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- Author or Editor: G. S. Janowitz x

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## Abstract

A formula for the barotropic Rossby wave drag exerted by an arbitrary shallow topography on a homogeneous eastward flow is obtained under the requirements that *U*/*f*
_{0}
*L*â‰ª1, *h _{M}
*/

*H*=

*O*(

*U*/

*f*

_{0}

*L*) and

*L*<

*L*â‰¡(

_{W}*U*/Î²)

^{Â½}, where

*U*is the speed of the flow,

*h*, the maximum height of the topography,

_{M}*L*the horizontal scale of the topography and

*H*the vertical distance between the horizontal planes confining the flow. The drag force,where

*V*is the volume of the topography, Î“(â‰¡

*f*

_{0}

*V*/

*H*) is the topographically induced circulation, and

*X*Â¯,

^{k}*Y*Â¯=âˆ«âˆ«(

^{k}*X*,

^{k}*Y*)h(

^{k}*x*,

*y*)

*dxdy*/

*V*. A typical case is computed and the wave drag per unit area is found to be approximately 1.3 N m

^{âˆ’2}. This implies an energy dissipation rate of 20 W m

^{âˆ’2}which is comparable to the kinetic energy generated in a cyclone, and is several times that due to frictional dissipation. The effects of stratification and compressibility are discussed; the former generally has no effect on the drag while the latter increases the drag by a factor of 1.6.

## Abstract

A formula for the barotropic Rossby wave drag exerted by an arbitrary shallow topography on a homogeneous eastward flow is obtained under the requirements that *U*/*f*
_{0}
*L*â‰ª1, *h _{M}
*/

*H*=

*O*(

*U*/

*f*

_{0}

*L*) and

*L*<

*L*â‰¡(

_{W}*U*/Î²)

^{Â½}, where

*U*is the speed of the flow,

*h*, the maximum height of the topography,

_{M}*L*the horizontal scale of the topography and

*H*the vertical distance between the horizontal planes confining the flow. The drag force,where

*V*is the volume of the topography, Î“(â‰¡

*f*

_{0}

*V*/

*H*) is the topographically induced circulation, and

*X*Â¯,

^{k}*Y*Â¯=âˆ«âˆ«(

^{k}*X*,

^{k}*Y*)h(

^{k}*x*,

*y*)

*dxdy*/

*V*. A typical case is computed and the wave drag per unit area is found to be approximately 1.3 N m

^{âˆ’2}. This implies an energy dissipation rate of 20 W m

^{âˆ’2}which is comparable to the kinetic energy generated in a cyclone, and is several times that due to frictional dissipation. The effects of stratification and compressibility are discussed; the former generally has no effect on the drag while the latter increases the drag by a factor of 1.6.

## Abstract

The effects of compressibility on a stably stratified eastward flow of air over a shallow topography in the beta plane are considered. The incompressible response of the flow to the topography is composed of a barotropic Rossby wave disturbance which extends far downstream and a baroclinic response which decays away from the topography. Compressibility increases the barotropic response by a factor of 1.6 and enhances that baroclinic response with height. The problem is formulated and a general solution obtained which includes the effects of shear in the approaching flow. The effects of shear are presently being studied and it appears that under certain circumstances shear may eliminate the Rossby wave response and thus localize the topographic disturbance.

## Abstract

The effects of compressibility on a stably stratified eastward flow of air over a shallow topography in the beta plane are considered. The incompressible response of the flow to the topography is composed of a barotropic Rossby wave disturbance which extends far downstream and a baroclinic response which decays away from the topography. Compressibility increases the barotropic response by a factor of 1.6 and enhances that baroclinic response with height. The problem is formulated and a general solution obtained which includes the effects of shear in the approaching flow. The effects of shear are presently being studied and it appears that under certain circumstances shear may eliminate the Rossby wave response and thus localize the topographic disturbance.

## Abstract

The effects of vertical shear on a steady eastward flow of a compressible, stably stratified fluid over a shallow topography in the beta plane are examined using a theory developed earlier by one of the authors (Janowitz, 1977). Shear increases the wavelength and decreases the particle deflections associated with the orographically generated Iee Rossby wave. These changes are greater than can be accounted for by replacing the sheared flow with an unsheared flow of equivalent mean or root-mean-square velocity. In addition, the vertical variation of the downstream wave is determined to he negligible for all cases considered. By superposing Green's function solutions, a realistic simulation of the Rocky Mountains and the Andes Mountains is achieved. Comparison with actual data verifies that orographic effects are the primary factor causing the deflection of the winter westerlies over the United States, and that the high upstream vertical shear is responsible for the smaller amplititude of the wave associated with the Andes.

## Abstract

The effects of vertical shear on a steady eastward flow of a compressible, stably stratified fluid over a shallow topography in the beta plane are examined using a theory developed earlier by one of the authors (Janowitz, 1977). Shear increases the wavelength and decreases the particle deflections associated with the orographically generated Iee Rossby wave. These changes are greater than can be accounted for by replacing the sheared flow with an unsheared flow of equivalent mean or root-mean-square velocity. In addition, the vertical variation of the downstream wave is determined to he negligible for all cases considered. By superposing Green's function solutions, a realistic simulation of the Rocky Mountains and the Andes Mountains is achieved. Comparison with actual data verifies that orographic effects are the primary factor causing the deflection of the winter westerlies over the United States, and that the high upstream vertical shear is responsible for the smaller amplititude of the wave associated with the Andes.

## Abstract

A simple model of time-dependent quasi-geostrophic upwelling over an outer continental shelf and slope region is considered with the velocity assumed independent of the alongshore coordinate The flow is at rest and stably stratified when a uniform alongshore wind stress Ï„ is applied. Initially, the onshore flow in the water column balances the offshore top Ekman volume flux. As time progresses the bottom Ekman layer supplies increasingly more of the required onshore flux and the onshore flow in the interior of the water column decreases. The shallower water spins up first leading to both a coastal jet and an upward bulge in the isopycnal surfaces which propagates offshore with a speed equal to 0.012(Ï„/*p*)^{Â½}/*h _{x}
*, where

*h*is the local slope. At the shelf break, if

_{x}*h*/

_{xx}h*h*

_{x}^{2}>2 another upward bulge of the isopycnal surfaces will develop at the onset of upwelling favorable winds and will be of greater amplitude than the propagating bulge. The theory is generalized to include the effects of a time-dependent wind stress and those of a specified time-dependent alongshore pressure gradient. The velocity induced by the deformation of the density field is then calculated. Comparisons of theory with moored meter data collected in Onslow Bay, North Carolina are made during upwelling favorable summertime wind conditions.

## Abstract

A simple model of time-dependent quasi-geostrophic upwelling over an outer continental shelf and slope region is considered with the velocity assumed independent of the alongshore coordinate The flow is at rest and stably stratified when a uniform alongshore wind stress Ï„ is applied. Initially, the onshore flow in the water column balances the offshore top Ekman volume flux. As time progresses the bottom Ekman layer supplies increasingly more of the required onshore flux and the onshore flow in the interior of the water column decreases. The shallower water spins up first leading to both a coastal jet and an upward bulge in the isopycnal surfaces which propagates offshore with a speed equal to 0.012(Ï„/*p*)^{Â½}/*h _{x}
*, where

*h*is the local slope. At the shelf break, if

_{x}*h*/

_{xx}h*h*

_{x}^{2}>2 another upward bulge of the isopycnal surfaces will develop at the onset of upwelling favorable winds and will be of greater amplitude than the propagating bulge. The theory is generalized to include the effects of a time-dependent wind stress and those of a specified time-dependent alongshore pressure gradient. The velocity induced by the deformation of the density field is then calculated. Comparisons of theory with moored meter data collected in Onslow Bay, North Carolina are made during upwelling favorable summertime wind conditions.

## Abstract

An analytical model is developed to describe the steady flow in an estuary-shelf interaction region where the system is treated as a two layer density stratified flow. The motion is expanded in terms of the relative thickness of the vertical Ekman layer. The zero-order flow is geostrophic in each layer. Balancing of order-one quantities reduces the system to two vorticity equations relating the pressure field with the displacement of the interface and the bottom topography. An explicit solution is obtained for the case of linear offshore sloping bottom. The flow behavior of the estuarine plume depends on the vertical structure of the flow at the river mouth, the bottom slope and the ambient coastal flow. Under certain conditions. a front exists as an offshore boundary of the plume. These results are compared with observations for the Changjiang River Estuary (in China), and both the Chesapeake Bay and Savannah River estuaries in the United States.

## Abstract

An analytical model is developed to describe the steady flow in an estuary-shelf interaction region where the system is treated as a two layer density stratified flow. The motion is expanded in terms of the relative thickness of the vertical Ekman layer. The zero-order flow is geostrophic in each layer. Balancing of order-one quantities reduces the system to two vorticity equations relating the pressure field with the displacement of the interface and the bottom topography. An explicit solution is obtained for the case of linear offshore sloping bottom. The flow behavior of the estuarine plume depends on the vertical structure of the flow at the river mouth, the bottom slope and the ambient coastal flow. Under certain conditions. a front exists as an offshore boundary of the plume. These results are compared with observations for the Changjiang River Estuary (in China), and both the Chesapeake Bay and Savannah River estuaries in the United States.