Sensitivity of Internal Structure to the Surface Boundary Condition

1977 ◽  
pp. 137-142
Author(s):  
Pierre Demarque
Keyword(s):  
Boundary Condition ◽  
Internal Structure ◽  
Surface Boundary ◽  
Surface Boundary Condition

scholarly journals Sensitivity of Internal Structure to the Surface Boundary Condition

1977 ◽  
Vol 4 (2) ◽  
pp. 137-142
Author(s):  
Pierre Demarque
Keyword(s):  
Boundary Condition ◽  
Internal Structure ◽  
Stellar Structure ◽  
Surface Boundary ◽  
Surface Layers ◽  
Surface Boundary Conditions ◽  
Deep Interior ◽  
Cool Stars ◽  
Surface Boundary Condition ◽  
Approach Zero

It is now nearly fifty years since Eddington and Milne had a lively controversy on the importance of the surface boundary condition on the internal structure of stars [see Eddington (1930) and Milne (1930)]. We remember that Eddington believed that the internal structure of stars is basically determined by the physical processes occurring in the deep interior and that what happens in the surface layers has little effect on the total stellar luminosity. On the other hand, Milne emphasized the importance of the properties of the outer layers and the effect these could have on the run of pressure and temperature in the deep interior of the stars. We know now that both Eddington and Milne were correct. Eddington’s considerations apply to the hot stars, the early-type stars which have surface layers in radiative equilibrium. Milne’s arguments are relevant to the cool stars, the late-type stars which have deep convective envelopes. In the former case, one can safely assume in calculations of stellar structure that the density and the temperature both approach zero simultaneously at the surface (the so-called “zero” surface boundary conditions).

scholarly journals Relating the Diffusive Salt Flux just below the Ocean Surface to Boundary Freshwater and Salt Fluxes

2019 ◽  
Vol 49 (9) ◽  
pp. 2365-2376 ◽  
Author(s):  
A. J. George Nurser ◽  
Stephen M. Griffies
Keyword(s):  
Boundary Condition ◽  
Mass Conservation ◽  
Ocean Surface ◽  
Boussinesq Approximation ◽  
Specific Form ◽  
Salt Flux ◽  
Surface Boundary ◽  
Flux Balance ◽  
Surface Boundary Condition ◽  
Diffusive Fluxes

AbstractWe detail the physical means whereby boundary transfers of freshwater and salt induce diffusive fluxes of salinity. Our considerations focus on the kinematic balance between the diffusive fluxes of salt and freshwater, with this balance imposed by mass conservation for an element of seawater. The flux balance leads to a specific balanced form for the diffusive salt flux immediately below the ocean surface and, in the Boussinesq approximation, to a specific form for the salinity flux. This balanced form should be used in specifying the surface boundary condition for the salinity equation and the contribution of freshwater to the buoyancy budget.

On the Suspended Sediment Concentration Profile

2012 ◽  
Vol 212-213 ◽  
pp. 20-24 ◽  
Author(s):  
Chen Cheng ◽  
Zhi Yao Song ◽  
Yi Gang Wang ◽  
Jin Shan Zhang
Keyword(s):  
Boundary Condition ◽  
Suspended Sediment ◽  
Suspended Sediment Concentration ◽  
Order Approximation ◽  
Sediment Concentration ◽  
Suspended Sediment Transport ◽  
Surface Boundary ◽  
Sediment Diffusion Coefficient ◽  
Surface Boundary Condition ◽  
First Order Approximation

After analyzing the surface-boundary condition of suspended sediment concentration (SSC), Cheng et al.[7] further improved the sediment diffusion coefficient which was proposed by Bose and Dey[6]. Then an improved Rouse law (IRL) was developed. This equation, which has a similar form as Rouse law, not only overcomes the zero concentration at the free surface, but also behaves generally better than Rouse law and van Rijn equation over the whole water depth in the verification analysis. In this paper, the surface-boundary condition of SSC is further analyzed. It is elucidated that IRL satisfies the surface-boundary condition more reasonably than Rouse law. In addition, a first-order approximation of IRL is developed. From this approximation, we can easily get the explicit expression of the depth-averaged SSC without any implicit integrals to be solved numerically or by the help of a chart. This is very useful in the further study of non-equilibrium suspended sediment transport (SST).

Sign in / Sign up

Export Citation Format

Share Document