Lecture 5: Wind-stress and Ekman layers Atmosphere, Ocean, Climate Dynamics EESS 146B/246B Wind-stress and Ekman layers • Distribution of the wind and wind-stress over the oceans. • Wind-driven turbulence. • Ekman layers • Ekman transport and pumping/suction. Atmospheric circulation Polar cell Ferrel cell Hadley cell •Rotation causes the atmospheric circulation to form three overturning cells: the Hadley, Ferrel, and Polar cells. •The Coriolis force causes winds to veer to the east or west, driving the trade winds, westerlies, and polar easterlies. Hadley cell in the lab SUBTROPICS SUBTROPICS TRADE WINDS EQUATOR EQUATOR Atmospheric circulation Westerlies Trade winds Westerlies Animation of water vapor in the atmosphere observed from a satellite Winds at the surface of the ocean Polar Easterlies Westerlies Trade Winds Westerlies •Winds measured at the sea surface via satellites reflect the large scale atmospheric circulation. Distribution of the wind-stress Relation between the wind-stress and the frictional force stress= - momentum flux MOMENTUM FLUX z Force equals net flux of momentum into volume x Force per unit volume Frictional Force=Force per unit mass Turbulence in the upper ocean •Winds blowing over the ocean induce sheared flows and waves that generate turbulence. This turbulence transfers the momentum imparted by the winds down into the ocean. Numerical simulation of wind-driven turbulence WIND STRESS The correlation between the vertical and horizontal turbulent velocity shows how turbulence transfers momentum downwards Parameterization of the turbulent momentum flux •Turbulence tends to flux momentum down the gradient of the mean flow in an analogous fashion to the viscous transfer of momentum. •Thus the turbulent flux of momentum can be parameterized in terms of a down-gradient flux with an eddy viscosity Typical eddy viscosity in the upper ocean Kinematic (molecular) viscosity of water Wind-driven acceleration without rotation depth WIND-STRESS Down-wind velocity Frictional force and acceleration •Without rotation, friction accelerates a flow that diffuses downward, extending through the water column over time. Wind-driven acceleration with rotation depth WIND-STRESS Down-wind velocity Frictional force Acceleration •With rotation, after a time Coriolis force friction is balanced by the Coriolis force. •The wind-driven flow is confined to the surface in an Ekman layer thick. Ekman force balance and transport •In the Ekman layer the frictional force is balanced by the Coriolis force. •Integrating the force balance in the vertical yields the net mass transport per unit length associated with the Ekman flow Ekman spiral and transport WIND Ekman transport N. HEMISPHERE •The Ekman flow spirals with depth, a phenomenon known as the Ekman spiral. •The net horizontal motion averaged in depth is to the right of the wind and is referred to as the Ekman transport. Ekman spiral and transport WIND Ekman transport S. HEMISPHERE •The Ekman transport is to the left of the wind in the Southern Hemisphere. Distribution of the wind-stress •What is the structure of the Ekman transport given the distribution of the wind-stress? Ekman pumping/suction •Convergence/divergence of the Ekman transport drives vertical motions: assume w=0 at z=0 vertical velocity at the beneath the Ekman layer Vertical motions associated with the curl of the wind-stress •When the Ekman vertical velocity is known as the Ekman pumping •When the Ekman vertical velocity is known as the Ekman suction Distribution of the Ekman pumping/suction suction •The Ekman vertical velocity is quite weak ~10s m/year but it is responsible for driving the circulation of the ocean gyres and the ACC.