Constant-eddy-viscosity models of vertical structure forced by periodic winds

Ekman revisited: Surface currents to the left of the winds in the Northern Hemisphere

“…7A and Eq. 7B reduce to at subinertial frequencies, and at superinertial frequencies ( 11 , 13 , 14 ). Note that there is no difference between dynamics in a semi-infinite ocean and in the surface layer of the ocean provided that the depth of the surface layer is much larger than the characteristic depth scales.…”

Ekman revisited: Surface currents to the left of the winds in the Northern Hemisphere

“…7A and Eq. 7B reduce to at subinertial frequencies, and at superinertial frequencies ( 11 , 13 , 14 ). Note that there is no difference between dynamics in a semi-infinite ocean and in the surface layer of the ocean provided that the depth of the surface layer is much larger than the characteristic depth scales.…”

Nonlinear interaction between wind‐forced currents and near‐inertial oscillations and internal waves in nearshore frontal regions

“…The reason for the rapid penetration to depth is that eddy viscosity is high in this well mixed region. As shown by Craig [1989], since for a given constant eddy viscosity A V the depth of penetration at the inertial frequency is only limited by the water depth and hence inertial energy penetrates to the sea bed. On the stratified side of the front the value of A V becomes small at the level of the thermocline due to the influence of stable stratification.…”

Wind‐induced motion in the vicinity of a bottom density front: Response to forcing frequency

“…The surface stress was set equal to the wind stress, which was taken as horizontally uniform with an amplitude of 0.05 Pa, and clockwise rotation. Clockwise rotation was chosen, as this gives rise to a greater depth of penetration of the wind's momentum than anticlockwise (see earlier discussion and Craig [1989]). An amplitude of 0.05 Pa was chosen to represent a typical wind stress.…”

“…In the case of forcing at the subinertial frequency, namely ω = 0.77 f (Calculation 8A), based upon the single point model [ Craig , 1989], the depth of penetration of the wind's momentum due to diffusion should be the same as that with ω = 1.23 f . This is confirmed by a comparison of the depths of corresponding u amplitude contours on the well‐mixed, western side of the front (compare Figure 12a, with Figure 4c (note differences in contour interval), in particular, the 2 cm s −1 contour at 57 m below surface, and the 4 cm s −1 contour at 24 m below surface).…”

“…A cross‐sectional model including a bottom front has been used to examine the influence of the front upon the depth of penetration of the wind's momentum at a range of frequencies. Previous research using a linear point model [ Craig , 1989], suggests that with constant eddy viscosity A V , the depth of penetration is given by (2 A V /∣ω − f ∣) 1/2 , and is consequently independent of whether ω is subinertial or superinertial.…”

Ekman revisited: Surface currents to the left of the winds in the Northern Hemisphere

“…7A and Eq. 7B reduce to at subinertial frequencies, and at superinertial frequencies ( 11 , 13 , 14 ). Note that there is no difference between dynamics in a semi-infinite ocean and in the surface layer of the ocean provided that the depth of the surface layer is much larger than the characteristic depth scales.…”

Nonlinear interaction between wind‐forced currents and near‐inertial oscillations and internal waves in nearshore frontal regions

“…The reason for the rapid penetration to depth is that eddy viscosity is high in this well mixed region. As shown by Craig [1989], since for a given constant eddy viscosity A V the depth of penetration at the inertial frequency is only limited by the water depth and hence inertial energy penetrates to the sea bed. On the stratified side of the front the value of A V becomes small at the level of the thermocline due to the influence of stable stratification.…”

Wind‐induced motion in the vicinity of a bottom density front: Response to forcing frequency

“…The surface stress was set equal to the wind stress, which was taken as horizontally uniform with an amplitude of 0.05 Pa, and clockwise rotation. Clockwise rotation was chosen, as this gives rise to a greater depth of penetration of the wind's momentum than anticlockwise (see earlier discussion and Craig [1989]). An amplitude of 0.05 Pa was chosen to represent a typical wind stress.…”

“…In the case of forcing at the subinertial frequency, namely ω = 0.77 f (Calculation 8A), based upon the single point model [ Craig , 1989], the depth of penetration of the wind's momentum due to diffusion should be the same as that with ω = 1.23 f . This is confirmed by a comparison of the depths of corresponding u amplitude contours on the well‐mixed, western side of the front (compare Figure 12a, with Figure 4c (note differences in contour interval), in particular, the 2 cm s −1 contour at 57 m below surface, and the 4 cm s −1 contour at 24 m below surface).…”

“…A cross‐sectional model including a bottom front has been used to examine the influence of the front upon the depth of penetration of the wind's momentum at a range of frequencies. Previous research using a linear point model [ Craig , 1989], suggests that with constant eddy viscosity A V , the depth of penetration is given by (2 A V /∣ω − f ∣) 1/2 , and is consequently independent of whether ω is subinertial or superinertial.…”

Ekman revisited: Surface currents to the left of the winds in the Northern Hemisphere

“…7A and Eq. 7B reduce to at subinertial frequencies, and at superinertial frequencies ( 11 , 13 , 14 ). Note that there is no difference between dynamics in a semi-infinite ocean and in the surface layer of the ocean provided that the depth of the surface layer is much larger than the characteristic depth scales.…”

Nonlinear interaction between wind‐forced currents and near‐inertial oscillations and internal waves in nearshore frontal regions

“…The reason for the rapid penetration to depth is that eddy viscosity is high in this well mixed region. As shown by Craig [1989], since for a given constant eddy viscosity A V the depth of penetration at the inertial frequency is only limited by the water depth and hence inertial energy penetrates to the sea bed. On the stratified side of the front the value of A V becomes small at the level of the thermocline due to the influence of stable stratification.…”

Wind‐induced motion in the vicinity of a bottom density front: Response to forcing frequency

“…The surface stress was set equal to the wind stress, which was taken as horizontally uniform with an amplitude of 0.05 Pa, and clockwise rotation. Clockwise rotation was chosen, as this gives rise to a greater depth of penetration of the wind's momentum than anticlockwise (see earlier discussion and Craig [1989]). An amplitude of 0.05 Pa was chosen to represent a typical wind stress.…”

“…In the case of forcing at the subinertial frequency, namely ω = 0.77 f (Calculation 8A), based upon the single point model [ Craig , 1989], the depth of penetration of the wind's momentum due to diffusion should be the same as that with ω = 1.23 f . This is confirmed by a comparison of the depths of corresponding u amplitude contours on the well‐mixed, western side of the front (compare Figure 12a, with Figure 4c (note differences in contour interval), in particular, the 2 cm s −1 contour at 57 m below surface, and the 4 cm s −1 contour at 24 m below surface).…”

“…A cross‐sectional model including a bottom front has been used to examine the influence of the front upon the depth of penetration of the wind's momentum at a range of frequencies. Previous research using a linear point model [ Craig , 1989], suggests that with constant eddy viscosity A V , the depth of penetration is given by (2 A V /∣ω − f ∣) 1/2 , and is consequently independent of whether ω is subinertial or superinertial.…”