Boltzmann statistical theory and asymptotics of the temperature distribution of spontaneous jets in the convective atmospheric surface layer

An ensemble of convective thermals is distinguished from the surface layer of penetrative turbulent convection over a heated horizontally uniform surface. A statistical model of the ensemble of convective thermals is developed that uses the idea of entropy in the Boltzmann-Jaynes form. The distribution of thermals by potential energies is shown to display an entropy maximum. On the basis of the Boltzmann distribution by potential energies, the temperature distribution of spontaneous jets is obtained and found to be consistent with known experimental data.     

自然对流条件下冰水界面换热系数的试验研究

在冰脊的固结过程中，由于接触面积与温差的大幅提升，冰水之间的换热强度显著增强。本文通过浸没试验对自然对流条件下冰水间的换热系数进行了研究。在试验过程中，对试样内部的温度分布与体积变化分别用温度梯度测试系统与数字图像进行测量。为研究初始条件对换热系数的影响，分别采用不同初始温度与厚度的试样在瞬态热传导的环境下进行测试。试验结果表明，换热系数与表面温差呈指数增长，且在本文试验条件下的变化区间为0.3~175 W/（m2·K）。试样的初始温度及厚度并不是影响换热系数的直接因素，而其根本因素为流-固界面的边界层状态。在自然对流状态下流体的驱动条件是热胀效应，即当边界层存在温度差时，虽然外界并不存在扰动流体状态的因素，但由于液体自身温差引起的密度差进而驱动流体运动并影响了换热系数。随着边界层温度梯度的增加，边界层的影响区域扩大，从而导致了较高的换热系数。     

Convection forced by a descending dry layer and low-level moist convergence

A narrow line of convective showers was observed over southern England on 18 July 2005 during the Convective Storm Initiation Project (CSIP). The showers formed behind a cold front (CF), beneath two apparently descending dry layers (i.e. sloping so that they descended relative to the instruments observing them). The lowermost dry layer was associated with a tropopause fold from a depression, which formed 2 d earlier from a breaking Rossby wave, located northwest of the UK. The uppermost dry layer had fragmented from the original streamer due to rotation around the depression (This rotation was also responsible for the observations of apparent descent—ascent would otherwise be seen behind a CF). The lowermost dry layer descended over the UK and overran higher  θ _w   air beneath it, resulting in potential instability. Combined with a surface convergence line (which triggered the convection but had less impact on the convective available potential energy than the potential instability), convection was forced up to 5.5 km where the uppermost dry layer capped it. The period when convection was possible was very short, thus explaining the narrowness of the shower band. Convective Storm Initiation Project observations and model data are presented to illustrate the unique processes in this case.     

Effect of the tangential component of a force field on convection in a rotating plane layer

Thermal convection in an inclined plane layer having boundaries with different temperatures and rotating around an axis perpendicular to its plane is studied experimentally. It is shown that the convection and heat transfer are determined by two different convective mechanisms—gravitational and thermovibrational ones; they manifest themselves in the threshold excitation of cellular convective structures with different sizes. The thermovibrational convection is caused by the period-averaged mass force arising as a result of tidal oscillations of a nonisothermal fluid with respect to the cavity under the action of the external force-field component tangential to the layer. The map of convection regimes on the plane of governing parameters—the gravitational Rayleigh number and its vibrational analog—has been constructed. It has been found that the thermovibrational convection can develop even in a layer heated from above. The role of the dimensionless velocity of rotation, which has a stabilizing effect on the excitation of both gravitational and thermovibrational convection, has been studied.     

Thermochaline Convection in the Edge-Ice Zone in the Barents Sea to the East of Spitsbergen

The analysis of the thermochaline (double-diffusive) convection in the edge-ice zone of the Barents Sea to the east of Spitsbergen was performed by using the data of two hydrological surveys of the Norwegian Polar Institute in 1999 and 2000. The Turner's model, where the critical Rayleigh number is determined by using the empirical relationship between the Nusselt number and the Rayleigh number normalized to its critical value, was used for analysis. The results of calculation of thickness of the convective layer were compared with the data of supervision. The estimates of the vertical convective velocity were obtained.     

Application of MEP Method to the Study of Statistical Properties of Random Waves

—The maximum entropy principle(MEP)method and the corresponding probability evaluationmethod are introduced,and the maximum entropy probability distribution expression is deduced in mo-ment of the second order.Fully developed wave height distribution in deep water and wave height and peri-od distribution for different depths in wind wave channel experiment are obtained from the MEP method,and the results are compared with the distribution and the experimental histogram.The waveheight and period distribution for the Lianyungang port is also obtained by the MEP method,and the re-sults are compared with the Weibull distribution and the field histogram.     

A numerical model for the evaluation of the depth of penetration of two-dimensional turbulent convection

For a one type of temperature turbulent convection observed in the ocean, i.e., for the two-dimensional roller-type convection, we propose a model intended for the evaluation of the intensity and depth of penetration of convective motions as functions of a given heat flow from the sea surface and the temperature gradient in the thermocline. This model is based on the methods of the theory of turbulent jets and experimental data on the vertical distribution of temperature in the course of convection. The comparison of the calculated dimensionless values of the depth of penetration of the thermocline in autumn and winter shows a good qualitative agreement with the data ofin situ measurements. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Characteristics of a front formed by cooling of the sea surface and inflow of the fresh water

Two numerical studies (Endoh, 1977;Harashima et al., 1978) have been proposed on a front formed by a coupling effect of cooling of the sea surface and inflow of the fresh water in a vertical two-dimensional plane without the rotation of the earth. It is, however, not easy to interpret their numerical results. A simple interpretation will be proposed by an analytical study in this paper.It is found that local convection due to the density inversion, which is expressed by the convective adjustment of the vertical diffusion coefficient in the actual numerical calculations, plays an important role on the front formation.The characteristics of the front is also clarified in the case of steady state. Namely, simple functional dependences are obtained of the position and the width of the front, the horizontal and the vertical velocities and the distribution of the buoyancy and the salinity in the neighborhood of the front on the horizontal coordinate, the cooling rate, the eddy coefficients of diffusion and viscosity, the water depth and the vertically averaged horizontal fluxes of buoyancy and salinity.     

Electricity of the convective atmospheric boundary layer: Field observations and numerical simulation

The electric state of the middle-latitude convective atmospheric boundary layer (ABL) is investigated during a point in time when it is not disturbed by clouds, precipitation, mist, or industrial aerosols. A numerical model is developed that estimates the electroaerodynamic state of the convective ABL. The model is parameterized using results of field observations and laboratory experiments. According to the model, vertical profiles of atmospheric electric field strength, space charge density, electric conductivity, and atmospheric electric current density are calculated in the horizontally homogeneous approximation with a high space-time resolution.     

Suspension of sediment particles over a ripple due to turbulent convection under unsteady flow conditions

We analyzed the motions of small sediment particles over a sinusoidal ripple due to an unsteady turbulent boundary layer flow using Large Eddy Simulation. The motions of sediment particles are described in terms of the Lagrangian framework as it is helpful in studying the structure of sediment suspension in detail. Strong coherent vortical structures are well developed along the upslope of the ripple surface during the accelerating flow phase, which effectively drag the particles to the ripple crest. At the maximum flow rate and at the decelerating flow phase, a cloud of vortical structures is developed vertically in the lee area of the ripple. Sediment particles render strong dispersion in the vertical direction when they are captured by these turbulent vortices, causing convective sediment flux that cannot be explained by the mean flows. The convective sediment suspension is strongest at the time of flow deceleration, while over a flat bed at the time of flow reversal. This observation suggests that bed form effect should be considered in modeling convective sediment flux.     

Double-diffusive convection with a nonlinear equation of state: Part II. Laboratory experiments and their interpretation

The term cabbeling describes the convection that can occur when a mixture of two oceanic water masses is more dense than both of the parent water masses. When the two water masses are situated one above the other, the temperature and salinity distributions are in the correct senses for double-diffusive convection to occur and it is found that the prime effects of the nonlinearity of the equation of state are firstly to drive a greater level of double-diffusive convective activity in the lower layer than in the upper layer, and secondly, to make the lower edge of the interfacial region less gravitationally stable. Both of these effects cause the interface to migrate upwards as the lower layer grows at the expense of the upper layer. We introduce a nondimensional parameter $\text{δ}$ (called the cabbeling parameter) which represents the importance of the nonlinearity of the equation of state:—$\text{δ}$ is zero when the equation of state is linear and when cabbeling is normally thought to be possible, $\text{δ}$ is greater than unity. Experiments set up in both the finger and diffuse sense show how the nondimensional measure of the upward interface migration (called the “entrainment” parameter $\text{E}$) varies with the density anomaly ration R_? for various values of $\text{δ}$ between zero and 2.0 and that no abrupt change in this behaviour occurs at $\text{δ}\text{= 1.0}$. It is impossible to explain these observation by neglecting double-diffusive convection and considering only the convection driven by the conventional cabbeling instability. The successful interpretation of the laboratory results relies on considering the effects of a non-linear equation of state on the double-diffusive convection process.     

Development of a Subcloud Layer over the Sea during a Cold Air Invasion

Evaporation and vertical moisture and heat transfer from the underlying surface are the basis of cloud formation. The situation when the coming relatively cold stably stratified air moves over a warm ocean is a typical problem in the development of a turbulent convective layer. The problem of cloud formation is also of scientific and practical interest. This paper considers the problems of the formation of a turbulent convective layer over a warmer ocean and the vertical distribution of relative humidity. The results of the theoretical model are compared with the data of observations of the development of the turbulent convective layer at low latitudes (in the Indian Ocean) and at higher latitudes (in autumn over Lake Michigan). Approximate equations describe well the dynamics of temperature and humidity of the layer as a function of the difference between the temperatures of the approaching and near-surface air layers. The theoretical results are compared with the data on measurements of the condensation heights obtained at the Novosibirsk Tolmachevo Airport. Some discrepancy between them is due to the unsteadiness measurement and the approximations adopted in the theoretical model.     

Transporting passive additives in a turbulent medium under convective mixing

The vertical transport of passive additives in a medium in the presence of both turbulent and convective mixing is studied. It is shown that, despite the fact that turbulent and convective fluxes are uncorrelated, no additive mechanism of mixing exists. On the basis of a theoretical model and a comparison with model calculations, it is shown that, in the presence of both turbulent and convective mixing in a medium, the effect of the interference of turbulent and convective transport mechanisms takes place. This effect is manifested in the following way: the presence of convection decreases the coefficient of turbulent transport and the presence of turbulence decreases the coefficient of convective transport; in this case, this effect depends on the parameter of the inhomogeneity (extension) of convective fluxes. The relative contribution of each of the mechanisms to the total transport is estimated. It is shown that the interference of turbulence and convection results in an anisotropy of the coefficient of turbulent transport in an isotropic turbulent velocity field. The effect of the coefficient of molecular diffusion is assumed to be negligibly small, and its effect is not taken into consideration when analyzing model results. The interference of the turbulent and convective mechanisms of transport is explained by the inclusion of an additional mechanism that decreases the distance of linear particle propagation.     

Linear Approximations of the Second Turbulent Moments of the Atmospheric Convective Surface Layer in a Forced-Convection Sublayer

The Monin–Obukhov similarity theory for the convective surface layer distinguishes two limiting cases: a dynamic limit and a free-convection limit. The dynamic limit for the convective surface layer is defined as a flow with a logarithmic profile of wind and a zero buoyancy flux at the underlying surface. The free-convection limit is characterized by a zero wind speed and a positive buoyancy flux at the underlying surface. The limits of the generalized Monin–Obukhov similarity theory are able to describe the higher order turbulent moments. In this paper, it is assumed that the convective surface layer consists of two sublayers: the lower dynamic sublayer adjacent to the surface and the upper forced-convection sublayer. The turbulent moments can be approximated separately for each sublayer. Linear approximations are suggested for the turbulent moments of the vertical velocity and the potential temperature variance in the forced-convection sublayer. The first-order expansion terms of them correspond to the free-convection limits of the Monin–Obukhov theory under no-wind conditions. The second-order expansion terms describe profiles of the turbulent moments in under convective conditions with a moderate wind. A comparison between the proposed approximations and experimental data strongly suggests that the linear approximation is correct within a forced-convection range.     

卫星SAR图像的海洋大气边界层特征参数的反演

针对中国南海ERS-2／SAR三维对流涡旋图像,分别利用Young的协方差方法和惯性子域方法,反演了对流海洋大气边界层高度、海洋大气边界层垂直对流尺度速度、表面浮力通量、Obukhov长度、稳定性校正后的海面风速和海面风速稳定性校正因子。结果表明,2种反演方法的结果符合较好,在一定程度上说明利用协方差方法和惯性子域方法从卫星SAR图像反演海洋大气边界层参数的有效性。     

Exponential leap-forward gradient scheme for determining the isothermal layer depth from profile data

Two distinct layers usually exist in the upper ocean. The first has a near-zero vertical gradient in temperature (or density) from the surface and is called the isothermal layer (or mixed layer). Beneath that is a layer with a strong vertical gradient in temperature (or density), called the thermocline (or pycnocline). The isothermal layer depth (ILD) or mixed layer depth (MLD) for the same profile varies depending on the method used to determine it. Also, whether they are subjective or objective, existing methods of determining the ILD do not estimate the thermocline (pycnocline) gradient. Here, we propose a new exponential leap-forward gradient (ELG) method of determining the ILD that retains the strengths of subjective (simplicity) and objective (gradient change) methods and avoids their weaknesses (subjective methods are threshold-sensitive and objective methods are computationally intensive). This new method involves two steps: (1) the estimation of the thermocline gradient G _th for an individual temperature profile, and (2) the computation of the vertical gradient by averaging over gradients using exponential leap-forward steps. Such averaging can filter out noise in the profile data. Five existing methods of determining the ILD (difference, gradient, maximum curvature, maximum angle, and optimal linear fitting methods) as well as the proposed ELG method were verified using global expendable bathythermograph (XBT) temperature and conductivity–temperature–depth (CTD) datasets. Among all the methods considered, the ELG method yielded the highest skill score and the lowest Shannon information entropy (i.e., the lowest uncertainty).     

Parameterization of vertical mixing in the Weddell Sea

A series of vertical mixing schemes implemented in a circumpolar coupled ice–ocean model of the BRIOS family is validated against observations of hydrography and sea ice coverage in the Weddell Sea. Assessed parameterizations include the Richardson number-dependent Pacanowski–Philander scheme, the Mellor–Yamada turbulent closure scheme, the K-profile parameterization, a bulk mixed layer model and the ocean penetrative plume scheme (OPPS). Combinations of the Pacanowski–Philander parameterization or the OPPS with a simple diagnostic model depending on the Monin–Obukhov length yield particularly good results. In contrast, experiments using a constant diffusivity and the traditional convective adjustment cannot reproduce the observations. An underestimation of wind-driven mixing in summer leads to an accumulation of salt in the winter water layer, inducing deep convection in the central Weddell Sea and a homogenization of the water column. Large upward heat fluxes in these simulations lead to the formation of unrealistic, large polynyas in the central Weddell Sea after only a few years of integration. Furthermore, spurious open-ocean convection affects the basin-scale circulation and leads to a significant overestimation of meridional overturning rates. We conclude that an adequate parameterization of both wind-induced mixing and buoyancy-driven convection is crucial for realistic simulations of processes in seasonally ice-covered seas.     

Spatial spectra and characteristic horizontal scales of temperature and velocity fluctuations in the convective boundary layer of the atmosphere

Using a high-resolution LES numerical model, we calculated the turbulent thermal convection for high ratios of horizontal and vertical sizes of the computational domain (26: 26: 1). The natural analog of the simulated process is a planetary boundary layer (PBL) of the atmosphere growing with height in the background of stably stratified overlying air layers over a horizontally homogeneous heated surface under a weak average wind. We obtained the spectral distributions of variances of fluctuations in potential temperature and velocity components in ranges corresponding to scales from a few tens of meters to a few tens of kilometers. We found energetically significant segments of the spectrum of large-scale fluctuations in the potential temperature for which the power dependences S ～ k ^?1/3 and S ～ k ^?4/3 are satisfied with good accuracy. We calculated the characteristic spatial scales of horizontal fluctuations in velocity and temperature. We obtained a dependence of these scales on the height of the growing convective PBL. We discuss the characteristic features of large-scale distributions in terms of the self-similarity of the growing boundary layer behavior.     

东海黑潮暖舌对热带气旋“派比安”(1807)强度的影响

通过使用天气研究与预报(Weather Research and Forecasting,WRF)模式对热带气旋(Tropical Cyclone,TC)个例“派比安”(1807)进行了一组数值试验,分析了东海黑潮暖舌对“派比安”强度的影响。研究结果表明,东海黑潮暖舌高海面温度(以下简称“海温”)导致TC区域内海气界面热通量显著增加,并造成TC边界层不稳定特征发展,形成了有利于垂直对流发展的边界层环境。因此TC内特别是TC眼墙处对流更为活跃,TC强度显著提高,同时黑潮暖舌对TC的局部加热还会引起TC内部对流活动的非对称分布。根据数值试验的结果,黑潮暖舌为“派比安”整体动能增加做出约24.7%的贡献,中心气压变化对东海黑潮暖舌高海温特征的响应时间约为10 h。此外,在黑潮暖舌作用下,“派比安”7级风圈半径扩张16.3%,最大风速半径收缩10.7%。     

The nested structure of Arctic thermohaline intrusions

Arctic thermohaline intrusions have a “nested” temperature/salinity structure characterized by the lining up of widely separated profiles along a series of well-defined lines in the T–S plane. The nesting pattern is coherent across much of the Arctic Basin (>2000 km), and roughly 90% of the water column between 150 and 350 m depth is found to lie along these nesting lines. We propose the nested structure results from a type of slanted convection occurring within the thick, salt-finger stratified layers in the intrusions. The convection cells are reminiscent of those investigated in laboratory experiments done by Thorpe, Hutt, and Soulsby, and it is estimated that the cells have horizontal dimensions ranging from 50 to 100 km at depths close to the Atlantic Water temperature maximum. Simple theoretical ideas suggest the convective cells may appear when the intrusions reach a critical amplitude, driving them toward a nested configuration. Our analysis provides a new estimate of the effective lateral diffusivity due to the intrusions (≃50 m² s⁻¹), as well as an estimate of the vertical diffusivity near the core of the Atlantic Water layer (≃0.8×10⁻⁵ m² s⁻¹).