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This paper describes an experimental and numerical study of an intrusion propagating along the interface of a two-layer fluid in a channel. We find that when the density of the intrusion is the depth-weighted mean of the layer densities the interface ahead of the intrusion is undisturbed, but for other densities the interface ahead of the intrusion is displaced vertically. We find that this vertical displacement, which takes the form of an upstream-propagating long wave, depends on the properties of the intrusion and not only on the relative depths of the two layers. For the case when the interface is undisturbed the intrusion propagation speed is a minimum. We develop an energy argument that describes the observed variation of the intrusion speed from this minimum speed as a function of the intrusion and layer densities and the ratio of the layer depths. We also show that if, and only if, the layer depths are equal, the speed of the intrusion is independent of the density of the intrusion.

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A tropical cyclone initialization method with an idealized three-dimensional bogus vortex of an analytic empirical formula is presented for the track and intensity prediction. The procedure in the new method consists of four steps: the separation of the disturbance from the analysis, determination of the tropical cyclone domain, generation of symmetric bogus vortex, and merging of it with the analysis data. When separating the disturbance field, an efficient spherical high-order filter with the double-Fourier series is used whose cutoff scale can be adjusted with ease to the horizontal scale of the tropical cyclone of interest. The tropical cyclone domain is determined from the streamfunction field instead of the velocities. The axisymmetric vortex to replace the poorly resolved tropical cyclone in the analysis is designed in terms of analytic empirical functions with a careful treatment of the upper-layer flows as well as the secondary circulations. The geopotential of the vortex is given in such a way that the negative anomaly in the lower layer is changed into positive anomaly above the prescribed pressure level, which depends on the intensity of the tropical cyclone. The geopotential is then used to calculate the tangential wind and temperature using the gradient wind balance and the hydrostatic balance, respectively. The inflow and outflow in the tropical cyclone are constructed to resemble closely the observed or simulated structures under the constraint of mass balance. The bogus vortex is merged with the disturbance field with the use of matching principle so that it is not affected except near the boundary of tropical cyclone domain. The humidity of the analysis is modified to be very close to the saturation in the lower layers near the tropical cyclone center. The balanced bogus vortex of the present study is completely specified on the basis of four parameters from the Regional Specialized Meteorological Center (RSMC) report and the additional two parameters, which are derived from the analysis data. The initialization method was applied to the track and the intensity (in terms of central pressure) prediction of the TCs observed in the western North Pacific Ocean and East China Sea in 2007 with the use of the Weather Research and Forecasting (WRF) model. No significant initial jump or abrupt change was seen in either momentum or surface pressure during the time integration, thus indicating a proper tropical cyclone initialization. Relative to the results without the tropical cyclone initialization and the forecast results of RSMC Tokyo, the present method presented a great improvement in both the track and intensity prediction.

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A dynamical core of a general circulation model with the spectral method using double Fourier series (DFS) as basis functions is presented. The model uses the hydrostatic balance approximation and sigma coordinate system in the vertical direction and includes no topography. The model atmosphere is divided into 25 layers with equal sigma depths. Prognostic equations for the vorticity, divergence, temperature, and logarithmic surface pressure are solved by the DFS spectral-transform method with the Fourier filtering at middle and high latitudes. A semi-implicit time-stepping procedure, which deals with the eigendecomposition and inversion of the 3D Helmholtz equation associated with the gravity wave terms, is incorporated for the gravity wave–related terms. The DFS model is tested in terms of the solution of the 3D Helmholtz equation, balanced initial state, developing baroclinic waves, and short- and long-term Held–Suarez–Williamson simulations for T42, T62, T84, and T106 resolutions. It is found that the DFS model is stable and accurate and produces almost the same results as the spherical harmonics method (SHM). The normalized difference (i.e., L2 norm error) measured from the results of highest-resolution SHM-T106 showed a desirable convergence of the DFS solution with the resolution. The convergence property, however, varies with the test case and prognostic variables. The total mass (or global integrated surface pressure) is conserved to a good approximation in the long-term simulations. Computing on the high-performance computer NEC SX-5 (parallel-vector architecture) indicated that DFS is more efficient than the SHM and the efficiency increases with the resolution, for example, by factors of 2.09 and 7.68 for T212 and T1022, respectively.