src/examples/bflux.h

    Boundary fluxes for the Gulf-Stream simulation

    This implements the “ports” described in Hurlburt & Hogan, 2000, section 3, page 289:

    “The nonlinear simulations also include effects of the global thermohaline circulation via ports in the northern and southern model boundaries, including a southward DWBC and a northward upper ocean return flow.”

    [hurlburt2000]

    Harley E Hurlburt and Patrick J Hogan. Impact of 1/8 to 1/64 resolution on Gulf Stream model–data comparisons in basin-scale subtropical Atlantic Ocean models. Dynamics of Atmospheres and Oceans, 32(3-4):283–329, 2000. [ DOI | .pdf ]

    These functions are non-zero at the locations (lon/lat) of the southern and northern ports. These locations are not precisely specified in H&H, 2000 (see Note b of Table 2 in H&H, 2000).

    #define northern_flux() (x > -50 && x < - 40 && y > 50.5 && val(zbs,0,0,0) < -4000)
#define southern_flux() (x > -60 && x < - 50 && y < 9.5 && val(zbs,0,0,0) < - 4000)

event viscous_term (i++)
{

    In order to distribute the fluxes within each layer, we first compute the volume of the northern and southern ports, for each layer.

      double sht[nl], shb[nl];
  for (int l = 0; l < nl; l++)
    sht[l] = shb[l] = 0.;
  foreach(reduction(+:sht[:nl]) reduction(+:shb[:nl]))
    foreach_layer() {
      sht[point.l] += northern_flux()*fmax(h[] - hmin[point.l]/10., 0.)*dv();
      shb[point.l] += southern_flux()*fmax(h[] - hmin[point.l]/10., 0.)*dv();
    }

    The fluxes (in m3/s i.e. Sverdrups/106) are given in Table 2 of H&H, 2000.

    See also the 2nd paragraph page 295 which discusses in more detail the chosen fluxes and their control of the northward, southward (Deep Western Boundary Current) and upward currents.

    #if NODWBC
  static const double northern[] =
    { 0., - 0.33e6, - 2.33e6, - 4.84e6, - 6.5e6 };
  static const double southern[] =
    { 0.,   0.33e6,   2.33e6,   4.84e6,   6.5e6 };
#else
  static const double factor = 0.9;
  static const double northern[] =
    { + 14e6, - 0.33e6, - 2e6*factor - 0.33e6, - 4.5e6*factor - 0.34e6, - 6.5e6*factor };
  static const double southern[] =
    { - 13e6, 0., 2e6*factor, 4.5e6*factor, 6.5e6*factor };
#endif

    The fluxes are imposed using a thickness-weighted sum over the northern and southern ports.

      assert (nl == 5);
  foreach()
    foreach_layer() {
      h[] += dt*northern_flux()*fmax(h[] - hmin[point.l]/10., 0.)*
	northern[point.l]/max(sht[point.l], dry);
      h[] += dt*southern_flux()*fmax(h[] - hmin[point.l]/10., 0.)*
	southern[point.l]/max(shb[point.l], dry);
      if (h[] < 0.)
	h[] = 0.;
    }
}