TY - JOUR
T1 - Top-to-bottom Ekman layer and its implications for shallow rotating flows
AU - Cushman-Roisin, Benoit
AU - Deleersnijder, Eric
PY - 2018
Y1 - 2018
N2 - The analytical solution is derived for rotational frictional flow in a shallow layer of fluid in which the top and bottom Ekman layers join without leaving a frictionless interior.This vertical structure has significant implications for the horizontal flow. In particular, for a layer of water subjected to both a surface wind stress and bottom friction, the vorticity of the horizontal flow is a function not only of the curl of the wind stress (the classical result for deep water known as Ekman pumping) but also of its divergence. The importance of this divergence term peaks for a water depth around 3 times the Ekman layer thickness. This means that a curl-free but non-uniform wind stress on a shallow sea or lake can, through the dual action of rotation and friction, generate vorticity in the wind-driven currents. We also find that the reduction of three-dimensional dynamics to a two-dimensional model is more subtle than one could have anticipated and needs to be approached with utmost care. Taking the bottom stress as dependent solely on the depth-averaged flow, even with some veering, is not appropriate. The bottom stress ought to include a component proportional to the surface stress, which is negligible for large depths but increases with decreasing water depth.
AB - The analytical solution is derived for rotational frictional flow in a shallow layer of fluid in which the top and bottom Ekman layers join without leaving a frictionless interior.This vertical structure has significant implications for the horizontal flow. In particular, for a layer of water subjected to both a surface wind stress and bottom friction, the vorticity of the horizontal flow is a function not only of the curl of the wind stress (the classical result for deep water known as Ekman pumping) but also of its divergence. The importance of this divergence term peaks for a water depth around 3 times the Ekman layer thickness. This means that a curl-free but non-uniform wind stress on a shallow sea or lake can, through the dual action of rotation and friction, generate vorticity in the wind-driven currents. We also find that the reduction of three-dimensional dynamics to a two-dimensional model is more subtle than one could have anticipated and needs to be approached with utmost care. Taking the bottom stress as dependent solely on the depth-averaged flow, even with some veering, is not appropriate. The bottom stress ought to include a component proportional to the surface stress, which is negligible for large depths but increases with decreasing water depth.
KW - Coriolis force
KW - Ekman layer
KW - Ekman pumping
KW - Shallow water
KW - Two-dimensional modeling
UR - http://www.scopus.com/inward/record.url?scp=85049603575&partnerID=8YFLogxK
U2 - 10.1007/s10652-018-9611-y
DO - 10.1007/s10652-018-9611-y
M3 - Article
AN - SCOPUS:85049603575
SN - 1567-7419
VL - 19 (2019)
SP - 1105
EP - 1119
JO - Environmental Fluid Mechanics
JF - Environmental Fluid Mechanics
ER -