows for non hydrostatic internal waves...In this study we concentrate on the perturbations of pressure and density caused by thermohaline and expect to discuss the instability of the primitive equations of stratified flows for non hydrostatic internal waves. Traditionally, under the assumption of hydrostatic pressure, the Lagrangian derivative of the vertical velocity is ignored and the vertical velocity can be computed by integrating the continuity equation. In the process of dense water formation, on the basis of a quasi non hydrostatic perturbation pressure, the time derivative of the vertical velocity and the Coriolis term in the vertical momentum equation are included. With non hydrostatic approach we obtain three typical forms of the instability with Synge′s theorem, Miles′ theorem and Howard′s semicircle theorem. With the non hydrostatic Synge′s theorem, the Coriolis acceleration appears while stratification exists. The non hydrostatic conclusions derived by Miles′ theorem and Howard′s semicircle theorem are the same as their hydrostatic counterparts.展开更多
文摘In this study we concentrate on the perturbations of pressure and density caused by thermohaline and expect to discuss the instability of the primitive equations of stratified flows for non hydrostatic internal waves. Traditionally, under the assumption of hydrostatic pressure, the Lagrangian derivative of the vertical velocity is ignored and the vertical velocity can be computed by integrating the continuity equation. In the process of dense water formation, on the basis of a quasi non hydrostatic perturbation pressure, the time derivative of the vertical velocity and the Coriolis term in the vertical momentum equation are included. With non hydrostatic approach we obtain three typical forms of the instability with Synge′s theorem, Miles′ theorem and Howard′s semicircle theorem. With the non hydrostatic Synge′s theorem, the Coriolis acceleration appears while stratification exists. The non hydrostatic conclusions derived by Miles′ theorem and Howard′s semicircle theorem are the same as their hydrostatic counterparts.
