## W v cgf pg

Assume the following values for the basic parameters of the circulation f 10 4 s, P 2 x 10-11 s m, Lx 2.5 x 107 m, Ly 107 m, Ln Lsy 1.5 x 106 m, Aj 1,000 m2 s, c 0.16, g' 0.01 m s2, k 10-5 m2 s and the typical values for these depth scales are de 313m, dw 685m, and dK 368m. Comparing these three depth scales, it is clear that pycnocline depth associated with wind stress is the dominating scale thus, it is convenient to use this depth scale and introduce the nondimensional depth d D dw, for...

## TyBx Ahfxxxx457

Where ty B is the boundary layer solution. The scale width of the western boundary layer is the vorticity equation is reduced to This equation is subject to the following boundary conditions. First, the boundary layer solution should be finite and it should match the interior solution at infinity (the outer edge of the boundary layer) tyB tyi, n (4.61) Second, the western boundary is a streamline, tyB 0, at n 0 (4.62) In addition, two types of boundary condition may apply a) No-slip condition...

## S T

The simplest choice is a two-box model for a single-hemisphere ocean, in which temperature is relaxed toward the specified reference temperature of T To, T 0 and an air-sea freshwater flux p, p . To simulate the effect of the wind-driven gyre, a volume transport m between the two boxes is added (Huang and Stommel, 1992). Following Guan and Huang (2008), this volume transport is prescribed a priori, independent of the energy for mixing and temperature salinity (Fig. 5.131). Assuming that the...

## D

Sm I Wmb + Vmb hm,max (5.38) where hm,max is the annual maximal depth of the mixed layer Sf wmb + Vmbddyhm (5.39) where hm is the annual mean mixed layer depth. Note that both of these definitions treat the subduction in the local sense, so these two subduction rates do not include the average over the trajectory downstream. As a result, the rates calculated from these two equations are smaller than the rates calculated from the above-defined SE and SL, both of which include the contribution...

## E 60e 90e 120e 150e 180 150w 120w 90w 60w 30w 0

Fig. 1.11 Annual mean (NCEP-NCAR) rate of evaporation minus precipitation (cm yr). Fig. 1.13 Geothermal heat flux based on a semi-empirical formula, seafloor shallower than 2.6 km is excluded (mW m2). Fig. 1.13 Geothermal heat flux based on a semi-empirical formula, seafloor shallower than 2.6 km is excluded (mW m2). Fig. 1.19 Annual mean sea surface temperature anomaly ( C), deviation from the zonal mean. Fig. 1.19 Annual mean sea surface temperature anomaly ( C), deviation from the zonal...

## U

If the outflow is in a channel, P can be specified a priori however, it can be calculated in the general case by where K tb H is the Ekman number the ratio of bottom drag to the Coriolis force. Given the initial values of U, , S, H, and W, Eqns. (5.22), (5.24a), (5.24b), (5.26), and (5.27) can be used to calculate the evolution of the streamtube downstream. Entraining density currents with rotation an end-point model We now discuss the simplified relations between the initial conditions and the...

## 2 hU

The potential vorticity balance for a closed streamline (or the whole basin) is between the frictional torque (mostly generated along the edge of the basin where the friction is non-negligible) and the wind stress torque imposed over the basin. Thus, no matter how small the frictional force is, it is essential for maintaining the basin-wide vorticity balance between wind stress input and frictional output. Furthermore, a purely inertial model is physically impossible, because vorticity input...

## Bpp Bxd p Bp Bxpb Bp Bx ps I Bp Bpxd p

Where the first term on the right-hand side is zero due to the matching boundary condition that horizontal velocity at the base of the wind-driven gyre vanishes. The last integral can be converted into another form d fpb 2 2 dpb 2 dps fpb dx I Bpdp Bp -Xp - Bp + 2i BpBxpdp (4.301) Combining equations (4.298, 4.299, 4.300, and 4.301), we obtain

## N 80n 70n 60n 50n 40n 30n 20n 10n

Fig. 5.55 a-d Transport of the western boundary current driven by a point sink specified at location 0q, in units of the total sink Sq. Fig. 5.55 a-d Transport of the western boundary current driven by a point sink specified at location 0q, in units of the total sink Sq. Fig. 5.56 Deep circulation in the world ocean postulated by Stommel (1958). Fig. 5.56 Deep circulation in the world ocean postulated by Stommel (1958). interior of each basin water uniformly moves upward, as assumed in the...

## McO Mg O Mt O

Since the vertical grids are uneven, in order to show the volume flux over a certain depth range, the volume flux in each layer is re-scaled as Gp Gpk-h , Gf Gth (5.380) where h0 100 m is the typical scale for most essential features associated with gyre-scale circulation. In comparison, the commonly used MOC streamfunction is defined as the vertical integration where m fk (Xf, 0j) is the meridional throughflow volume flux defined above. Thus, the MOC streamfunction includes both positive and...

## Info

Fig. 3.21 The time evolution of the normalized wind energy input through the geostrophic current (circles), surface waves (inverted triangles), and Ekman layer (squares) (Huang et al., 2006). Changes in wind stress energy input Perhaps the most important point deserving serious attention is that wind stress energy input to surface geostrophic current varies greatly from year to year, and has been increasing over the past 50 years, as shown in Figure 3.20. Similarly, wind energy input to surface...

## P dJpSp VdSJp

Equations (2.152) and (2.153) combined with Eqns. (2.144) and (2.147) constitute a complete set of basic equations of a dynamical system under the so-called Boussinesq approximations, i.e., the following simplifications are assumed Using the volume conservation to replace the mass conservation Retaining the buoyancy forcing associated with small density deviation Using volume conservation in the tracer (temperature and salinity) prognostic equations. 2.7.2 Potential problems associated with...

## S

Fig. 5.97 A finite difference grid box in the x z plane. dJL + (us)+ (us) + (wS)+ (wS) (S+ ) where (uS)+ and (uS) are the salt fluxes advected across the right and left boundaries, and S+ and S are the horizontal salinity gradients at the right and left boundaries similarly, (wS)+ and (wS) are the salt fluxes advected through the upper and lower boundaries, and Sf and (wS) are the vertical salinity fluxes at the upper and lower boundaries. In addition, vertical velocity is prescribed on the...

## N Wt

D) If the slippery boundary condition applies, fB,nn 0, at n 0 thus, C4 -03 3. The final solution is e) Structure of the western boundary current the layer thickness of the boundary current can be obtained from the semi-geostrophic relation h2 2f fi + hW, hW hi - 2f fi g' (4.67) The corresponding velocity field can be calculated accordingly as v . inertial western boundary current The existence of an inertial western boundary current was postulated first by Stommel (1954). His basic idea is...

## Thermohaline circulation

The balance of water masses in the world's oceans consists of two major processes water mass formation and erosion. Most water masses are formed near the upper surface and sink. Furthermore, through either transformation or erosion, water mass properties are continually transformed, so that a water mass gradually loses its identity. Therefore, some types of water mass are formed below the surface layers through the mixing of water masses originated from the sea surface however, in this chapter,...

## Ojm

Fig. 5.122 Three equilibriums for a two-box model of Stommel (1961) the stable note (indicated by a), the saddle (indicated by b), and the stable spiral (indicated by c) the arrows indicate the behavior of the model's solutions in the T-S diagram. density difference due to the temperature component. Such a large salinity difference is possible for a slow circulation only because of the long relaxation time scale. An unstable state that is thermally controlled, represented by the saddle point b...

## E 20e 30e 40e 50e 60e

Fig. 4.33 Isolines of potential vorticity in the bottom layer, with the heavy dashed line indicating the outcropping line of the upper layer. Although east of the thin dashed line potential vorticity contours are blocked by the eastern boundary, west of the thin dashed line potential vorticity contours disconnected from the eastern boundary are closed through the western boundary. boundary, along which geostrophic motion is forbidden. However, there are contours stemming from the western...

## E 150e 180 150w 120w 90w

Fig. 4.90 Climatological-mean circulation on four isopycnal surfaces a oq 23.2 b 24.2 c 25.0 and d 26.0 kg m3. Gray lines indicate depths (m) black and gray thick lines indicate pathways. The ventilation time for the pathways (in years) is indicated by a pair of numbers the left for the western boundary pathway and the right for the interior pathway. Gray thick lines near the eastern boundary in a and b indicate a narrow local pathway, a short-cut, from the subtropics to the equatorial regime...

## N 30n 45n 60n

Fig. 5.199 a Poleward heat flux in the 3-D ocean model (in 1015 W) b meridionally accumulated energy required for sustaining subsurface diapycnal mixing in the 3-D ocean model (in 109 W) (Huang et al., 2007). the ocean interior, which may enhance the MOC and poleward heat flux. On the other hand, more mechanical energy input can increase the mixed layer depth. This process also plays an important role in regulating the MOC and poleward heat flux. For example, tropical cyclones can input a large...

## Pp QB p

Bp -gh(x, y) at p ps (4.305) B Ba, Bp Bap, at p pb ( pb is unknown) (4.306) ' 2 rpb a2 2 g p f2 rxe B2dp + Ba dp wedx (4.307) Although this approach seems to be a simple extension of the early work by Welander (1971a), there are subtle differences between the new formulation and Welander's old formulation. In Welander's formulation, it was assumed that potential vorticity Q(B, p) in Eqn. (4.304) is a given function of B and p, and this equation is subject to boundary conditions specified at the...

## N 20n 30n 40n 50n 60n

Fig. 5.145 Meridional velocity distribution along the western boundary of the model basin, in The meridional overturning circulation constitutes the most important component of the thermal circulation (Fig. 5.146). In turn, this consists of the following four branches 1. a poleward flow of warm water in the upper ocean, as indicated by the relatively compact streamlines in the upper ocean 2. a narrow sinking branch near the northern boundary 3. a relatively broad and slow upwelling in the ocean...

## Is Pacific Ocean In Western Hemisphere

Where we is the Ekman pumping velocity calculated from wind stress. The total meridional volume flux involved in the wind-driven gyre across a latitudinal section of the basin interior is the sum of these two fluxes, i.e., MSv ME MG. The return flow into the western boundary is MSv. The bifurcation of the western boundary current is a nonlinear phenomenon however, here we assume that the bifurcation latitude of the western boundary current is the latitude where MSv vanishes this can be...

## N

Fig. 5.151 Sketch of the northward heat flux associated with the two equilibrium states redrawn from F. Bryan, 1986 . surface. Water has a much higher heat capacity than air thus, the ocean is the dominating factor influencing the climate, and climate on a planet without oceans would be extremely different from that on a planet with oceans. However, as shown in the numerical experiments by F. Bryan, this poleward heat flux can be changed substantially if the thermohaline circulation in the...