Dr. Grumbine: What is your opinion on the shortcomings of the Boussinesq approximation, if any, in oceanic models ? ( i refer to ignoring dro/rho tems unless multiplied by g)
but it gets the volume wrong...this has been causing me unquiet and anxiety for some tie, have you any thoughts ?
Sorry about the delay sidd. Back when I was taking geophysical fluid dynamics, I was concerned about the approximations we would make, including the Boussinesq. As I remember it, of all the approximations, Boussinesq was one of the best -- as long as the ocean is markedly less than 200 km deep (the average being a bit less than 4 km, and extreme is about 10 km). Rather, the scale of vertical motions in the ocean. Since I was concerned with deep convection in the ocean, the depth of the ocean was what I had to pay attention to.
Volume is a different concern. The Boussinesq approximation applies only to the conservation of momentum equation. Mass conservation is in the drho/dt + div(u*rho) = 0, which is accurately simplified to div(u*rho) = 0 if you ignore sound waves in the ocean. But mass is a somewhat different issue than volume. Volume (and density) conservation properly requires tracking conservation of energy (temperature) and salinity. But, again, both of these are indeed tracked in ocean models, necessarily.
The potentially ugly part comes in dealing with the effects of salinity changes on density, through to volume (sea surface elevation). It is common to treat the mass conservation from surface waves as d(surface)/dt + div(u*H) = 0. This ignores density variation, which is a good, but not perfect approximation. Separately precipitation/evaporation and freeze/melt of ice are tracked in the salt conservation, but may not be allowed to affect the sea surface height, which is a less good approximation.
This is where I'd look in a model for concerns about volume (and thence sea level). Some do indeed include the sea level effect of the temperature and salinity variations.
Dr. Grumbine: What is your opinion on the shortcomings of the Boussinesq approximation, if any, in oceanic models ? ( i refer to ignoring dro/rho tems unless multiplied by g)
ReplyDeletebut it gets the volume wrong...this has been causing me unquiet and anxiety for some tie, have you any thoughts ?
sidd
Sorry about the delay sidd. Back when I was taking geophysical fluid dynamics, I was concerned about the approximations we would make, including the Boussinesq. As I remember it, of all the approximations, Boussinesq was one of the best -- as long as the ocean is markedly less than 200 km deep (the average being a bit less than 4 km, and extreme is about 10 km). Rather, the scale of vertical motions in the ocean. Since I was concerned with deep convection in the ocean, the depth of the ocean was what I had to pay attention to.
ReplyDeleteVolume is a different concern. The Boussinesq approximation applies only to the conservation of momentum equation. Mass conservation is in the drho/dt + div(u*rho) = 0, which is accurately simplified to div(u*rho) = 0 if you ignore sound waves in the ocean. But mass is a somewhat different issue than volume. Volume (and density) conservation properly requires tracking conservation of energy (temperature) and salinity. But, again, both of these are indeed tracked in ocean models, necessarily.
The potentially ugly part comes in dealing with the effects of salinity changes on density, through to volume (sea surface elevation). It is common to treat the mass conservation from surface waves as d(surface)/dt + div(u*H) = 0. This ignores density variation, which is a good, but not perfect approximation. Separately precipitation/evaporation and freeze/melt of ice are tracked in the salt conservation, but may not be allowed to affect the sea surface height, which is a less good approximation.
This is where I'd look in a model for concerns about volume (and thence sea level). Some do indeed include the sea level effect of the temperature and salinity variations.