Summer school on "Dynamics of the North Indian Ocean" Ekman drift & inertial oscillations

B) Ekman drift & inertial oscillations (June 24)

These solutions illustrate the generation of Ekman drift and the excitation of inertial and gravity waves in response to a switched-on wind stress. To isolate these features, the wind stress lacks curl. As a result, there is no Ekman pumping in the interior ocean (except for the weak pumping in Experiment B2b), and hence no geostrophic flows are generated in the interior ocean.

Domain: 20ºE–100ºE, 10ºN–50ºN Resolution: 0.25º f-plane:f = 2Ωsinθ, θ = 30ºN Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on, spatially uniform τy Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 cm^{2}/s^{3} Movie time step: 1 hour (2X each model time step) Description:
In response to the switched-on, uniform τy, an eastward Ekman drift plus inertial oscillations are generated. The velocity vectors circulate clockwise, as expected for inertial oscillations in the northern hemisphere. Initially, the length of the vectors decreases to zero each cycle, a result of destructive interference between the eastward Ekman drift and an equal westward flow associated with the negative (u < 0) phase of the inertial oscillations. Subsequently, damping slowly weakens the inertial oscillations and the cancellation is no longer complete. Furthermore, the oscillations are initially uniform throughout the basin, but as time passes they slowly change in different parts of the basin, a result of gravity waves that reflect from basin boundaries.
The wind has an alongshore component on the eastern and western boundaries of the basin. The coastal ocean responds there by radiating Kelvin waves, and after their passage an alongshore pressure gradient is established at the coast that balances the wind and stops the coastal jet from accelerating. The Kelvin waves wrap around the basin, complicating the response. Horizontal viscosity gradually broadens the coastal currents.

Domain: 20ºE–100ºE, 10ºN–50ºN Resolution: 0.25º f-plane:f = 2Ωsinθ, θ = 30ºN Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on, spatially uniform τ^{x} Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 cm^{2}/s^{3} Movie time step: 15 minutes (each model time step) Description:
As in Experiment B1a, except for τ^{x} forcing. The response is essentially the same as in Experiment B1a, except that the Ekman drift is directed southward.

Domain: 20ºE–100ºE, 10ºN–50ºN Resolution: 0.25º β-plane:f = f_{0} + β(y – y_{0}), y_{0} = 30º Characteristic speed:c1 = 264 cm/s Forcing: switched-on, spatially uniform τy Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 cm^{2}/s^{3} Movie time step: 1 hour (2X each model time step) Description:
As in Experiment B1a, except on the β-plane. The response is remarkably different from the f-plane case. Because the inertial frequency changes with latitude, the velocity vectors spin slower closer to the equator. As a result, convergences and divergences develop across the interior ocean that alternately deepen and shallow the thermocline, allowing for meridionally-propagating gravity waves, a process referred to as β-dispersion.
The group velocity of all the gravity waves is initially directed equatorward, as indicated by the equatorward propagation of lines of zero contours (located between green bands). Eventually, though, the gravity waves reflect from the southern boundary to propagate northward to the latitude where they were generated, a process that is indicated by the presence of poleward-propagating zero contours in the movie. Towards the end of the movie, it is difficult to identify phase propagation in either direction because of the interference of both poleward- and equatorward-propagating waves.
Because of β-dispersion, the adjustment to steady Ekman flow happens much more rapidly than on the f-plane.

Domain: 20ºE–100ºE, 10ºN–50ºN Resolution: 0.25º β-plane:f = f_{0} + β(y – y_{0}), y_{0} = 30º Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on, spatially uniform τ^{x} Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 cm^{2}/s^{3} Movie time step: 1 hour (2X each model time step) Description:
As in Experiment B2a, except for τ^{x} forcing. The response is similar to that of Experiment B2a. A significant difference is that the Ekman pumping velocity, wek = –(τ^{x}/f)y = (β/f^{2})τ^{x} > 0, is not zero, even though the wind curl, –(τ^{x})y, is zero. Thus, p continues to rise slowly throughout the integration everywhere in the basin.

Domain: 80ºE–100ºE, 10ºN–30ºN Resolution: 0.1º f-plane:f = 2Ωsinθ, θ = 20ºN Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on, spatially uniform τ^{x} confined east of 90ºE Mixing:ν_{h} = 10^{6} cm^{2}/s, A = 0.00013 cm^{2}/s^{3} Movie time step: 1 hour (each model time step) Description:
When the wind is cut off west of 90º so that the wind has an edge there, gravity waves with a short zonal wavelength radiate away from the edge, as well as reflect from basin boundaries. As in the previous movies in this set, the waves are indicated by the propagation of lines of zero contours (located between green bands). Waves that emanate from the edge reflect from the eastern and western boundaries of the basin, and return to the interior ocean. Because of the edge radiation, the solution adjusts to a steady Ekman balance faster than when the wind is uniform.

Domain: 20ºE–100ºE, 10ºN–50ºN Resolution: 0.25º β-plane:f = f_{0} + β(y – y_{0}), y_{0} = 30º Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on, band of τy Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 cm^{2}/s^{3} Movie time step: 1 hour (each model time step) Description:
In this solution, the wind has the form τy = τ_{o}X(x)Y(y)T(t), where

θ is a step function, and τ_{o} = 2 dyn/cm^{2}, that is, τ^{y} is a band of wind confined between 40º and 45º. In response, a band of inertial oscillations develops that propagates equatorward because of β-dispersion. The band reflects from the southern boundary, propagates back to the latitude at which it was generated, and then returns equatorward once again toward the end of the movie. These reflections are evident from the direction of phase propagation of zero contours (between alternating green bands).

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