ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY Lecture 17 Learning objectives: understand the concepts & physics of 1. Ekman layer 2. Ekman transport 3. Ekman pumping
1. The Ekman Layer Scale analyses show that: Interior Ocean: large scale ocean circulation obeys geostrophy; Ro<<1; E k <<1 Boundary layer (western boundary, surface layer, bottom boundary layer): geostrophy does not necessarily hold. Why? Critical thinking Oceanic surface: subject to forcing by winds, heat and salinity fluxes (buoyancy flux). Not solely in geostrophic balance.
1 The Ekman layer Fridtjof Nansen, Norwegian explorer: Fram: ship 1893-1896 expedition; Icebergs: 20-40 to the right of wind Walfrid Ekman, Swedish physicist, (1905) : Explained Nansen s observation The ocean surface boundary layer is sometimes called the Ekman layer, the layer in which the surface wind stress directly acts. This layer is sometimes called: mixed layer because oceanic properties (T & S) are often well mixed.
In fact: Ekman layer thickness & Mixed layer depth: are not exactly the same Ekman layer: determined by wind Ekman layer thickness: will be defined later (determined by viscosity & f) Mixed layer: wind & buoyancy driven-turbulent mixing Usually: the depth at which density increase is equivalent to 0.5C (some uses 1C, etc) temperature decrease
Vertical profiles of density, T, S Surface mixed layer
Surface mixed layer Thermocline Observed Temperature along EQ Pacific. Depth of 20C Isotherm (D20): Used to represent Thermocline depth Surface mixed layer Pycnocline σ = ρ 1000 (halocline: Vary a lot Regionally, not shown)
Surface wind exerts stress, on the ocean 1 2 Y s = 0 n X s = 0 Y s = 0 at the bottom of Ekman layer Laminar: layered flow; non-turbulent
Important: the ocean is viscous; assume stress linearly decreasing with depth (constant viscosity, laminar flow: non-turbulent). Force for a unit area: Top of layer 2, Top of layer 3, similarly, we can obtain stress for top of layer n.
The net stress working on layer n is: top - bottom Net stress in x, y directions: Force per unit mass: They are momentum fluxes: vertical flux of horizontal momentum
Consider small Rossby number (Ro<<1), steady, and constant density: the equations of motion in Ekman layer are: Stress X, Y decreases quickly with depth, their direct influence is felt only in the surface boundary layer.
z Surface Ekman layer: Ekman+geostrophic current Interior: Only geostrophic current Bottom Ekman layer x
Because Thus, Ekman current; Ekman flow
2. Ekman Transport Vertically integrate Ekman flow in the entire Ekman layer with depth H E, we obtain: U E = V E = 0 U E = u E dz = τ y,, H E ρ 0 f 0 HV E = v E dz = τ x E. H E ρ 0 f 0 0 (X,Y ) = 0@z = H E, (u E, v E ) = 0@z = H E. H E u E dz = τ y ρ 0 f 0 u Ex + v Ey + w Ez dz = 0 H E v dz = τ x E ρ 0 f Following boundary conditions are used: (X,Y ) = 0@z = H E, (u E, v E ) = 0@z = H E.
U E = u dz = τ y 0, H E E ρ f 0 NH V E = 0 H E v E dz = τ x ρ 0 f
Somalia Somali coastal upwelling (Western Indian Ocean) Summer monsoon
Somali coastal downwelling Somalia Winter monsoon
3. Ekman pumping Interaction between the surface Ekman layer and the interior ocean beneath Surface windstress varies spatially, z into Producing convergence and divergence of Ekman transports out x isopycnals
curlτ > 0 Downwelling upwelling Northern Hemisphere h E
Ekman convergence/divergence cause ispycnals move up and down, generating horizontal pressure gradient force in the ocean interior below the Ekman layer, and thus driving the deep ocean in motion. Surely, in the surface mixed layer, they cause both Ekman flow and geostrophic currents (the sum of the two). Note: this is in a linear system.
Ekman pumping can be clearly demonstrated by integrating the continuity equation: Or: Because We have 0 H E u Ex + v Ey + w Ez dz = 0 At z = H E ( is used in a baroclinic ocean) Ekman transports
U E = V E = u E dz = τ y 0, H E ρ 0 f 0 H E v E dz = τ x ρ 0 f So, w E = x ( τ y ρ f ) y ( τ x ρ f ) This expression is valid for both constant and varying density.
Winds => Ekman convergence, negative (downward) z into out x isopycnals curlτ > 0 h E