Internal tide generation at a continental shelf/slope junction: A comparison between theory and a laboratory experiment

Observations of internal tide generation over continental slopes in a laboratory experiment have been carried out, with the objectives of making comparisons with linear generation theory and investigating its limitations. Both continuous and layered stratification have been considered. A measure of the amplitude of the barotropic tidal forcing (and hence of non-linearity) is given by the Froude Number F = u_sb/c_w, where u_sb is the maximum barotropic tidal velocity at the shelf break, and c_w is the long-wave speed of the lowest internal mode.For continuous stratification, good agreement was obtained for “steep” slopes (α/c > 1), where α is the slope at the continental slope and c is the slope of the internal wave rays of tidal frequency), even for quite large amplitude motions (F < 1.6), and the upper limit of its quantitative usefulness was not reached. For “flat” slopes (α/c < 1) reasonable agreement was also obtained, even up to quite amplitudes (F < 3.1), although some departure from linear theory was apparent.For two-layer flows the applicability of linear theory was much more restricted. For F 0.5 there was only qualitative agreement and for larger F (>1) significant differences were observed. The latter were due to the substantial advection and associated hydraulic jumps which occured seaward of the shelf-break during the ebb-phase of the barotropic tide. Shelf-break values of F > 1 are common in the ocean.     

Condensed water in tropical cyclone “Oliver”, 8 February 1993

On February 8, 1993, the NASA DC-8 aircraft profiled from 10,000 to 37,000 feet (3.1–11.3 km) pressure altitude in a stratified section of tropical cyclone “Oliver” over the Coral Sea northeast of Australia. Size, shape and phase of cloud and precipitation particles were measured with a 2-D Greyscale probe. Cloud/ precipitation particles changed from liquid to ice as soon as the freezing level was reached near 17,000 feet (5.2 km) pressure altitude. The cloud was completely glaciated at −5°C. There was no correlation between ice particle habit and ambient temperature. In the liquid phase, the precipitation-cloud drop concentration was 4.0 × 10³ m⁻³, the geometric mean diameter D_g=0.5−0.7 mm, and the liquid water content 0.7−1.9 g m⁻³. The largest particles anywhere in the cloud, dominated by fused dendrites at concentrations similar to that of raindrops (2.5 × 10³ m⁻³) but a higher condensed water content (5.4 g m⁻³ estimated) were found in the mixed phase; condensed water is removed very effectively from the mixed layer due to high settling velocities of the large mixed particles. The highest number concentration (4.9 × 10⁴ m⁻³), smallest size (D_g=0.3−0.4 mm), largest surface area (up to 2.6 × 10² cm² m⁻³ at 0.4−1.0 g m⁻³ of condensate) existed in the ice phase at the coldest temperature (−40°C) at 35,000 feet (10.7 km). Each cloud contained aerosol (haze particles) in addition to cloud particles. The aerosol total surface area exceeded that of the cirrus particles at the coldest temperature. Thus, aerosols must play a significant role in the upscattering of solar radiation. Light extinction (6.2 km⁻¹) and backscatter (0.8 sr⁻¹ km⁻¹) was highest in the coldest portion of the cirrus cloud at the highest altitude.     

Prediction of the abiotic degradability of organic compounds in the troposphere

A statistically relevant correlation between the reaction rate coefficient, k _OH, for the OH radical reaction with 161 organic compounds in the gas phase at 300 K, and the corresponding vertical ionisation energies E _i,v, reveals two classes of compounds: aromatics where –log(k _OH/cm³s^-1)3/2E _i,v(eV)–2 and aliphatics where –log(k _OH/cm³s^-1)4/5E _i,v(eV)+3. The prediction of the rate coefficient, k _OH, for the reaction of OH with organic molecules from the above equations has a probability of about 90%. Assuming a global diurnal mean of the OH radical concentration of 5×10⁵ cm³, the upper limit of the tropospheric half-life of organic compounds and their persistence can be estimated.     

Mean turbulent properties of the stable boundary layer observed during the “coast” experiment

An acoustic Doppler sounder has been used to document the behaviour of the stable atmospheric boundary layer during the “Coast” experiment, in April-May, 1983, on a homogeneous terrain near the Dutch coast. It has been shown that kaimal's model of the spectrum of velocity in the stable surface layer can be applied and that surface-layer parameterization can be used in the whole stable surface layer. Velocity spectra have been computed between .0005 c.p.s. and .1 c.p.s. and for the stability range for z/L between 0 and 10. It is to be noted that the information has been obtained using only sodar data.     

Rapid vertical sampling in stably stratified turbulent shear flows

A new method for obtaining instantaneous vertical profiles of two components of velocity and temperature in thermally stratified turbulent shear flows is presented. In this report, the design and construction of the traversing system will be discussed and results to date will be presented. The method is based on rapid vertical sampling whereby probe sensors are moved vertically at a high speed such that the measurement is approximately instantaneous. The system is designed to collect many measurements for the calculation of statistics such as vertical wave number spectra, mean square vertical gradients, and Thorpe scales. Results are presented for vertical profiles of temperature and compared to vertical profiles measured by single-point Eulerian time averages. The quality of the vertical profiles is found to be good over many profiles. Some comparisons are made between vertical measurements and standard single-point Eulerian measurements for three cases of stably stratified turbulent shear flow in which the initial microscale Reynolds number, Re_λ≈30. In case 1, the mean conditions are characterized by a gradient Richardson number, Ri_g=0.015, for which the flow is “unstable”, meaning the spatially evolving turbulent kinetic energy (E_k) grows. In case 2, Ri_g=0.095, for which the evolving turbulent kinetic energy is almost constant. In case 3, the flow is highly stable, where Ri_g=0.25 and E_k decays with spatial evolution. The measurements indicate anisotropy in the small scales for all cases. In particular, it is found that the ratio grows initially to a maximum and then decays with further evolution. Maximum Thorpe displacements are measured and compared to single-point measures of the vertical scales. It is found that vertical length scales derived from single-point measurements, such as the Ozmidov scale, L_O=(ε/N³)^1/2 and the overturn scale, L_t=θ′/(dT/dz), do not represent well the wide range of overturning scales which are actually present in the turbulence.     

The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

Decaying stratified turbulence: comparison between a two-point closure EDQNM model and direct numerical simulations

A new statistical two-point closure EDQNM (Eddy Damped Quasi Normal Markovian) model for axisymmetric stratified turbulence is presented. This model takes into account the detailed anisotropic structure of the flow, including angular dependence, and its closure assumption may involve explicit effects of the stratification. In the present paper, a simplified closure assumption is used, in which these explicit effects are not taken into account. The model is tested against three-dimensional direct numerical simulations (DNS) of decaying homogeneous stratified turbulence. A very good agreement is found between DNS results and EDQNM predictions, when energy transfers between the different modes of motion are considered. However, transfers among wavenumbers are insufficiently damped by the EDQNM model, because of the simplified closure assumption, thus yielding a somewhat less satisfactory agreement. An interesting prediction of the EDQNM model is the existence of a ‘directional’ anisotropy at all scales of motion, to the smallest: the level of the total (kinetic + potential) energy density spectrum E(k,θ_k) varies with the angle θ_k that the wavenumber vector k makes with the vertical.     

Coastal-trapped waves with finite bottom friction

Coastal-trapped waves with finite-amplitude bottom friction are explored. “Finite-amplitude” in this context means that the bottom stresses are large enough to change the wave modal structure. The importance of bottom friction is measured by the nondimensional number r/(ωh), where r is a bottom resistance coefficient, ω the wave frequency and h the water depth. Increasing bottom drag causes free wave modes to adjust by having their amplitude maxima for alongshore current translate offshore to the point that, with relatively large bottom stress, the alongshore current variance is trapped entirely on the slope, even though pressure variations remain substantial right up to the coast. In conjunction with these adjustments, wave frequency, hence propagation speed, varies and the wave damping is usually less than would be expected based on a weak-friction perturbation calculation. Stronger density stratification increases wave damping, all else being the same. A mean alongshore flow can strongly affect modal structure and wave damping, although general trends are difficult to discern. Results suggest that bottom friction may cause an observed tendency for lower frequency alongshore current fluctuations to become relatively more important with distance offshore.     

Stability classification by acoustic remote sensing

Two different Doppler acoustic sounders have been operated at the Kernforschungszentrum Karlsruhe (KfK) since 1982. It has been investigated whether meteorological data from these sounders can be used for dispersion modeling and monitoring in the environment of pollutant-emitting plants. Data from the sounders and from a 200 m high meteorological tower have been sampled continuously for intercomparison.Two schemes of stability classification are presented. They are based on 30-min mean values of the following meteorological data measured by the acoustic sounders: (a) standard deviation σ_w of the vertical wind speed and horizontal wind speed u, at a height of 100 m; and (b) standard deviation σ_φ of the vertical wind direction at a height of 100 m and vertical profile of the backscattered amplitude A_w.The class limits applied in these schemes are determined by “statistical equivalence” with a standard classification scheme. This standard scheme is based on σ_φ, measured by a vector vane at the 100 m level of the tower. Statistical equivalence in this context means that the frequency distributions of the classes are approximately equal at the same site and during the same period.The reliability of these schemes is investigated and compared to the standard scheme by correlation analysis. Finally, the schemes are compared with other commonly applied classification methods.     

Structure of the atmospheric surface layer over an industrialized equatorial area

This paper is written to report observations of the structure of the atmospheric surface layer over a coastal industrialized equatorial area. The observations were recorded at Prai Industrial Park, Penang (5° 22′ N, 100° 23′ E) a relatively simple terrain area during the south-west monsoon season in the period of three months using slow response systems. The limitations of the instruments used and its effects on the results are discussed. Wind turbulence and temperature were measured on a 10 m tower and analyzed using eddy correlation method and Monin–Obukhov similarity relations to obtain the normalized standard deviation of longitudinal (σ_u/u), lateral (σ_v/u) and vertical wind velocity fluctuations (σ_w/u) with respect to stability parameter z/L. From the results of the analysis, we found that most of turbulence is generated by shear or mechanical force. It was found that the average neutral value of σ_u/u is 2.35, 1.98 for σ_v/u and 1.47 for σ_w/u with a significantly lower than the proportionality to the power of 1/3 during unstable atmospheric conditions, and thus do not obey Monin–Obukhov similarity theory. It was observed that σ_u/u and σ_v/u values increase linearly in the range of 0 < z/L < 2 and fairly well correlated while σ_w/u does not.     

The reflection and diffraction of internal waves from the junction of a slit and a half-space, with application to submarine canyons

We consider the three-dimensional reflection and diffraction properties of internal waves in a continuously stratified rotating fluid which are incident on the junction of a vertical slit and a half-space. This geometry is a model for submarine canyons on continental slopes in the ocean, where various physical phenomena embodying reflection and diffraction effects have been observed. Three types of incident wave are considered: (1) Kelvin waves in the slit (canyon); (2) Kelvin waves on the slope; and (3) plane internal waves incident from the half-space (ocean). These are scattered into Kelvin and Poincaré waves in the slit, a Kelvin wave on the slope and Poincaré waves in the half-space. Most of the discussion is centered around case (1). Various properties of the wave field are calculated for ranges of the parameters c/cot θ, γα and ƒ/ω where cot θ is the topographic slope, c is the internal wave ray slope, α is the canyon half-width, γ is the down-slope wave-number, ƒ is the Coriolis parameter and ω is the wave frequency. Analytical results are obtained for small γα and some approximate results for larger values of γα. The results show that significant wave trapping may occur in oceanic situations, and that submarine canyons may act as source regions for internal Kelvin waves on the continental slope.     

Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale L_U = (ε/U_Z³)^1/2. At wavenumbers between the inertial-convective (k^−5/3) and wak turbulence (k⁻³) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E k⁻¹, E_T k⁻²). The upper boundary of these subranges is determined as L_U, and the lower boundaries as L_R (ε/U_ZN²)^1/2(χ/T_Z²). It is shown that the scale L_U is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale L_U is equivalent to the Thorpe scale L_Th for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E k^−11/5, E_T k^−7/5). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L_** = 3(χ^1/2/N^1/2T_Z), which is equivalent to the Thorpe scale L_Th. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale L_N ε^1/2/N^3/2 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.     

Barrier destruction and Lagrangian predictability at depth in a meandering jet

Numerical simulations of a jet with large amplitude meanders are used to explore chaotic advection processes and underlying geometry changes as functions of the ambient potential vorticity gradient β. Variations in β in the 2D model qualitatively simulate changes in depth in 3D, surface-intensified jets such as the Gulf Stream. As β is reduced, corresponding to motion on increasingly deep isopycnal surfaces, a number of geometrical transitions take place in the flanges and across the core of the jet. The most important is a joining (or separatrix reconnection) of heteroclinic cat’s eyes structures lying to the north and south of the jet core. The jet core acts as a barrier to transport, but this barrier is breached when the cat’s eyes merge. The subsequent chaotic transport across the jet is demonstrated by calculations of effective invariant manifolds (EIMs) originating in hyperbolic regions to the north and south of the core. Destruction of the central barrier occurs as β is lowered through a narrow window W about β=0 and is marked by transitions form a meandering jet through a vortex street with no central meandering flow to a vortex street with a retrograde meander. Such small values of β are deemed reasonable in view of measurements of low potential vorticity gradients in the deep Gulf Stream. The strength of the central barrier for β outside W is tested by varying β about a mean value β₀ and detecting the minimum amplitude of fluctuation necessary for destruction of the barrier. It is found that the barrier is stronger for β₀>0, at least by this measure. A striking difference is that, for β<0, some disturbances may destroy the barrier without oscillating across W; whereas for β>0, destruction of the barrier may only occur when β passes through W. Changes in underlying geometry also occur in the flanges of the jet and these changes alter the locations in which fluid is preferentially stirred and mixed. Float trajectories can be regular or irregular depending upon where the instrument is launched and this is demonstrated by plotting trajectories from inside and outside regions of chaotic advection.     

Error analysis of backscatter from discrete dipole approximation for different ice particle shapes

Ice sphere backscatter has been calculated using both Mie theory and the discrete dipole approximation (DDA) at a wavelength of 3.2 mm (94 GHz). The electric dipole, magnetic dipole and electric quadrupole contributions to spherical particle backscatter have been analyzed. The results show that there is a resonance area around particle size parameter of 1.5, where the calculated backscatter errors are very large due to the neglect of the magnetic dipole, and this is confirmed by applying Mie theory to 8.66 mm (35 GHz) and 3.21 cm (X-band) wavelengths. Based on the backscatter calculation using a cube and a hexagon column randomly oriented in space, it was found that the backscatter error from the inaccurate representation of the particle surface shape is much smaller than that from the neglect of the magnetic dipole, and the resonance occurs at different particle sizes depending upon the exact particle shapes. At a wavelength of 3.2 mm, the particle shape has little effect on backscatter when volume-equivalent spherical particle radius r_v < 500 μm, and Rayleigh backscatter can be used as a reasonable approximation for r_v < 300 μm.     

On the effects of rotation on fluid motions in cylindrical containers of various shapes and topological characteristics

Previous theoretical and laboratory studies of mechanically driven fluids in general rotation relative to an inertial frame have shown that there is a special class of flows for which the (Eulerian) flow field u(r, t) relative to the rotating frame of reference is unaffected by gyroscopic (Coriolis) forces, and therefore remains the same for all values of the rotation vector Ω. (Here t denotes time and r the position of a general point R in a reference frame attached to the rotating apparatus.) Such flows occur when (a) Ω is independent of time t; (b) u(r, t) is independent of the coordinate z (say) parallel to Ω, (c) the fluid has constant density and is therefore ‘barotropic’ (i.e. no density variations on horizontal surfaces) and (d) the topology of the cross-section of the (cylindrical) container, in planes z = constant, is such that the bounding surfaces can support the concomitant field of (kinematic) pressure P₁ satisfying P₁ + 2 Ω × U = 0 Condition (d) is equivalent to the requirement that any fluid sources or siks within the system be multipole in character, but not monopole. In the present study the ‘baroclinic’ case is treated, where buoyancy forces due to the action of gravity (and centripetal forces) on horizontal density variations have to be taken into account. These include investigations of flows due entirely to buoyancy forces, such as thermal convection in fluids in rotating cylindrical containers of various shapes and topological characteristics subject to horizontal temperature gradients. The implications for the impressed temperature field of the mathematical requirements that the fields of kinematic pressure P₁ and density (where denotes the mean density) be everywhere single-valued are guiding such investigations and facilitating the interpretation of their findings. The investigations include laboratory studies, reported elsewhere, of convection in a rotating fluid annulus with a circular cross-section blocked by a radial barrier, where it is found inter alia that advective heat transfer is virtually independent of |Ω| over a wide range of conditions. They also include (as yet unpublished) studies of thermal convection in rotating systems with topologically triply connected cross-sections which can be rendered doubly or simply connected by the insertation of suitable barriers.     

Rate constants for the reactions of the NO3 radical with HCOOH/HCOO− and CH3COOH/CH3COO− in aqueous solution between 278 and 328 K

The kinetics of the aqueous phase reactions of NO₃ radicals with HCOOH/HCOO^– and CH₃COOH/CH₃COO^– have been investigated using a laser photolysis/long-path laser absorption technique. NO₃ was produced via excimer laser photolysis of peroxodisulfate anions (S₂O ₈ ^2– ) at 351 nm followed by the reactions of sulfate radicals (SO ₄ ^– ) with excess nitrate. The time-resolved detection of NO₃ was achieved by long-path laser absorption at 632.8 nm. For the reactions of NO₃ with formic acid (1) and formate (2) rate coefficients ofk ₁=(3.3±1.0)×10⁵ l mol^–1 s^–1 andk ₂=(5.0±0.4)×10⁷ l mol^–1 s^–1 were found atT=298 K andI=0.19 mol/l. The following Arrhenius expressions were derived:k ₁(T)=(3.4±0.3)×10¹⁰ exp[–(3400±600)/T] l mol^–1 s^–1 andk ₂(T)=(8.2±0.8)×10¹⁰ exp[–(2200±700)/T] l mol^–1 s^–1. The rate coefficients for the reactions of NO₃ with acetic acid (3) and acetate (4) atT=298 K andI=0.19 mol/l were determined as:k ₃=(1.3±0.3)×10⁴ l mol^–1 s^–1 andk ₄=(2.3±0.4)×10⁶ l mol^–1 s^–1. The temperature dependences for these reactions are described by:k ₃(T)=(4.9±0.5)×10⁹ exp[–(3800±700)/T] l mol^–1 s^–1 andk ₄(T)=(1.0±0.2)×10¹² exp[–(3800±1200)/T] l mol^–1 s^–1. The differences in reactivity of the anions HCOO^– and CH₃COO^– compared to their corresponding acids HCOOH and CH₃COOH are explained by the higher reactivity of NO₃ in charge transfer processes compared to H atom abstraction. From a comparison of NO₃ reactions with various droplets constituents it is concluded that the reaction of NO₃ with HCOO^– may present a dominant loss reaction of NO₃ in atmospheric droplets.     

Comment on “Glory phenomenon informs of presence and phase state of liquid water in cold clouds” by Anatoly N. Nevzorov

In a recent publication “Glory phenomenon informs of presence and phase state of liquid water in cold clouds” Nevzorov [Nevzorov, A., 2006. Glory phenomenon informs of presence and phase state of liquid water in cold clouds. Atmospheric Research 82, 367–378] claims that “the convincing evidence has been provided that this sort of glory forms as a first-order bow from spherical particles with a refractive index of 1.81–1.82 and diameter over 20 μm”. This is a highly unusual finding because the refractive index of liquid water and ice is between 1.30 and 1.35 in the visible spectral range. The author concludes that “once more corroboration is gained […] of droplets of liquid water in specific phase state referred to amorphous water, or A-water”. Here we show that the phenomena described by the author are easily explained assuming liquid water with a refractive index of 1.33 and a realistic droplet size distribution with an effective radius of around 10 μm. We conclude that this type of observations does not corroborate the existence of amorphous water in the atmosphere. In a recent publication we showed how to quantitatively derive cloud optical thickness, effective droplet radius, and even the width of the size distribution from observations of the glory [Mayer, B., Schröder, M., Preusker, R., Schüller, L., 2004. Remote sensing of water cloud droplet size distributions using the backscatter glory: a case study. Atmospheric Chemistry and Physics 4, 1255–1263].     

A group-kinetic theory with a closure by memory loss for modeling turbulence in the atmosphere and the oceans

Summary The principle of the group-kinetic method is elucidated. This method of renormalization serves as the basis for analyzing the spectral structure of turbulence. The spectral distributions include the Kolmogoroff lawk ^–5/3 for isotropic turbulence, the power lawk ^–1 for shear turbulence, the spectrum for stratified turbulence not in the power law form, the power lawk ^–3 for two-dimensional geostrophic turbulence, and the power lawsk ^–3,k ^–2 andk ^–5 for two-dimensional Rossby wave turbulence with uniform and differential rotations. We discuss a spectrum-dependent modeling in reference to the problems of the universal functions and parameters in the similarity theories for the atmospheric surface layer and the planetary boundary layer. A renormalization-based modeling of atmospheric turbulence is proposed.     

Refraction of Rossby waves on a multiple β-plane

A multiple β-plane is introduced to explore the relation between plane and spherical Rossby waves. The fundamental problem, the refraction of a plane Rossby wave across a discontinuity in β, is solved. It is shown that refraction on the multiple β-plane agrees in the limit with refraction on the full sphere only if a suitable correction is made for the geometric distortion of the β-plane. The full spherical modes of Rossby waves trapped in a band about the equator (Longuet-Higgins, 1964) have their counterpart in a simple model consisting of an “equatorial” β-plane bounded above and below by “polar” β-planes.     

The structure and propagation of stationary planetary wave packet in the barotropic atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (Uλ/y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.