ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY Lecture 18 Learning objective: understand concepts & physical processes 1. Ekman transport: coastal and equatorial upwelling, fishery; 2. Ekman spiral: Ekman flow within the surface Ekman layer; 3. Bottom boundary layer; 4. Concepts review: turbulent mixed layer, thermocline & seasonal thermocline. Previous class • Ekman transport (volume transport)

• Ekman pumping

∂ τ y ∂ τ x w = ( )− ( ) E ∂x ρ f ∂y ρ f 1: Ekman transport & upwelling Previous class: Somali coastal Somalia upwelling (Western Indian Ocean summer monsoon)

Ekman transport: Coastal upwelling; Marine life. Units: Ekman current & volume transport

uE, vE : m/s, speed Ekman transport at a specific (lon,lat): m2/s

Usually, in research: we calculate Ekman transport across an area (e.g., along 50E, 5N-10N) within the mixed layer Hmix. Then, Ekman transport is: 3 UE × Ly : m /s 1 Sverdrup(sv) = 106m3/s) Wind-driven Coastal upwelling • Physical description: Alongshore winds – offshore surface Ekman divergence – coastal upwelling (colder, subsurface water upwells to the surface layer);

• Mathematics: UEx +VEy > 0,

w E =UEx +VEy > 0, upwelling. The above equation comes from: Northeast Pacific & Atlantic: Wind-driven Coastal upwelling, fishery

Southeast Pacific & Atlantic TAO data in the eastern Pacific: Color: SST; black arrow: winds;White arrow: Ekman transport

Coastal & Equatorial Upwelling! Critical thinking questions • Can offshore wind (perpendicular to the coast) induce coastal upwelling/downwelling?

• Assume the Ekman layer is 50m thick; at 10m depth, Ekman flow is 90degree to the right of the wind. Is this correct?

2. Ekman Spiral: Ekman flow within the surface Ekman layer Vertical structure of flow within the Ekman layer Ekman 1905: a simple wind-driven ocean model Assumptions: viscous, laminar boundary layer Non-turbulent (Re is small) Ekman assumed: internal stress is balanced by viscosity Recall that in the Ekman layer:

Applying

We have: Using boundary conditions: as

and

at z=0,

Equations

yield: Important features: 2A a) The Ekman layer thickness is H = z , which Ekman f is the e-folding decay scale of Ekman flow. The stronger the viscosity, the thicker the Ekman layer. b) The flow in the Ekman layer is not in geostrophic balance because viscosity is so important. c) Ekman transport is the vertical integral of Ekman spiral. Ekman spiral Critical thinking questions

• Assume the Ekman layer is 50m thick; at 10m depth, Ekman flow is 90degree to the right of the wind. Is this correct?

3. Bottom Ekman layer

Surface Ekman

geostrophy

Bottom Ekman

Bottom drag due to roughness and torques due to bathymetry can affect fluid motion; Currents slow down or use: . No slip boundary condition For a flat bottom ocean, when the interior geostrophic flow approaches the bottom, it is slown down by the bottom drag. Following similar procedure, we can obtain bottom Ekman layer thickness: 4. Turbulent mixed layer Turbulent S T Mixed layer (not laminar!)

Definition (often used by researchers): The depth at where T decreases by 0.5C from the SST; or density increases by a value that is equivalent of 0.5C decrease. Vertical mixing processes can be affected by: Wind mechanical stirring (Kraus-Turner Mixed layer physics: Kraus and Turner 1967);

Surface cooling that weakens stratification; Shear instabilities (K-H), baroclinic instabilities

Critical thinking Questions

Validity of Ekman Spiral solution: In reality, Ekman Spiral is very difficult to observe. Why??

(a) Real ocean is turbulent, rather than laminar; (b) geostrophic component sometimes can obscure the Ekman component. Thermocline & seasonal thermocline a) Thermocline heating T

Thermocline theory: Pedlosky 1987. Wind-driven ocean circulation: Won’t be covered in this class. Vertical diffusion can not balance vertical advection, because of diffent timescales. b) Seasonal thermocline

winter Spring,sst=29C Seasonal thermocline

A challenging question:

Assume both the western and eastern boundaries of an ocean are subjected to upwelling favorable wind forcing only during April-September season of each year.

In your opinion, how does the eastern and western boundary upwelling affect the ocean interior? What’s the major different?