Search Results

You are looking at 1 - 10 of 24 items for

  • Author or Editor: Wen-yih Sun x
  • All content x
Clear All Modify Search
Wen-Yih Sun

Abstract

No abstract available.

Full access
Wen-Yih Sun

Abstract

The forward-central (forward in time, central differencing in space) scheme and the Dufort-Frankel scheme applied to the transient heat equation are discussed here. The Dufort-Frankel scheme is shown to be unable to damp the oscillation of the high oscillatory 2Δx wave. It can even become unstable for this wave which may be produced by the initial conditions, nonlinear interactions, or other forcing. On the other hand, the forward-central scheme works well if μ<0.5. Examples of the applications of these schemes in fluid dynamics are also presented in this paper. It is also noted that none of the schemes are accurate for the high-frequency short wave.

Full access
Wen-Yih Sun

Abstract

A linearized two-dimensional model was used to study the formation of convective rolls in the prestorm stage and organized squall lines near the dryline in the Great Plains. With a strong virtual potential temperature gradient across the dryline zone, the results show the without condensation symmetric instability can produce convective rolls with a horizontal wavelength of a few tens of kilometers. With condensation, a large cloud develops near the center of the dryline zone. This cloud subsequently splits into two clouds; one moves to the west and disappears, and the other moves to the east, where the PBL is relatively moist, and grows. The numerical results are qualitatively comparable with observations. This study provides a possible explanation that symmetric instability with condensation can generate storms near the center or on the east side of the dryline zone, whereas low-level convergence develops at the western edge according to the inland sea-breeze circulation.

Full access
Wen-Yih Sun

Abstract

A modified forward-backward scheme applied to the anelastic system is proposed. This modified scheme not only retains all the advantages of the conventional forward-backward scheme but also is more consistent with the original differential equations. This scheme is used to investigate inertial waves and internal gravity waves in three different lattices. It is found that the lattice C proposed by Deardorff is better than either lattice A or lattice B when applied to internal gravity waves and thermal convection in the atmosphere.

The difference between a hydrostatic system and a nonhydrostatic system is also discussed in detail in this paper. Here we propose to apply Shuman's smoothing on a hydrostatic system to filter out the undesirably, highly oscillatory short waves, or stroll small-scale convection, so that we may produce reasonable results compared with those of a nonhydrostatic system. The validity of this method has been proved by the numerical results of a study on the mesoscale cloud bands which are produced by the effect of condensation in a conditionally unstable atmosphere with vertical wind shear.

Full access
Wen-Yih Sun

Abstract

The linear stability of penetrative convection is investigated for three different undisturbed temperature profiles, each characterized by a stable layer on the top: case A) a two-layer profile with constant but different lapse rate in each layer, case B) a continuous and smooth mean temperature profile with the depth of the unstable layer fixed, and case C) a temperature profile determined by the conduction equation with the surface temperature undergoing a diurnal variation. The increase of the critical Rayleigh number Rc of the unstable layer with increasing stability number S of the top layer is prominent in case A, less appreciable in case B, and also less noticeable for case C. It appears that the relation between the temperature gradient in the unstable layer and that in the stable layer is more sensitive and meaningful than the relation between Rc and S for a smooth temperature profile, especially for case C in which the depth of the unstable layer is not kept constant. The results obtained from case C show that the depth of the unstable layer is about 55 m and the horizontal wavelength is about 250 m when convection starts. It is also shown that convection tends to produce a superadiabatic layer near the ground, a deep mixed layer above, and an inversion layer at the top of the mixed layer.

Full access
Wen-Yih Sun

Abstract

This paper shows that in the linearized shallow-water equations, the numerical schemes can become weakly unstable for the 2Δx wave in the C grid when the Courant number is 1 in the forward–backward scheme and 0.5 in the leapfrog scheme because of the repeated eigenvalues in the matrices. The instability can be amplified and spread to other waves and smaller Courant number if the diffusion term is included. However, Shuman smoothing can control the instability.

Full access
Wen-Yih Sun

Abstract

Linear stability analysis of cloud streets is investigated by including the latent heat and considering a few types of wind profiles. The release of latent heat follows the wave-CISK hypothesis. The results indicate that as the buoyance force released by latent heat becomes dominant, the most unstable mode is stationary relative to the mean wind, and the orientation of cloud streets is parallel to the direction of the wind shear. On the other hand, if the conversion of kinetic energy becomes important, the cloud streets which are perpendicular to the wind shear and propagating relative to the mean wind become most unstable. Results also show that the wavelength, growth rate and orientation angle of the most unstable mode are very sensitive to the height of cloud tops, the strength of wind shear, static stability and the environmental moisture profile. These results compare well with other theoretical results and observations.

Full access
Wen-Yih Sun and Isidoro Orlanski

Abstract

The nonlinear equations are applied to study the interactions between the sea breeze circulation and trapeze instability in low latitudes. The well-developed sea breeze circulation produced by the nonlinear model at coast is not so affected by the trapeze instability as shown in Part I of this study. However, the waves over the land are quite similar to those of Part I, but with a smaller growth rate. This study suggests that a strong diurnal temperature variation over the land and/or the latent heat may be required to produce the observed cloud bands in the tropical continental region.

Full access
Wen-Yih Sun and Yoshi Ogura

Abstract

The level 3 turbulence closure model proposed by Mellor and Yamada (1974) is modified 1) to incorporate the formulations for the turbulence third-order moments and pressure terms proposed by Zeman and Lumley (1976) and 2) to introduce turbulence length scales which depend upon the stratification of the atmosphere. The vertical heat and moisture fluxes and the temperature-humidity covariance are determined from differential equations. The model includes two other differential equations, one for the turbulence kinetic energy and the other for virtual potential temperature variance. All other turbulence variables are determined from algebraic equations.

The model is used to simulate the daytime evolution of the planetary boundary layer observed on day 33 of the Wangara boundary-layer experiment. The calculated vertical profiles of the mean wind, temperature and humidity are found to be in good agreement with the observations. The calculated vertical distributions of turbulence variables, including kinetic energy, temperature variance, heat and moisture fluxes, temperature and moisture variance, molecular dissipation, and some third-order moments, compare favorably with those estimated from other numerical models, aircraft observations and laboratory experiments.

Full access
Wen-Yih Sun and Isidoro Orlanski

Abstract

The interactions between the sea breeze circulation and trapeze instability are investigated using a set of linearized equations. The results show that mesoscale waves associated with trapeze instability can be easily triggered by the sea breeze circulation and can propagate far inland, but no mesoscale waves are observed over the ocean. The wavelength is a few hundred kilometers. The period of the waves, which depends on the Coriolis parameter, eddy viscosity and the strength of land-sea contrast, can be either one day or two days, or a combination of one and two days. The waves obtained here are similar to the cloud bands observed in West Africa and South America.

Full access