Thermal and dynamical effects of mountain on the land and sea breezes are studied numerically, by paying special attention to the growth and decay of the circulations and the extent of them. A two dimensional model in a vertical plane perpendicular to a seacoast line and a mo untain chain is used. The horizontal extent and the depth of the computational region are assumed to be 130km and 3km, respectively. The mountain is assumed to have a simple trapezoidal form with 8km in width and 450m in height, and is located at 18km from the coastal line. In order to estimate the thermal and dynamical effects of the mountain, numerical experiments are conducted for the following three cases: case (a) no mountain case (b) mountain with thermally insulated boundary condition (insulated mountain) case (c) mountain with the diurnal change of its surface potential temperature (heating mountain) Main conclusions are summarized as follows: (1) The sea breeze can not invade inland beyond the heating mountain, while the breeze invades inland beyond the insulated mountain faster and deeper than expected in case of no mountain. (2) The land breeze develops strong in case of the heating mountain. This is due to the down-slope winds. In case of the insulated mountain, this down-slope winds do not develop and the land breeze remains weaker than that of no mountain case. (3) The phase difference between the time of the maximum land-and-sea surface temperature contrast and that of the strongest induced circulation is much reduced, compared to the case of no mountain, regardless of the thermal boundary condition of the mountain surface.
The second order mean motion induced around an internal Rossby wave packet, having an infinite zonal length and propagating vertically in an inviscid Boussinesq fluid at rest in a channel, is discussed, and the validity of photon analogy to such a wave packet is examined.It is shown that the second order mean zonal momentum averaged in the meridional direction is just equal to the wave momentum E/C (where E and C are the wave energy and the phase velocity in the zonal direction respectively). This guarantees the validity of photon analogy to the wave packet, and also implies that the treatment done rather intuitively in the previous paper by the author (Uryu, 1974) is essentially correct.It is shown that, to the first order in * (where * is a small parameter characterizing the slowness of variation of wave amplitude), the vertical component of Lagrangian mean velocity is zero, as a result of the cancellation between the Stokes drift and the Eulerian mean velocity.The case of propagation in a shear flow is also treated, and it is shown that the absorption of wave at the critical level occurs as a result that the wave momentum is stored up in the mean zonal flow there.It is also shown that the results obtained in case of Rossby wave packet can be obtained without any essential change also in case of internal gravity wave packet under the same situation.
Lagrangian mean motion induced by a growing baroclinic wave is discussed, based on the solution of Eady type problem of baroclinic instability including non-geostrophic effect. It is shown that to the leading order of Rossby number, the Lagrangian mean meridional motion is convergent toward the center of the channel.This means that air particles are mixed horizontally as a consequence of the instability. It is also shown that to the second order, air particles move downward near the northern wall and upward near the southern wall, while in the central region they move southward in the upper layer and northward in the lower, except for weak reverse flows near the top and the bottom. This Lagrangian mean picture is completely different from the usual Eulerian mean picture, and agrees qualitatively well with the result of Kida's (1977) numerical experiment as far as the behaviors of tropospheric particles are concerned, and with the result by Riehl and Fultz (1957) obtained in a rotating annulus experiment as far as the distribution of Lagrangian mean vertical flow is concerned.The result that the Lagrangian mean velocity field is convergent (divergent) even under Boussinesq assumption (cf. Andrews and McIntyre, 1978) is attributed mainly to horizontal mixing term and partly to a term of transverse-gradient transport. Eliminating the horizontal mixing term from the latitudinal component of Stokes drift and also a term of transversegradient transport from the vertical component,we can obtain the solenoidal part of Lagrangian mean meridional velocity field. This residual circulation is somewhat similar to the Eulerian mean meridional circulation, and it may be equivalent to the Lagrangian mean meridional circulation induced by a dissipating planetary wave (cf. Matsuno and Nakamura, 1978). It is shown that only a part of the second order field mentioned above can be responsible to the change in Lagrangian mean zonal flow. As a result, the direction of the mean zonal flow acceleration is reverse to that in the Eulerian mean problem.Finally, we estimate the so-called eddy diffusivity, to obtain that KH=9.6*10'9 cm2/sec and KV=8.1 * 103cm2/sec under the assumed condition of baroclinic wave which is chosen as a typical cyclone. It is further pointed out that latitudinal buoyancy (heat) flux consists of down-gradient transport (or particle mixing) term and transverse-gradient transport term, and that the latter is about 20% of the former in magnitude.
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