The effects of finite-amplitude disturbances and nonlinear lower boundary in the leewave problem are discussed as an initial value problem by separating both governing equation system and lower boundary condition into linear and nonlinear forms. Physical relations among the four cases, i.e. combinations of two equation systems (linear and nonlinear forms) and two boundary conditions (linear and nonlinear forms), are discussed. The nonlinear interactions between the disturbances and the mountain are found to cause the following effects on the flow: (1) weakening of the approaching flow in the lowest layer ahead of the mountain, (2) generation of the strong wind zone near the level of the mountain crest, (3) intensification of the downslope winds and (4) extension of the strong winds far downstream in the lowest layer. These strong winds are associated with weak wind zone, where an S-shaped or closed circulation pattern develops. Such features are obtained also when the waves are not so strongly resonant (when the amplitudes of the resonance leewaves are relatively small). These nonlinear effects become enhanced when the mountain height is increased beyond the critical value for the overturning instability. It is stressed that how to include a finiteness of the mountain is essentially important to simulate such nonlinear phenomena. Our experiments are compared with the analytical solutions by Long (1955). This paper is a supplement to the paper by Furukawa (1973).
A mathematical model consisting of a complete set of the linearized Boussinesq equations governing atmospheric convection has been solved. The significant new features of the model include (1) anisotropic eddy heat and momentum diffusion coefficients with the eddy viscosity for momentum varying with height through the convecting layer; (2) convection cells of general horizontal geometry as determined by parameter values appearing in a modified form of the generalized Christopherson shape function; (3) a non-zero complex stability factor allowing for steady and time-dependent convective modes; (4) a diabatic heating term in the conservation of energy equation allowing for the development of a moist atmospheric Rayleigh number (Ra); and (5) an atmospheric Prandtl number (Pγ) where molecular viscosity and conductivity have been replaced by their eddy counterparts. The important physical parameters in specifying the convective state are Ra, Pγ, and the eddy anisotropy coefficients for momentum and heat diffusion. Results obtained show that: (1) aspect ratio, cell geometry, and stability of the convective mode are very sensitive to variations in Ra, Pγ, and the anisotropy coefficients; (2) Regime-Stability (R-S) diagram reveals a convective order which closely corresponds to stability diagrams obtained in laboratory studies using different species of fluids; (3) cell flatness, as determined by values of the aspect ratio, is found to be inversely proportional to the square of the convective depth, with the proportionality constant being an increasing function of the momentum diffusion anisotropy coefficient; (4) a family of curves is found to exist where the diameter to depth ratio increases with increasing eddy anisotropy, supporting the observational evidence that such atmospheric convective phenomena as open and closed mesoscale cellular convection (MCC), radar cells in clear air, isolated tropical rings and thunderstorm cells are ordered according to their degree of anisotropy on a cell flatness versus depth diagram. Using an assumed periodic form of the perturbation solutions, the eigenvalue problem is reduced to one of solving a sixth-order differential equation for the vertical wind field with variable coefficients and accompanying boundary conditions. By applying the two-variable small perturbation technique, a Regime-Stability diagram was constructed yielding information concerning: (1) the geometry of the convective mode; (2) the stability of the convective mode; and (3) the anisotropic character of the eddy diffusion coefficients.
In order to obtain a theoretical base of formation and development of a tropical cyclone, properties of unstable waves produced by cumulus convection which is expressed by a parameterization scheme proposed by Arakawa and Schubert (1974) are investigated by a linear analysis. The model used is a four-layer model containing three layers of the free atmosphere and one mixed layer. Thus three cloud types such as the highest type (H), the middle type (M) and the lowest type (L) are defined. The following seven combinations may be considered; (HML), (HM), (HL), (ML), (H), (M) and (L), depending on the co-existence of these cloud types. Among these seven, the combination which is accompanied by a large scale disturbance is uniquely determined as an eigen solution for almost all cases if the basic field and the scale of the disturbance are specified. In general, the mode (H), the mode (HM) and the mode (HML) appear in turn with increasing wavelength. The mode which becomes most unstable depends on the vertical distribution of temperature and water vapour of the basic field. The typhoon-scale disturbance whose preferred scale is less than a few hundred kilometers and growth rate is in a range of 10-610-5sec-1 belongs to eigher the mode (H) or the mode (HM). These modes can be unstable as the lower layer of basic field becomes conditionally unstable and humid. The convective heating in the lower layer plays an essential role for the typhoon-scale disturbance to become unstable. Finally, a comparison is attempted between the typhoon-scale disturbance mentioned above and the typhoon mode of Ooyama (1964).
Roll type Rayleigh convection with a linear temperature distribution along the bottom is experimentally investigated with silicone oil. Results are: a) Convection due to the horizontal temperature gradient is an asymmetric single circulation. b) Rayleigh convection is deformed by the differential heating so that large direct convection cells (whose sense of rotation is same with that driven by the differential heating) and small indirect convection cells stand alternately. c) When stable and unstable regions exist side by side, a single convection due to the horizontal temperature gradient develops in the stable region, while deformed Rayleigh convections develop in the unstable region. d) As the horizontal gradient increases, the wave length of the Rayleigh convection tends to increase to converge to a certain value.
Roll-type convection in a viscous Boussinesq fluid layer heated differentially at the bottom is numerically investigated by a spectral model. The differential heating along the bottom is assumed sinusoidal for the sake of simplicity. Results are summarized as follows: a) as the horizontal temperature gradient increases, Rayleigh convection cells tend to be deformed so that reinforced large (so-called) direct cells and suppressed small indirect cells stand alternately; b) the horizontal temperature gradient acts to suppress the vertical heat transport due to convective rolls; c) as the horizontal temperature gradient increases, the longer wave components of the spectrum tend to be intensified; d) when stable and unstable regions exist side by side, the Rayleigh-type con vection seems to develop in the unstable region only if the width of the unstable region exceeds that of Rayleigh convection cells in qualitative agreement with our experimental observations (Part I).
In a rotating fluid annulus subjected to a horizontal temperature difference, near the transition point from the (upper) Hadley regime to the Rossby regime, waves with smaller amplitudes than those of the main baroclinic waves are observed on the temperature records. The periods of the temperature oscillations due to these waves are longer than those due to inertial oscillations and shorter than those due to the baroclinic waves. These new waves have their maximum amplitude near the central region of the fluid layer. Furthermore, even when these waves are detected on the temperature records, the surface flow is axially symmetric so far as it is observed by eye-measurements. These results suggest that the new waves may belong to a different category from the main baroclinic waves.
A spectral formula in complex representation is derived to compute space-time power spectrum by applying the maximum entropy method. This method gives finer spectral resolutions for shorter time records than conventional methods and is particularly useful in analyzing waves whose amplitude and frequency vary with time. Examples of its application and computer code are also given.
Horizontal wind components, potential temperature, and mixing ratio fields associatedwith a severe storm environment in the south central U.S, were objectively analyzed from synoptic upper air observations with a non-homogeneous, anisotropic weighting function. The grid dimensions of the area of study were near 125 kilometers horizontally and 50 millibars vertically at 18 pressure levels. Each data field was filtered and the vertical motion field was then analyzed using variational methods to insure that the three-component wind field satisfied mass continuity. The local time change of potential temperature and mixing ratio was determined in order to correlate the temperature and moisture advection patterns with severe storm development. A three-dimensional advection equation was used to produce advective forecasts of the potential temperature and mixing ratio fields. The case study discussed in this article is 26 May 1973, when a tornado producing squall line moved through eastern Oklahoma. The synoptic situation which preceded squall line development was cyclogenesis and frontogenesis in the lee-of-the-mountain trough, which produced a well-defined surface dry line (or dew point front) and a pronounced mid-level dry air intrusion. Results indicated that the mid-level dry air intrusion was also characterized by warm air, with a lapse rate approaching the dry adiabatic. The advection of this warm air produced a well-defined upward motion pattern. A corresponding downward motion pattern apparently comprising a deep vertical circulation in the warm air sector of the low pressure system was detected. The squall line that subsequently developed was aligned closely with the axes of the maximum dry and warm advection above the 850mb surface. Below the 850mb surface, the squall line coincided with the axis of maximum moisture advection.
The atmospheric heat energy budget over the Kuroshio region has been analysed for the period of polar air outbreak (cold period for short) in AMTEX '75. The situations of this period are somewhat different from those in AMTEX '74 described in Ninomiya and Akiyama (1976). Three undisturbed periods of polar air outbreak, i.e., Period I (25-27 February 1974), Period II (15-16 February 1975) and Period III (20-23 February 1975) are selected for comparison. Period I is characterized by the weak subsidence of the polar air mass and large amount of precipitation (˜5mm/day) from the cloud layer capped by the inversion layer which distinctly separates the northerly subinversion layer from westerlies aloft. Periods II and III are characterized by the non-precipitating cloud layer capped by the inversion existing in the thick subsiding polar air mass. The large apparent heat and moisture sources in the subinversion layer are commonly found for the three periods. Significant differences among these periods are found in 175˜'250mb (p*) layer including the inversion base. In Period I, both apparent heat and moisture sources show rapid decrease above the inversion. In Periods II and III, maximum of apparent moisture source and maximum of apparent heat sink are found around the inversion base, which are accounted for by the evaporation from the top of the non-precipitating cloud layer. The results of comparison evidently demonstrate the difference between the energy balance in the precipitating and non-precipitating cloud layers and the controlling influence of large-scale subsiding motions upon the thermodynamic . process of the polar air-mass transformation.
The mean vertical structure of monsoon lows over the inland area of northern Indiais investigated by the method of spectral analysis. It is compared with the result of Murakami (1976) in which the data of the station located on the coast of the Bay of Bengal are used. The structures of both stations show that the cyclonic circulation of monsoon lows prevails in the lower troposphere and their axis tilts slightly westward with height. They also bear warm-cored structure in common in the upper levels. The most remarkable contrast appears in the field of specific humidity. When monsoon lows are in the vicinity of the Bay of Bengal, moistening occurs in coincidence with southerly winds, i.e. in the east of the trough. On the contrary, moist and cold anomalies appear in the west of the trough with northerly winds over the inland area. These contrasts suggest an intense geographic effect of Indian subcontinent on the life cycle of monsoon lows.
Under the provision of a time series of radiosonde and surface marine observations conducted by three research vessels, an investigation was made on the behaviour of the stability terms in heat and moisture transfer relations (similarity functions C and D for heat and moisture, respectively) for the convective condition of the planetary boundary layer. Similarity functions were analysed in terms of stratification parameterμi it is found that the magnitude of C and its distribution versus μi came out comparable with what other workers obtained and that the values of D are generally smaller than those of C for the entire range of μi which might be due to the existing baroclinicity in the AMTEX area. It is also revealed that the value of C decreases and that of D increases as the baroclinicity weakens, suggesting that the values of C and D become close one another in the limit of decreasing baroclinicity. Distributions of C and D versus μi are given by logarithmic expressions. The dependence upon μi the ratio of the height of PBL height zi and the neutral height scale λ was obtained. For the stronger instability region zi/λ∞(-μi)0.46. For the near neutral region zi would be linearly related to λ, accordingly to u*/_??_ with proportionality 0.15.
We decided the size distribution functions of stratospheric aerosols using the two-color lidar technique, and compared those with the measurements by other technique. The size distribution function of the stratospheric aerosols decided by this technique does not contradict with previous results. The method described here is useful technique to measure remotely the size distribution function of stratospheric aerosols.