Experiments with viscous source flows in rotating systems

The dynamics of oceanic bottom currents are examined both theoretically and in the laboratory. A class of similarity solutions for steady flow indicates that the geostrophic current is drained by Ekman flux at its downslope edge and ultimately extinguished at a downstream distance of order $\text{(}\text{fQ}\text{s}{}^2\text{g}{}_{\mathrm{r}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ magnified by $\text{E}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$.Laboratory source flows are found to be consistently wave-like. Nevertheless, certain gross features of the steady Ekman flux mechanism are observed. Instabilities are classified according to the magnitudes of Rossby (?) and Ekman (E) numbers for the steady flow scaling. Characteristic were forms include: (1) a meandering jet (E < ?, 10^?2); (2) transverse waves on broad contour current (? < E, 10^?2); and (3) transverse waves on a viscous flow (?, E > 10^?2). The dispersion relation for source flow waves resembles that of baroclinic instabilities for a uniform two-layer channel flow, and an empirically determined stability boundary is in rough agreement with the inviscid channel flow criterion.An interpretation of field measurements from the Denmark Strait Overflow in terms of the laboratory results is presented.     

旋转球面上行星波的共振相互作用

本文从球面非线性位涡方程出发,应用多重尺度法导出了三波共振的耦合方程.求得非线性耦合方程的通解可以用椭圆函数表示,因而扰动的能量及其变化是有界的.同时,还探讨了共振三波组的守恒律以及共振激发过程中能量的转换.指出在一定的初始条件下,非线性相互作用是可逆的;且就纬向波数谱而言,大波数模态的初始扰动能量在共振激发过程中可以完全转化为较小波数模态的能量.并揭示了旋转大气中非线性行星波动的孤立子性质.     

Experiments on numerical modeling of intense convection

Results of numerical simulations using the WRF-ARW nonhydrostatic model are presented for eight episodes of intense convection over European Russia in the summer of 2007. The calculations were performed on four nested grids with horizontal grid meshes of 27, 9, 3, and 1 km. Convection was parametrized on the first two grids and explicitly resolved on the other two. It has been found that simulations on finer grids with explicit calculation of convective flows make it possible to reproduce heavy rainfalls and strong-wind zones in the areas of intense convection. A preliminary verification of the short-range predictions of convective systems shows that the maximum 12-h precipitation totals and the maximum winds at 10 m are close, in the order of magnitude, to the observed values. Prediction of convection centers is the weakest point. Difficulties in the model verification associated with the absence of data with high space-time resolution are discussed.     

Experiments with density currents on a sloping bottom in a rotating fluid

The behaviour of a density current on a sloping bottom in a rotating system is investigated by laboratory experiments. The main result is that the dense bottom outflow induces cyclonic vortices in the upper fluid layer, which are formed periodically and move to the west parallel to coast. Two regimes of vortex formation have been identified. For strong density currents and weak rotation, vortices are formed by stretching of the upper layer near the source as found also in the experiments by Lane-Serff and Baines (1998) [Lane-Serff, G.F., Baines, P.G., 1998. Eddy formation by dense flows on slopes in a rotating fluid. J. Fluid Mech. 363, 229–253]. For weak density currents and strong rotation vortices are due to instability of the bottom plume itself as found in the numerical simulations of Jiang and Garwood (1996) [Jiang, L., Garwood, W. Jr., 1996. Three-dimensional simulations of overflows on continental slopes. J. Phys. Oceanogr. 26, 1224–1233].     

Experiments on high Richardson number instability of a rotating stratified shear flow

A recently discovered mechanism for producing step-like structure in a fluid's density field is explored under controlled laboratory conditions. Measurements of the conditions under which these “layers” exist, their direction, wavelength, and growth rate, are made and compared to the predictions of instability theory. The good agreement indicates that the layers are a result of a diffusive instability of a geostrophic shear flow. The instability can occur at higher and higher Richardson numbers, as the Schmidt number (ratio of diffusivities of momentum and salt) increases. Comparison of the density and velocity fields in the presence and absence of fully developed layers indicates that the instability functions mainly to transport momentum. Extrapolation of the measured wavelength to midlatitude oceanic conditions suggests that the momentum-density diffusive instability may play a role in producing meter-size oceanic microstructure.     

Penetrative convection in rapidly rotating flows: preliminary results from numerical simulation

Turbulent convection forced by a surface heat flux into a stably stratified region is a feature of both the atmospheric and oceanic planetary boundary layers. Of particular interest is the interface between the convective layer and the stable stratification, where the entrainment of fluid into the convective layer by penetrating plumes may lead to a reverse buoyancy flux, and an enhancement of the stable stratification. Whereas in the atmosphere the influence of rotation on this penetrative convection is negligible, oceanic convection may be subjected to lower Rossby numbers and hence greater rotational influence. To isolate the effects of rotation, we present three numerical solutions for turbulent penetrative convection, characterised by different rotation rates, with all other parameters being held constant. Our results indicate that at lower Rossby numbers the lateral scale of the plumes is reduced, whereas the vertical vorticity of the plumes is much enhanced. Vertical transports of buoyancy and kinetic energy across the convective layer are reduced, leading to less efficient penetration at the interface with the stratified layer, and hence less reverse buoyancy flux in this region.     

The lower symmetric regime and its transition to waves in rotating annulus convection

Measurements of the temperature and zonal velocity fields which develop in a rotating annulus of fluid with an upper surface, differentially heated from the inner to outer cylinder, are described for the lower symmetric regime (small radial temperature differences). The temperature field is essentially conductive for moderate to large rotation rates, Ω (>1.0 sec⁻¹). The zonal velocity field is poorly approximated by the thermal wind equation.Measurements of the transition to waves from the lower symmetric regime at very large rotation rates are presented for positive and negative radial temperature differences. They suggest that the centrifugal buoyancy force and the free surface curvature may be important factors for the lower symmetric-wave transition at large Ω. By varying the stratification of the fluid over a range of 10³ independently of the radial temperature difference, Δr_wT, it is conclusively shown that several theories are correct in predicting that the lower symmetric transition is independent of the stratification at small Δr_wT > 0 for large enough Ω.     

Interaction between atmospheric flows and obstacles: Experiments in a rotating channel

We performed an experimental study using scale models in a hydrodynamic rotating channel, concerning the interactions between fluid flows and obstacles of different shapes. The study was meant to analyze the characteristics of the wakes observed on the lee side of quasi-bidimensional obstacles, in a neutral atmosphere.The obstacles were half-cylinders (with aspect ratio 0.87), placed transversally on the channel bottom and totally submerged in the fluid. We call them quasi-bidimensional since their width was a little smaller than the channel width, thus allowing the flow to partially go round their edges.The simulations were performed in the rotating hydraulic channel of ICG-CNR in Turin, and included various conditions of rotation period and flow speed. An interesting behaviour of the wakes was found on the lee side of subsynoptic-scale obstacles, modelled in conditions of Reynolds-Rossby similitude. More precisely, if a given threshold of flow velocity is exceeded, wake size is constant and is fully determined by the height of the obstacle.     

Onset of convection in a rotating semi‐infinite fluid: Theory and experiment

Abstract

We look at the development of the first plumes that emerge from a convectively unstable boundary layer by modelling the process as the instability of a fluid with a time‐dependent mean density field. The fluid is semi‐infinite, rotating, dissipative ‐ characterized by the ratio of its viscosity to thermal diffusivity (Prandtl number Pr = ν/κ) ‐ and initially homogeneous. A constant destabilizing heat flux is applied at the boundary and the stability of the evolving density field is investigated both mathematically and in laboratory experiments.

Using a “natural convective” scaling, we show that the behaviour of the non‐dimensional governing equations depends on Pr and the parameter γ = f(ν/B)^1/2, where f is the Coriolis parameter, and B is the applied buoyancy flux. For the ocean, γ ≈ 0.1, whilst for the atmosphere γ ≈ 0.01. In the absence of rotation, the behaviour of the differential equations is independent of B, depending only on Pr. The boundary‐layer Rayleigh number (Ra_bl) is also independent of B. We show that Ra_bl, evaluated at the onset of rapid vertical motion, depends on the form of the perturbation.

Due to the time‐dependence of the mean density field, analytic instability analysis is difficult, so we use a numerical technique. The governing equations are transformed to a stretched vertical coordinate and their stability investigated for a particular form of perturbation function. The model predictions are, for the ocean: instability time ～2–4 h, density difference ～0.002–0.013 kg m^‐3, boundary‐layer thickness ～50–75 m and horizontal scale ～200–300 m; and for the atmosphere: instability time ～10 min, temperature difference ～2.0–3.0°C, boundary‐layer thickness ～400–500 m and horizontal scale ～1.5–2.0 km.

Laboratory experiments are performed to compare with the numerical predictions. The time development of the mean field closely matches the assumed analytic form. Furthermore, the model predictions of the instability timescale agree well with the laboratory measurements. This supports the other predictions of the model, such as the lengthscales and buoyancy anomaly.     

A note on circulation in differentially heated rotating stratified fluid and other elliptic problems

This note relates to the paper Circulation and boundary layers in differentially heated rotating stratified fluid by Whitehead and Pedlosky [Whitehead, J.A., Pedlosky, J., 2000. Circulation and boundary layers in differentially heated rotating stratified fluid. Dyn. Atmos. Ocean. 31, 1–21]. Here, we describe an alternative method of solution for the theoretical model developed therein, and provide a comparison with the original method used in the paper.     

A note on circulation in differentially heated rotating stratified fluid and other elliptic problems

This note relates to the paper Circulation and boundary layers in differentially heated rotating stratified fluid by Whitehead and Pedlosky [Whitehead, J.A., Pedlosky, J., 2000. Circulation and boundary layers in differentially heated rotating stratified fluid. Dyn. Atmos. Ocean. 31, 1–21]. Here, we describe an alternative method of solution for the theoretical model developed therein, and provide a comparison with the original method used in the paper.     

Results on planetary boundary layer sounding by automatic rass

A radio acoustic sounding system (RASS), operating at an acoustic frequency ƒ 360 Hz, proved to be capable of measuring the vertical temperature profile in the planetary boundary layer (PBL) with an accuracy and vertical resolution comparable to those of traditional apparatus (radiothermosondes borne by tethered or disposable balloons, thermosondes borne by aircraft and so on, yet combined with the advantages typical of remote sensing techniques.Since summer 1983 the system has been running in a completely automatic way by means of a microprocessor and can provide the average thermal profile at preset time intervals (typically 0.5 h). (Previously, the acoustic sounding frequency affording the fundamental condition of Bragg resonance between acoustic and radio wavelengths had to be identified by an operator).The maximum range of measurement has been 1000 m in 50% of cases. Temperature measurements are reliable from an altitude of a few tens of meters.Results for different thermodynamic stability conditions, together with good performances achieved in adverse atmospheric conditions such as strong wind, snow, rain, etc., are presented here.Such results indicate the usefulness of the automatic RASS as a tool for meteorological purposes and for the application of air pollution control strategies.Maximum sounding range attained for different areas of the acoustic antenna is also analysed in order to evaluate the performance of an automatic mobile RASS.     

A note on the multi-α solutions of the upper bounding problem for thermal convection

The transition to “multi-α” solutions of the upper bounding problem for thermal convection is discussed. For convection in a fluid contained between parallel stress-free perfectly conducting boundaries, the “single-α” solutions of Straus (1973) are used to determine the Rayleigh number R at which the first transition occurs. Two upper bounding problems are treated: one valid for all values of the Prandtl number and one valid only for large Prandtl numbers. A significant difference between the two problems is noted. The former has a transition at R ～ 28200; the latter has no transition within the range of Rayleigh numbers treated here: R ? 2.3 · 10⁵.     

播撒碘化银粒子进行人工防雹的数值试验

本文在二维完全弹性冰雹云数值模式中，引入冰晶浓度和播撒物质AgI粒子的守恒方程，建立了一个二维催化模式，考虑了人工冰核的三种成核机制，即凝华核化（包含凝结—冻结核化）及与云、雨滴的接触冻结核化，模拟了几种不同冰雹云、不同催化方案下的人工防雹催化效果，指出了防雹的最佳催化方案和适宜催化作业的冰雹云条件。     

夏季西藏高原对北半球定常行星波形成的热力作用

本文应用一个包括Rayleigh摩擦、Newton冷却与水平涡旋热力扩散的准地转34层球坐标模式来研究西藏高原对夏季北半球定常行星波形成的热力作用. 计算结果表明夏季位于西藏高原上空的热源对于北半球夏季定常行星波形成的热力作用要比高原地形的动力作用大得多. 本文还计算了夏季北半球地形与热源强迫所产生的定常行星波与等高面上定常扰动系统的分布,其计算结果与由实际观测所得到的分布比较一致.     

On the formation and shedding of vortices from side-wall mounted obstacles in rotating systems

The flow of a homogenous, incompressible, rotating (vertically upward) fluid past cylinders of triangular and semi-circular cross-section mounted on either the left or right wall (facing downstream) of a channel is investigated experimentally. The pertinent system parameters are the Rossby and Ekman (or Reynolds) numbers and the obstacle width to fluid depth ratio. The experiments indicate that the shedding of tip eddies from the triangular obstacle leads to a rather complex wake motion which is critically dependent on the system parameters. For certain parameter combinations the tip eddies advect downstream as single entities while in other regions of parameter space two or more eddies merge and advect downstream as large-scale eddy structures.The Strouhal numbers for both the shedding of the tip eddies as well as of the large-scale structures are measured as functions of the system parameters. Measurements of the dimensionless size of the large-scale starting eddies are made as functions of a dimensionless time and other system parameters. It is shown that eddies formed in the lee of obstacles mounted on the right (anticyclonic) tend to shed more quickly, other parameters being fixed, than those on the left (cyclonic).Measurements of the dimensionless vorticity of the cores of the large-scale structures at a fixed dimensionless time indicate that, within the accuracy of the experiments and for the range of parameters considered, this quantity is independent of the Rossby and Reynolds numbers and the side to which the obstacle is mounted. Finally some of the experimental flow patterns are shown to be similar to a recent observation of a southeastward ocean current past the western tip of Grand Bahama Island.     

Quasi-stationary organized convection in the presence of an inversion near the surface: Experiments with a 2-D numerical model

Summary Quasi-steady states of organized convection are studied in a two-dimensional nonhydrostatic primitive-equation numerical model. Uni-and multi-cellular patterns are identified in the presence of a low-level inversion, and discussed in relation to those obtained, by various authors, in the more traditional monotonic-sounding case. The stable layer near the ground is shown to be responsible for a configuration of flow normally not observed in cases of monotonic sounding and reminiscent of an orographically generated wave. Exploring the conditions conducive to quasi-steady convection it is found that in the presence of a low-level inversion, a strong shear of the wind component perpendicular to the squall line is required near the surface, deeper than that required in the absence of the inversion.With 10 Figures     

旋转大气中运动适应过程问题的研究(二)

本文试图对旋转大气中运动适应过程问题的研究作一全面的评述,这里是全文的第二篇,包括三方面的内容,即球面上大气的地转适应过程和旋转适应过程;快波的激发以及涡旋和快波的相互作用问题;适应过程理论结果在天气分析和预报以及数值天气预报等方面的应用问题。     

循环同化相控阵雷达数据模拟对流触发同化方案研究

利用WRF-EnKF同化系统,以2020年7月5日北京大兴发生的一次强对流天气背景下对流触发过程为个例,研究同化C波段相控阵雷达数据时更优的同化方案设置。本研究从同化频率、晴空数据处理阈值以及边界层杂波处理高度3个方面进行了研究。结果显示,高频同化可以抑制虚假回波,并有利于获得更准确的对流预报结果。将可靠晴空回波识别阈值设为-10 dBZ并剔除边界层内的低值回波可以有效改进对流触发的预报效果。为以后C波段相控阵雷达同化应用提供了新的同化方案思路。