Summer school on Dynamics of North Indian Ocean : Yoshida Jet

F) Yoshida jet (June 29)

The Yoshida Jet is perhaps the most fundamental, forced equatorial response, one that distinguishes equatorial from midlatitude dynamics. The Yoshida Jet exists because f vanishes at the equator, so that the zonal momentum equation reduces to ut +px = τx/H. For x-independent forcing (idealized), px = 0 and the Yoshida Jet continuously accelerates (ut = τx/H). When the forcing is zonally bounded (realistic), the radiation of equatorial Kelvin and Rossby waves establishes the balance px = τx/H, and the jet stops accelerating to form a “bounded” Yoshida Jet. No Yoshida Jet is generated by τy winds.
The steady-state currents for all the solutions found here are Sverdrup flows. It is noteworthy that they are exactly the same as they are off the equator, a consequence of the Sverdrup circulation not depending on f, but only β.

Domain: 20ºE–100ºE, 30ºS–30ºN Resolution: 0.25º Equatorial β-plane:f = βy Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on τx wind patch Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 Movie time step: daily Description:
The wind has the form τx = τ_{o}X(x)Y(y)T(t), where

X(x) = cos[2π(x–60º)/30º], 20º ≤ x ≤ 40º (F1a)

Y(y) = (1 + y2/Ly2)exp(y2/Ly2), (F1b)

T(t) = θ(t), (F1c)

where L_{y} = 10º, τ_{o} = 1.5 dyn/cm2, and X(x) is zero outside the designated range The form of Y(y) ensures that the wind has zero curl at the equator.
In order to see the development of the bounded Yoshida Jet, slow down your video player as much as possible (3%, say). As soon as the wind switches on, the equatorial jet accelerates. Within a month or so, wind-generated Kelvin and Rossby waves have propagated across the wind patch, a pressure gradient develops to balance the wind, and the jet stops accelerating, locally forming a “bounded” Yoshida Jet. Subsequently, the radiation of Kelvin and Rossby waves extends the jet farther from the forcing region, more rapidly in the eastern ocean since the Kelvin wave speed is 3x faster than the fastest Rossby (ℓ = 1) wave.
At later times, ℓ = 1 Rossby waves, which reflect from the eastern boundary, propagate across the basin and reflect there as Kelvin waves that then return to the eastern ocean. The time it takes for an ℓ = 1 Rossby wave to cross the basin and a Kelvin wave to return is 4L/c1 = 154 days, the natural ringing time for the equatorial ocean. The curved bands of radiating away from the eastern boundary are a set of reflected Rossby waves generated by this process (also see the discussion of Exp G1).
Eventually, reflected waves from both the eastern and western boundaries eliminate the equatorial jet. As a result, the steady-state response is the same Sverdrup circulation that develops at midlatitudes. Note that the Sverdrup gyres are located off the equator, a consequence of Y(y) having zero curvature there.

Domain: 20ºE–100ºE, 30ºS–30ºN Resolution: 0.25º Equatorial β-plane:f = βy Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on τx wind patch Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 Movie time step: daily Description:
As in Experiment F1a, except that

Y(y) = 0.5{1+cos[2π(y–30º)/30º]}. –15º ≤ y ≤ 15º, (F2)

and vanishes outside the designated range. The response is similar to that of Experiment F1a, except that, because there is wind curvature near the equator, the steady-state Sverdrup gyres are joined together.

Domain: 20ºE–100ºE, 30ºS–30ºN Resolution: 0.25º Equatorial β-plane:f = βy Characteristic speed:c_{5} = 59.7 cm/s Forcing: switched-on τx wind patch Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 Movie time step: daily Description:
As in Experiment F1a, except for the n = 5 baroclinic mode. The terms proportional to A/cn2 damp equatorial waves. The terms are small for the first baroclinic mode, but not for intermediate modes like n = 5. The impact of damping in the response of the n = 5 baroclinic mode is striking. For example, the eastern-boundary Rossby waves are strongly damped before they can propagate into the interior ocean to eliminate the equatorial jet. As a result, the equatorial jet remains a strong feature of the flow in steady state. Surprisingly, then, damping actually strengthens the equatorial current.

Domain: 20ºE–100ºE, 30ºS–30ºN Resolution: 0.25º Equatorial β-plane:f = βy Characteristic speed:c_{1} = 264 cm/s Forcing: switched-on τy wind patch Mixing:ν_{h} = 10^{7} cm^{2}/s, A = 0.00013 Movie time step: daily Description:
As in Experiment F1a, except for a meridional wind of the form τ^{y} = τ_{o}X(x)Y(y)T(t), where X(x), Y(y), and T(t) are given in (F1). In response to the switched-on τy wind, Yanai and Rossby waves radiate away from the patch, and the response quickly adjusts to Sverdrup balance. There are no strong flows because τy winds do not drive a Yoshida Jet.
The Yanai-wave packet has a remarkable structure. Fourier analysis allows the packet to be viewed as a superposition of sinusoidal waves with wavelengths k that are both positive and negative. Because the group velocity of Yanai waves with positive k (eastward phase velocity) is greater than those with negative k (westward phase velocity), the leading (trailing) edge of the packet has eastward (westward) phase velocity. Between these two parts, the Yanai wave becomes quite elongated because k ≈ 0.

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