# Topic 3: surface ocean circulation

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## I. INTRODUCTION

1. The driving force for the ocean’s surface currents comes from winds

• Winds push the water at the surface of the ocean (<100m)

• Horizontal Pressure Gradients are produced when winds pile up surface water in some regions and remove surface water from other regions

• The strength and direction of surface ocean currents depends on strength and direction of winds, horizontal pressure gradient forces and the Coriolis Force

2. There are consistent features of the ocean’s surface circulation (Fig. 1)

• Subtropical Gyres are large regions of clockwise or counterclockwise rotating currents found in both hemispheres and in all ocean basins

• East-west (zonal) currents are found in the Equatorial Ocean and the Antarctic Circumpolar Current in the Southern Ocean

3. NOTE: The surface circulation shown in Figure 1 represents the generalized typical pattern of surface circulation averaged over many years

- there are day to day, month to month and year to year changes in this pattern because wind patterns change over these time scales
4. Why is there an organized pattern to the surface currents in the ocean? Why don’t currents move in random directions?

- because winds that drive surface currents have an organized pattern of motion on large spatial scales (hundreds and thousands of kilometers) and over long time scales (years or decades)

II. WHAT HAPPENS WHEN WIND BLOWS OVER THE OCEAN?
A. Wind Stress
1. Winds blowing over the ocean exert a force on the surface water that it contacts

• this transfer of energy between the wind and ocean occurs because of friction

• friction couples the water movement to the air movement

• without friction there wouldn't be any transfer of wind energy to the ocean

2. The wind force acting on the surface of ocean is called wind stress and is denoted by Tau (t)

• wind stress is a force that acts in the direction that the wind is blowing on the surface

• in contrast, pressure is a force that acts perpendicular to the surface

3. Wind stress depends strongly on wind speed, i.e., the faster the wind, the greater the stress

• Tau (t) = r*c*U2, where U is wind speed (m/s at ~10m height), ‘c’ is a proportional constant (unitless), and r is air density (~1.3 kg/m3)

• c is called the Drag Coefficient and accounts for the ability of wind to drag the ocean water with it and is a measure of the efficiency of transfer of wind energy to the ocean

• c has been empirically (by experiment) determined to be in the range of 0.001 to 0.003 (unitless)

• c depends in part on roughness of the ocean surface (presence of waves)

4. Forces

• Remember that a Force = mass * acceleration (F = ma)

• Where acceleration is the time rate of change of velocity (how fast the velocity is increasing or decreasing)

• Thus the units for Force must be, for example, kg *(m/sec2)

• Newtons are the units of Force, where 1 Newton = 1 kg (m/s2)

• Thus, it takes 1 Newton of force to increase the speed of 1 kilogram of mass by 1 meter per second every second

5. Wind stress () is a Force per unit area

• Thus  = mass*acceleration/area

• the units of stress should be kg*(m/s2)/m2

• so  is in Newton/m2

• Stress is a force that acts in the same plane as the water surface

6. Example of wind stress calculation

• Assume wind speed = 10 m/s, drag coefficient [c] = 0.002 and air density = 1.3 kg/m3

• so  = 0.002 * 1.3 kg/m3 * (10 m/s)2

= 0.26 kg/m3 * m2/s2 = 0.26 kg*(m/s2)/m2

= 0.26 Newtons/m2

7. Wind stress is the force that causes the surface layer of the ocean to move
8. Does wind stress drag only a very thin layer of water molecules in direct contact with the wind?

• No. Water has a property called viscosity that ‘links’ neighboring parcels of water

• the viscosity of a fluid transfers the movement of parcels of water to neighboring water parcels

• viscosity also results in a friction force that opposes motion, that is, the linkages to other neighboring water parcels resists the movement of the parcel of water (viscosity causes the neighboring water parcels to exert a drag on the moving water parcel)

9. Mixing (or turbulence) in the ocean is a process that effectively uses the viscosity of seawater to transfer the energy of the wind downward through the ocean.

• turbulence is the random movement of parcels of waters

-in contrast a current is organized flow of water in a certain direction

• without turbulence, the currents produced by wind blowing on the ocean’s surface would not be measurable below a depth of 2m even after 2 days of constant winds

• with turbulence, this same wind produces water motion to a depth of ~100 meters

10. Viscosity and turbulent mixing transfers the wind stress force exerted at the surface of the ocean downward to water parcels that are not directly exposed to the wind

B. Steady Surface Currents Resulting from Constant Winds
1. Despite being exposed to steady winds, the surface ocean current velocities aren’t continuing to increase with time. Why not?

• Let’s start with an ocean at rest (no motion) and no wind

• When the wind starts, the water begins to move because there has been a force (wind stress) exerted on the surface layer of the ocean

• Since Force = mass * acceleration, when the wind stress force begins the ocean water begins to accelerate and increase its velocity

• However as the wind continues to blow (assuming a constant wind speed and direction), we notice that eventually the current reaches a constant speed (no longer accelerating) and constant direction. Why does this happen?

2. When a water parcel is no longer accelerating despite the continued input of wind stress, this situation implies that the net force exerted on the water must be zero. Another way to say this is that there is a force balance when the net force equals zero and, as a result, acceleration equals zero.

• A force balance exists when the force causing the currents to accelerate (wind stress) is exactly offset (or balanced) by a force (or forces) opposing the wind stress force

• thus under steady winds, ocean currents ultimately reach a velocity and direction that cause a force balance to exist in response to a constant input of wind stress force

3. A force balance must exist in the surface ocean to keep ocean currents from constantly accelerating over time as the winds continue to blow day after day (year after year, etc.)

• to achieve a force balance a force is needed that opposes current flow

• Frictional force is one such force

4. Frictional force opposes current flow and increases as the current speed increases

• Thus the frictional force would build up, as current speed increases, to a point where the frictional force opposing motion equaled the wind stress force causing motion

• at this point, a force balance between wind stress and friction would exist, the net force on the water parcel would be zero, thus acceleration would be zero and, as a result, the current speed would no longer increase

• frictional forces are most important near the ocean boundaries (i.e., the atmosphere-ocean boundary, ocean-sea floor boundary)

5. However, on a rotating earth the Coriolis Force also impacts the force balance affecting currents

-once the water begins to move, in response to wind stress, a Coriolis Force is exerted which will attempt to deflect the current (to the right in the northern hemisphere and to the left in the southern hemisphere).

6. Thus there are three forces that influence the speed and direction of currents in the surface layer of the ocean, i.e., wind stress, friction, and Coriolis forces.

7. Thus in the surface ocean, a constant current speed (and direction) occurs under the influence of steady winds, when a force balance exists between wind stress, friction and Coriolis forces.

-note that both Frictional force and Coriolis force increase as the current velocity increases.

-in contrast, if the wind speed is steady, then wind stress force remains constant over time