Coastal Upwelling
Coastal Upwelling.
Coastal upwelling brings together many of the physical oceanographic processes that we’ve learned this year. —and thus is perhaps an excellent ending to the class. These include:
Wind stress
Ekman Transport
Ekman Depth
Rossby Radius
Continuity equation
Coastal upwelling occurs near a coast when the wind stress has a component in the along-shore direction with the shore to its left (in the Northern Hemisphere). In the case of New Jersey this would be a southerly wind (wind blowing to the north), while in California upwelling occurs when the wind blows from the north to the south. Note that in both cases upwelling occurs when the wind blows in a direction opposite to the direction of Kelvin wave propagation.
Upwelling occurs because the wind-driven Ekman transport in the surface layer is away from the coast—and this off-shore transport of surface water is replenished by an onshore transport of bottom waters. If the surface water is warm and the lower layer cold—as often is the case because cold water is heavier—then the upwelled water will be cold. Similarly, as often is the case, if the lower layer is nutrient rich then the upwelling will bring nutrient rich water up into the euphotic zone and drive a phytoplankton bloom. This is clearly seen in satellite imagery of an upwelling event along the US west coast that followed a period of persistent northerly winds.
Similarly, along the New JerseyShore southerly winds generate upwelling. In the summer months this can drop beach temperature to below 60 degrees in the middle of July!.
In fact fact this past year the upwelling was so persistent along the US east coast that it attracted the attention of the national media.
Interaction between bathymetry and tends to focus the upwelling in upwelling centers—and this give rise to the along-shore variability seen in the figure to the right. THe increased plankton growth associated with this upwelling—and concentration of the associated organic matter appears to produce regions of recurrent low dissolved oxygen along the New JerseyCoast.
If the wind began to blow to the north along the New Jersey coast a 10 m/s how long would it take for the thermocline to upwell?
We know that the wind stress, associated with this wind will be Cd W2, where Cd is a drag coefficient (let’s assume it is 1x10-3) and W is the wind speed. This corresponds to a surface wind stress of 0.1 Pa/m2.
We know that the Ekman Transport is
Where H is the Ekman depth.
In a two layer system—when the surface layer is shallow—we can often assume that the Ekman depth is equal to the depth of the surface mixed layer. This occurs because the strong stratification in the thermocline suppresses mixing and thus the wind stress is confined to the surface layer.
So the off-shore transport in the upper layer is , with f=10-4 1/s and kg/m3 the off shore transport is 1 m2/s.
To calculate the vertical velocity we need to use the continuity equation—which if we neglect along shore variability (i.e. dv/dy =0) – can be written as:
Integrating this vertically over the surface layer ( which we assume is the Ekman Layer) we get
Where wH is the vertical velocity at the base of the upper layer, and w0 is the vertical velocity of the sea surface. If we integrate the first term over the surface layer—this is simply the cross-shelf transport, which we know is and if assume that the vertical velocity at the surface is zero (this is not quite right—for the upwelling to occur requires the surface layer to drop down a cm or two and this drives the on-shore flow at depth—but most of the thinning of the upper layer is due to the upward vertical motion of the thermocline—so the assumption is valid) we get:
At the coast we know that the cross-shore transport is zero—and it increases to the Ekman transport-- -- approximately on internal Rossby Radius, R, from the coast than the cross shore divergence in the upper layer is simply which equals the upwelling velocity.
R is approximately 10 km and plugging rest of the values given above we f nind that the upwelling velocity is 0.1 mm/s or approximately 8 meters per day. Given that the surface mixed layer on the New Jersey shelf is typically 10 meter deep—upwelling will generally occur if a 10 m/s wind were to blow persistently for two days.
Note that the cross-shore Ekman flow appears in the along-shelf momentum equation because it includes the Coriolis term that involves the cross-shelf flow. What drives the bottom layer on-shore is the tilting down of the surface layer. This cross-shelf slope is expressed in the cross-shelf momentum equation.
In the interior geostropic flow would then be up the coast. In the cross shl
HOwever, other complications are:
Initial condition—for example if the cold water is far off-shore then it will take more time for upwelling to occur for the cold water must first move onshore.
Also this 2-dimensional model does not fully describe the upwelling that we observe because of complications arising due to bathymetry and spatial and temporal variability in the wind field.
Example include the one I showed in class where off-shore transport in the surface layer tends to agree with the Ekman Theory—but the on-shore transport in the lower layer does not—suggesting that upwelling is a fully 3-dimensonal process that cannot be fully described by this simple 2-dimenonal model.
Opposite of Upwelling is Downwelling.
Ask in class what sea-surface would do
What would the cross-shore circulation look like.
The above discussion is on the along-shore momentum balance, which is Ekman. But in the cross-shore momentum balance (assuming winds are strongly along shore) the tilting sea-surface, and tiltling isopycnals, develop a cross-shore pressure gradient which is balanced by a strong along shore flows that are in geo-strophic balance.
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