Modeling time dependence in a tidal boundary layer

Although the rate of acceleration and deceleration in a depth-limited tidal flow can be quite large, it has been found that quasi-steady logarithmic models or steady eddy diffusivitics can explain the turbulent field quite well (Gross andNowell, 1983;Long, 1981). A simple, time-dependent model was devised based on kinetic energy closure (Bradshaw et al., 1967) to simulate a depth-limited tidal boundary layer without the assumption of a time-independent eddy diffusivity. Computer solutions revealed that the parameterS = u_s/δΩ (u_s is a turbulent velocity scale, δ is depth, Ω is tidal frequency) governs the phasing of the velocity to the forcing pressure gradient. However, for values ofS reasonable for depth-limited estuarine tidal flow the ratio of the turbulent energy production-dissipation balance to rate of change of turbulent energy is always quite large, indicating that the turbulent adjustment rate is fast enough for the flow to be modeled with quasi-steady techniques.     

边界层参数化方案对边界层热力和动力结构特征影响的比较

本文利用高分辨率中尺度WRF模式,通过改变边界层参数化方案进行多组试验,评估该模式对美国北部森林地区边界层结构的模拟能力,同时比较了五种不同边界层参数化方案模拟得出的边界层热力和动力结构.结果表明：除个别方案外,配合不同边界层方案的WRF模式都能成功模拟出白天对流边界层强湍流混合特征和夜间稳定边界层内强逆温、逆湿和低空急流等热力和动力结构.非局地YSU、ACM2方案在白天表现出强的湍流混合和卷夹,相比于局地MYJ、UW方案,模拟的对流边界层温度更高、湿度更低、混合层高度更高、感热通量更大,更接近实际观测,这表明在不稳定层结下考虑非局地大涡输送更为合理,但局地方案在风速和风向的预报上存在一定优势.TEMF方案得到的白天局地湍流混合强度为所有方案中最弱,混合层难以发展,无法体现对流边界层内气象要素垂直分布均匀的特点.对于夜间稳定边界层的模拟,不同参数化方案之间的差异较小,但是YSU方案在一定程度上高估了机械湍流,导致局地湍流混合偏强,从而影响了其对稳定边界层的模拟能力.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

The earth's thermal profile: Is there a mid-mantle thermal boundary layer?

Shock observations on melting of iron by Brown and McQueen with the inner core boundary (ICB) density contrast estimated by Masters are used with the assumption that the light ingredient of the outer core is oxygen to calculate the boundary temperature T_ICB = (5000 ± 900) K. Adiabatic extrapolation to the core-mantle boundary (CMB) gives T_ICB = (3800 ± 800) K. The temperature increment across the D″ layer is not well constrained, but is estimated to be T_D″ = (800 ± 400) K and a slightly superadiabatic extrapolation to 670 km gives T_{670 +} = (2300 ± 950) K. This is only about 300 K higher than the extrapolation to the same level from the upper mantle, T_670? = (1970 ± 150) K. The difference is far too small to make a viable mid-mantle boundary layer. Remaining unceertainties are too large to discount such a boundary layer with certainty, but agreement of our new temperature profile with temperatures deduced from equation of state studies on the lower mantle and core encourages the view that we are converging to a well-determined temperature profile for the Earth.     

Implications of a concentration-dependent growth rate on the boundary layer crystal-melt model

The influence of a melt boundary layer on crystal growth is analyzed. The treatment extends the results of Burton, Prim and Slichter (1953) and incorporates composition-dependent growth rates. It is shown that in these general cases the growth rate cannot be arbitrarily fixed but must satisfy a self-consistent equation. Self-consistency problems arise because the growth rate determines the composition profile in the melt and, in turn, the composition profile determines the growth rate. The self-consistent growth rate is shown to vary markedly with the ratio δ/D, where δ is the thickness of the boundary layer and D is the appropriate diffusion coefficient in the melt. This self-consistency can be very important in the analysis of both field and laboratory growth rates as well as in trace element partition kinetic models.     

The wave-induced boundary layer under long internal waves

The boundary layer formed under the footprint of an internal solitary wave is studied by numerical simulation for waves of depression in a two-layer model of the density stratification. The inviscid outer flow, in the perspective of boundary-layer theory, is based on an exact solution for the long wave-phase speed, yielding a family of fully nonlinear solitary wave solutions of the extended Korteweg–de Vries equation. The wave-induced boundary layer corresponding to this outer flow is then studied by means of simulation employing the Reynolds-averaged Navier–Stokes (RANS) formulation coupled with a turbulence closure model validated for wall-bounded flows. Boundary-layer characteristics are computed for an extensive range of environmental conditions and wave amplitudes. Boundary-layer transition, identified by monitoring the eddy viscosity, is correlated in terms of a boundary-layer Reynolds number. The frictional drag is evaluated for laminar, transitional, and turbulent cases, and correlations are presented for the friction coefficient plus relevant measures of the boundary-layer thickness.     

Convection and gravity waves in two layer models. I. Overstable modes driven in conducting boundary layers

Abstract

Stability analysis is formulated for a two-layer fluid model in which the upper and lower layers are convectively stable and unstable, respectively. With discontinuities in viscosity and conductivity at the interface, the exchange of stability does not generally hold and overstability is possible. A detailed analytical treatment is presented for the case of small viscosity and conductivity in which viscous and conducting boundary layers are formed at the interface.

The usual damping effect due to the energy dissipation by viscosity and thermal conductivity exists irrespective of whether the mode is the convection or the gravity wave, but, for larger horizontal wave lengths, the effect of the boundary layer can become more important. The jump in the thermal conductivity in the boundary layer can give rise to overstability of the gravity wave in agreement with Souffrin and Spiegel (1967). The jump in the viscosity provides a self-catalytic action for the unstable flow if the viscosity is assumed to be the nonlinear turbulent viscosity due to the motion itself. The effect, however, is not strong enough to overcome the usual viscous damping.     

Stability of the boundary layer between the lithosphere and convecting mantle and the steady-state lithospheric geotherm

In the steady state, the convective boundary layer (CBL) (the transition from the lithosphere to the convecting mantle, the lithosphere-asthenosphere boundary) is on the verge of stability. This determines its depth, thickness, and the steady-state temperature distribution in the lithosphere. Had the mantle been homogeneous, the base of the lithosphere at the current potential temperature would lie globally at the same depth H _rh of 50 to 70 km. Actually, the regime of interaction of the mantle convection with the lithosphere is determined by the relationship between this depth and the thickness H _depl of the chemical boundary layer including the crust and the layer of the depleted rock. If the thickness of the chemical boundary layer is small H _depl < H _rh, as it is the case in the present-day oceanic mantle, the suboceanic regime is established with the mantle convection that does not reach the base of the chemical boundary layer. In this case, the top of CBL is located at depth H _rh, while the oceanic heat flow and the depth of the seafloor only depend on the potential temperature T _p and, within the areas where the crust is older than 60 to 70 Ma, are the same everywhere far from the disturbed territories (the hot points and the subduction zones). The absence of noticeable distinctions between the heat flow in the different oceanic basins suggests a global constancy of the potential temperature. If H _depl > H _rh, the subcontinental regime of the interaction of the mantle convection with the lithosphere is established. In this case, the CBL is immediately adjacent to the depleted lithosphere, its top is located at depth H _depl, and the surface heat flow q(T _p, H _depl) not only depends on the potential temperature T _p but also on the the thickness of the depleted lithosphere H _depl; it decreases with increasing H _depl and, therefore, with the age of the lithosphere. Given the potential temperature, the dependence q(T _p, H _depl) agrees well with the envelope of the results of kimberlite xenolith thermobarometry presented in the diagram of the deepest xenolith depth as a function of the heat flow. It is likely that in the lowest part of the continental lithosphere there is a zone of horizontal shear deformation, from where kimberlites entrain the strongly deformed and, at the same time, the deepest xenoliths. Besides, the azimuthal anisotropy of seismic velocities can be associated with this zone. The change in its direction with depth can be observed as the Lehmann discontinuity.     

The surface roughness and planetary boundary layer

Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 $$\begin{gathered} \frac{{\sigma _w }}{{u^* }} = \left( {\frac{2}{{9Aa}}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \left( {1 - 3^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \frac{a}{k}\frac{{d_n }}{z}\frac{{\sigma _w }}{{u^* }}\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ = 1.28(1 - 0.945({{\sigma _w } \mathord{\left/ {\vphantom {{\sigma _w } {u^* }}} \right. \kern-\nulldelimiterspace} {u^* }})({z \mathord{\left/ {\vphantom {z L}} \right. \kern-\nulldelimiterspace} L})^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ \end{gathered} $$ where \(u^* = \left( {{\tau \mathord{\left/ {\vphantom {\tau \rho }} \right. \kern-0em} \rho }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , σ _w is the standard deviation of the vertical velocity,z is the height andL is the Obukhov scale lenght. The constantsa, A, k andd _n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these,a andA, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements of widely varying sizes are combined this paper shows how the surface roughness parameter,z ₀, can be calculated for an ideal case of a random distribution of vertical cylinders of the same height. To treat a water surface, with various sized waves, such an approach modified to treat the surface by the superposition of various sized roughness elements, is likely to be helpful. Such a theory is particularly desirable when such a surface is changing, as the ocean does when the wind varies. The formula, 2 $$\frac{{0.118}}{{a_s C_D }}< z_0< \frac{{0.463}}{{a_s C_D (u^* )}}$$ is the result derived here. It applies to cylinders of radius,r, and number,m, per unit boundary area, wherea _s =2rm, is the area of the roughness elements, per unit area perpendicular to the wind, per unit distance downwind. The drag coefficient of the cylinders isC _D . The smaller value ofz _o is for large Reynolds numbers where the larger scale turbulence at the surface dominates, and the drag coefficient is about constant. Here the flow between the cylinders is intermittent. When the Reynolds number is small enough then the intermittent nature of the turbulence is reduced and this results in the average velocity at each level determining the drag. In this second case the larger limit forz ₀ is more appropriate.     

黄土高原复杂地形上边界层低空急流对近地层湍流的影响

利用中尺度气象数值模式（Weather Research and Forecasting Model,WRF）模拟风场,结合兰州大学半干旱气候与环境观测站（Semi-Arid Climate and Environment Observatory of Lanzhou University,SACOL）湍流观测资料,分析了黄土高原复杂地形上稳定边界层低空急流对近地层湍流活动的影响.黄土高原复杂地形上稳定边界层低空急流的形成与地形作用引发的局地环流有关.低空急流对近地层湍流活动有强烈影响,剪切作用使小尺度湍涡活动加剧,湍动能增大,同时非平稳运动被压制.低空急流发生时,观测数据有87.3%是弱稳定情形（梯度理查森数小于0.25）;而无低空急流时,对应时段的观测表明65.4%属于强稳定层结（梯度理查森数大于0.3）,非平稳运动造成湍流功率谱在低频端迅速增大.与无低空急流和弱低空急流情形相比,强低空急流发生时,近地层湍动能增大1倍,湍动能在垂直方向上的传递增大1个量级,且方向向下,约为-3 × 10^-3 m³·s^-3,湍流在上层产生并向下传递.     

Buoyant boundary layer flows- an analogy to the Ekman spiral

Abstract

Flow details inside the buoyant boundary layer in the heat-up process of a contained, stably stratified, fluid are presented. Numerical solutions were obtained for the heatup problem in a cylinder considered by Sakurai and Matsuda (1972). By plotting the scaled vertical velocity W versus the scaled temperature θ as functions of the normal distance from the sidewall, the precise shape of the buoyant layer spiral is constructed. The analogy between this spiral and the Ekman spiral in rotating fluids is apparent. As the Rayleigh number Ra increases, the magnitude of the scaled vertical velocity increases substantially, but the scaled temperature does not vary appreciably. The buoyant layer thickness is determined by measuring the zero-crossing normal distance for the vertical velocity. The buoyant layer suction increases significantly as Ra increases. The effects of vertical level and of time on the qualitative behavior of buoyant layer flows are found to be small. The buoyant layer flows decay over the heat-up time scale t _n ; t _h characterizes the time span over which the overall adjustment process in the inviscid interior region is accomplished. This work clarifies that the analogy between heat-up and spin-up, which has been known to exist in the main body of inviscid fluid, applies equally well to the boundary layer regions.     

Excess222Rn and the benthic boundary layer in the western and southern Indian Ocean

We present 9 bottom²²²Rn profiles measured from the western and southern Indian Ocean during the 1977–1978 GEOSECS expedition. These profiles can be grouped into three cypes: one-layer, two-layer, and irregular types. The one-layer profiles with quasi-exponential distributions allow one to estimate the apparent vertical eddy diffusivity,K_v, with a simple model. The two-layer profiles show that there is a benthic boundary layer of the order of 50–100 m in which the excess²²²Rn distribution shows a vertical gradient much smaller than that of the layer immediately above. Within the boundary layer, the STD potential temperature (θ) and density(σ₄) profiles are practically constant, and theK_v values are of the order of 1000 cm²/s. The STD profiles for the water column above the boundary layer show gradients of increasing stability, and theK_v values are of the order of 100 cm²/s. Modeling of the Rn data in the water column above the boundary layer indicates that there is a transition layer which effectively reduces the penetration of excess Rn from the benthic boundary layer into the upper layer.Sarmiento et al. [10] have shown that the buoyancy gradient or stability is inversely correlated with the apparent vertical eddy diffusivity, and the resulting buoyancy flux is fairly uniform, ranging from 1 to 14 × 10^?6 cm²/s³ in the Atlantic and Pacific Oceans. However, Sarmiento et al. [11] show that a much higher buoyancy flux is associated with an intensified flow of the bottom water through a passage. In the Indian Ocean basins, we have found that the buoyancy flux has a comparable range (3–14 × 10^?6 cm²/s³), except for a couple of stations where both stability and apparent vertical diffusivity are higher, resulting in a much higher buoyancy flux, probably indicative of rapid bottom water flow.     

A three‐dimensional numerical investigation of the idealized planetary boundary layer

Abstract

The nonlinear equations of motion are integrated numerically in time for a region of x‐y‐z space of volume 3h × h × h, where h turns out to be a height slightly above the level where the wind first attains the geostrophic flow direction. Only the ideal case is treated of a horizontal lower boundary, neutral stability, horizontal homogeneity of all dependent mean variables except the mean pressure, and statistically steady state. The resulting flow patterns are turbulent and the eddies transport required amounts of momentum vertically.

Topics which are investigated include the relative directions of stress, wind shear and wind; differences in Ekman wind spirals for the neutral numerical case and a stable atmospheric case; profiles of dimensionless turbulence statistics; effect of allowing the mean density to be either constant or to decrease with height; effect of the wind direction or latitude upon the turbulence intensities; and characteristic structure of the eddies in the planetary boundary layer.     

Power-law velocity profile in turbulent boundary layers: An integral reynolds-number dependent solution

Geophysical flows of practical interest encompass turbulent boundary layer flows. The velocity profile in turbulent flows is generally described by a log- or a power-law applicable to certain zones of the boundary layer, or by wall-wake law for the entire zone of the boundary layer. In this study, a novel theory is proposed from which the power-law velocity profile is obtained for the turbulent boundary layer flow. The new power-law profile is based on the conservation of mass and the skin friction within the boundary layer. From the proposed theory, analytical expressions for the power-law velocity profile are presented, and their Reynolds-number dependency is highlighted. The velocity profile, skin friction coefficient and boundary layer thickness obtained from the proposed theory are validated by the reliable experimental data for zero-pressure gradient turbulent boundary layers. The expressions for Reynolds shear stress and eddy viscosity distributions across the boundary layer are also obtained and validated by the experimental data.     

Estimation of orographically induced wave drag in the stable boundary layer during the CASES-99 experimental campaign

This paper addresses the quantification of gravity wave drag due to small hills in the stable boundary layer. A single column atmospheric model is used to forecast wind and temperature profiles in the boundary layer. Next, these profiles are used to calculate vertical profiles of gravity wave drag. Climatology of wave drag magnitude and “wave drag events” is presented for the CASES-99 experimental campaign. It is found that gravity wave drag events occur for several relatively calm nights, and that the wave drag is then of equivalent magnitude as the turbulent drag. We also illustrate that wave drag events modify the wind speed sufficiently to substantially change the surface sensible heat flux.     

Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Voronoi analysis

This paper presents the numerical investigation of the distribution of inertial sediment particles in the turbulent boundary layer of an open channel flow with the particle Stokes number ranging from 0.6 to 20.4. The methodology is a combination of three numerical approaches, i.e. direct numerical simulation of turbulent flow, the point-particle immersed boundary method, and the discrete particle method. By applying the Vorono analysis, the preferential concentration characteristics of sediment particles were investigated quantitatively. It was found that the normalized area of the Voronoi cells follows a lognormal particle distribution. The inertial sediment particles distributed unevenly in the turbulent boundary layer and the unevenness, governed by the particle Stokes number, was more significant as the particle Stokes number approaches unity. The inertial sediment particles in the turbulent boundary layer accumulated preferentially in streamwise-aligned streaky structures and this pattern was less significant with increasing particle Stokes number.     

森林冠层和森林边界层大涡模拟

在采用各向异性湍流动能闭合方案和3阶Runge Kutta时间积分方案的大涡模式中,引入由森林冠层粗糙元造成的动量拖曳项、热量输入项和TKE耗散项,以模拟森林冠层和森林边界层的气象场. 通过中性和不稳定层结条件下不同叶面积指数算例的模拟分析及与已有观测结果的比较表明,本文所建大涡模式对森林冠层和森林边界层有较好的模拟效果. 进一步研究表明：不稳定层结条件下较稠密的森林冠层中特有的Kinking & Pairing湍涡结构与森林边界层中湍流的大涡运动相互作用,形成了森林冠层附近的温度斜坡型结构.     

Turbulent measurements in the stable atmospheric boundary layer during SHEBA: ten years after

This paper surveys results of the comprehensive turbulent measurements in the stable boundary layer (SBL) made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) in the Beaufort Gyre from October 1997 through September 1998. Turbulent fluxes and mean meteorological data were continuously measured and reported hourly at five levels on a 20-m main SHEBA tower. Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification, and allow studying the SBL in detail. A brief overview of the SBL regimes, the flux-profile relationships, the turbulent Prandtl number, and other parameters obtained during SHEBA is given. The traditional Monin—Obukhov approach, z-less scaling, and gradient-based scaling are evaluated and discussed based on the data from SHEBA.