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1.
《Dynamics of Atmospheres and Oceans》1999,29(1):1-40
With the purpose of studying the upper part of the ocean, the shallow water equations (in a `reduced gravity' setting) have been extended in the last decades by allowing for horizontal and temporal variations of the buoyancy field ϑ, while keeping it as well as the velocity field u as depth-independent. In spite of the widespread use of this `slab' model, there has been neither a discussion on the range of validity of the system nor an explanation of points such as the existence of peculiar zero-frequency normal modes, the nature of the instability of a uniform u flow, and the lack of explicit vertical shear associated with horizontal density gradients. These questions are addressed here through the development of a subinertial model with more vertical resolution, i.e., one where the buoyancy ϑ varies linearly with depth. This model describes satisfactorily the problem of baroclinic instability with a free boundary, even for short perturbations and large interface slopes. An enhancement of the instability is found when the planetary β effect is compensated with the topographic one, due to the slope of the free boundary, allowing for a `resonance' of the equivalent barotropic and first baroclinic modes. Other low-frequency models, for which buoyancy stratification does not play a dynamical role, are invalid for short perturbations and have spurious terms in their energy-like integral of motion. 相似文献
2.
In this paper, the adaptation process in low latitude atmosphere is discussed by means of a two-layer baroclinic model on the equator β plane, showing that the adaptation process in low latitude is mainly dominated by the internal inertial gravity waves. The initial ageostrophic energy is dispersed by the internal inertial gravity waves, and as a result, the geostrophic motion is obtained in zonal direction while the ageostro-phic motion maintains in meridional direction, which can be called semi-geostrophic balance in barotropic model as well as semi-thermal-wind balance in baroclinic model. The vertical motion is determined both by the distribution of the initial vertical motion and that of the initial vertical motion tendency, but it is unrelated to the initial potential vorticity. Finally, the motion tends to be horizontal. The discussion of the physical mechanism of the semi-thermal-wind balance in low latitude atmosphere shows that the achievement of the semi-thermal-wind balance is due to the adjustment between the stream field and the temperature field through the horizontal convergence and divergence which is related to the vertical motion excited by the internal inertial gravity waves. The terminal adaptation state obtained shows that the adaptation direction between the mean temperature field and the shear flow field is determined by the ratio of the scale of the initial ageostrophic disturbance to the scale of one character scale related to the baroclinic Rossby radius of deformation. The shear stream field adapts to the mean temperature field when the ratio is greater than 1, and the mean temperature field adapts to the shear stream field when the ratio is smaller than 1. 相似文献
3.
Robert E. Hall 《Dynamics of Atmospheres and Oceans》1980,5(2):113-121
A new semicircle theorem is derived for unstable barotropic disturbances to a class of rectilinear barotropic currents u(y) in systems with an ambient potential vorticity gradient (f/h)y which satisfies (u—us)(f/h)y ? 0 throughout the y domain, where us is some value of u. In the conventional semicircle theorem for this flow, the radius of the semicircle is a function of both the range of u and the maximum speed of the stable Rossby waves that can exist in the system when u = 0. In the new semicircle theorem, the radius is only a function of the former when it is small compared to the latter. Currents which do not satisfy the above condition, as well as stable modes and baroclinic systems, are also discussed. 相似文献
4.
Xiuzhang Zhang Don L. Boyer Gabriel Chabert d'Hires Denis Aelbrecht Henri Didelle 《Dynamics of Atmospheres and Oceans》1993,19(1-4)
Laboratory experiments are conducted on a physical system in which an oscillatory, along-shore, free stream flow of a homogeneous fluid occurs in the vicinity of a long coastline with vertical slope; the model sea-floor is horizontal. Particular attention is given to the resulting rectified (mean) current which is along the coastline with the shore on the right, facing downstream. In the lateral far field region defined by
(1), where y is the offshore coordinate and H is the depth of the fluid, the motion field is approximately independent of the lateral distance from the coast. The vertical structure of the cross-stream motion in this region consists of Ekman layers near the sea-floor and interior adjustment flows, both periodic in time. In the near field, defined by
(1), the motion is strongly dependent on the cross-stream coordinate as well as time, and rectified currents are observed. The mechanism responsible for the rectification is a complex nonlinear coupling between laterally directed adjustment flows driven by the transport in the bottom Ekman layers, and the free stream motion field. The rectified current is found to be substantially wider than the Stewartson layer thickness but much narrower than the Rossby deformation radius. The characteristic width, δy, of the rectified current is shown to scale as
, where Ro is the Rossby number Rot is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling. 相似文献
5.
6.
We describe laboratory experiments on the instability and later evolution of a front in a two-layer rotating fluid. In particular, we focus on the influence of a nearby boundary on instability growth and eddy formation. The front is produced through the adjustment of a buoyant fluid initially confined within a bottomless cylinder. Typically a front in quasi-cyclostrophic balance establishes after two rotation periods, after which it becomes unstable. Measurements of the velocity and vorticity fields at the surface are made which provide detailed information on the evolution of the front as the instability grows to finite amplitude. We focus on the time evolution of the vorticity and distinguish between the cyclonic and anticyclonic components. The spatial averages of the cyclonic and anticyclonic vorticity first grow exponentially. This growth saturates when eddies form and are advected across the front. The growth rate depends upon two nondimensional parameters: the width W of the upwelling region in units of the internal radius of deformation and the depth ratio δ between the two layers. Measurements of the growth rates for the average of the cyclonic and anticyclonic vorticity are compared to the values inferred from a simplified model for baroclinic instability. A good agreement is obtained when the front develops far from the boundary (i.e. W1). However, the agreement is only qualitative when the front is near the boundary (i.e. W1). We find that, as W decreases, the growth of cyclonic eddies consisting of dense—“coastal”—water is enhanced compared to that of anticyclonic vorticity consisting of buoyant—“off-shore”—water. This crucial effect of the boundary with respect to the instability of the front has significant impact on exchanges across the front. 相似文献
7.
A horizontal shear flow having a Rossby number, Ro, greater than unity on a rotating plane can become unstable when its shear value is less than −f, the Coriolis frequency. In this paper, this instability is investigated for an O(10 km) submesoscale, sinusoidal shear flow in a thin homogeneous fluid layer as in an oceanic mixed layer or a shallow sea. The most unstable mode is shown by a linear analysis to occur in a narrow localized region centered around the maximum anticyclonic current shear. However, nonlinear numerical calculations show that the instability can grow to encompass both unstable and stable regions of the current. A consequence of this finite-amplitude evolution is the formation of surface convergence/shear fronts. The possibility that inertial instability mechanism is a source of some surface convergence/shear features seen in remote sensing images of the sea surface is discussed. A comparison is made with the shear-flow instability that can occur concurrently in a sinusoidal shear current, and inertial instability is shown to be the dominant instability mechanism in the immediate range above Ro=2. 相似文献
8.
Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies 总被引：1，自引：1，他引：0
How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first simulation, the rod density is chosen so that much of the momentum is absorbed within the canopy volume yet the canopy is not dense enough to induce separation on the lee side of the hill. In the second simulation, the rod density is large enough to induce recirculation inside the canopy on the lee side of the hill. For this separating flow case, zones of intense shear stress originating near the canopy-atmosphere interface persist all the way up to the middle layer, ‘contaminating’ much of the middle and outer layers with shear stress gradients. The implications of these persistent shear-stress gradients on rapid distortion theory and phase relationships between higher order velocity statistics and hill-induced mean velocity perturbations (Δu) are discussed. Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (~ ?Δu/?z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with Δu than with ?Δu/?z. However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream. This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases ${\sigma_p/u_{*}^{2}}$ near the canopy top, where u * is the longitudinally averaged friction velocity at the canopy top and σ p is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction. This scaling argument also predicts the spatial variations in σ p above the canopy reasonably well for both simulations, but not inside the canopy. 相似文献
9.
《Dynamics of Atmospheres and Oceans》2003,37(1):55-88
Numerical models demonstrate that a broad class of geophysical vortices freely evolve toward vertically aligned, axisymmetric states. In principle, this intrinsic drive toward symmetry opposes destructive shearing by the environmental flow.This article examines the case in which a discrete vortex-Rossby-wave dominates a perturbation from symmetry, and symmetrization occurs by decay of the wave. The wave is damped by a resonance with the fluid rotation frequency at a critical radius, r*. The damping rate is proportional to the radial derivative of potential vorticity at r*. Until now, the theory of resonantly damped vortex-Rossby-waves (technically quasi-modes) was formally restricted to slowly rotating vortices, which obey quasigeostrophic (QG) dynamics. This article extends the theory to rapidly rotating vortices.The analysis makes use of the asymmetric balance (AB) approximation. Even at a modest Rossby number (unity), AB theory can predict damping rates that exceed extrapolated QG results by orders of magnitude. This finding is verified upon comparison of AB theory to numerical experiments, based on the primitive equations. The experiments focus on the decay of low azimuthal wave-number asymmetries.A discrete vortex-Rossby-wave can also resonate with an outward propagating inertia-buoyancy wave (Lighthill radiation), inducing both to grow. At large Rossby numbers, this growth mechanism can be dynamically relevant. All balance models, including AB theory, neglect inertia-buoyancy waves, and therefore ignore the possibility of a Rossby-inertia-buoyancy (RIB) instability. This article shows that a large potential vorticity gradient (of the proper sign) at the critical radius r* can suppress the RIB instability, and thereby preserve balanced flow, even at large Rossby numbers. 相似文献
10.
《Dynamics of Atmospheres and Oceans》2005,38(3-4):173-193
A three-dimensional spectral analysis of Topex altimeter data reveals a large meridional component ky of the wavevector k for baroclinic Rossby waves of all timescales. Its existence necessitates some refinements in our estimates of certain basic properties of the Rossby wave field. In particular, by taking into account an actual off-zonal direction of k (often exceeding 70°), one finds that the wavelength, phase speed, and group velocity of mid-latitude Rossby waves (with periods less than 2 years) are much smaller than they appear to be on the assumption of a purely zonal wavenumber vector. Because of a shorter wavelength (yielding kL as high as 0.6, where L is the Rossby radius of deformation), these waves are essentially dispersive. Their group velocity vector may depart from zonal by more than 30°. An important intrinsic feature of the wave spectrum confirmed by our analysis is a broad-band distribution with respect to ky. Some of the dynamical implications of the large ky/kx ratio are discussed. 相似文献
11.
利用线性化的两层正压原始方程模型，对有水平和垂直切变基流的圆形涡旋中螺旋波的不稳定作了研究。结果表明，当基流失稳时，涡旋中不稳定扰动的厚度场、速度场在上、下两层都具有明显的螺旋结构，下层的螺旋结构要较上层复杂。基流垂直切变越大则越易失稳。失稳时上、下层扰动的配置接近反位相，故该螺旋波结构相应于斜压模。此时螺旋波上的扰动中心在切向是逆基流传播的，在径向则基本没有传播，而螺旋臂的整体运动缓慢。失稳的螺旋波其散度场要较涡度场明显，物理量的配置也大体符合重力惯性波的情况，故可认为其是重力惯性波的不稳定所致。本模型中该螺旋波的形态与实际热带气旋中的螺旋云(雨)带很相象。 相似文献
12.
Fronts are ubiquitous dynamic processes in the ocean, which play a significant role in the ocean dynamical and ecological environments. In this paper strong temperature fronts are investigated on the shelf of the Northern South China Sea using high resolution satellite data. These fronts have large horizontal gradients exceeding 1 °C km−1 with spatial scales around several kilometers. The fronts generate meanders and eddies due to baroclinic instability, since these instabilities have spatial scales around the local first baroclinic mode deformation radius. The estimated Rossby number of the fronts is O(0.4), suggesting that the fronts tend to be ageostrophic and show submesoscale features. The Finite Size Lyapunov Exponent analysis of the generation mechanism indicates that the fronts are tightly related to the combined flow straining of geostrophic and Ekman currents. 相似文献
13.
Charles A. Lin 《大气与海洋》2013,51(2):143-157
Abstract Baroclinic instability of zonal flows with different latitudinal structures is examined, using a linear, quasi‐geostrophic two‐level ß‐plane model. The flows have different amounts of skew, with respect to the channel centre, at different vertical levels. The results are interpreted in terms of the instability of the baroclinic components of the zonal flows. Because of the presence of latitudinal asymmetries, a spectrum of meridional modes is generated in the perturbation. In general, the meridional spectrum has two peaks: a primary peak at the planetary basic flow scale, and a secondary peak near the radius of deformation. As neutral stability is approached, the latter scale becomes more important, i.e. there is a tendency for more small‐scale structure near neutral stability. The perturbation zonal scale is close to the radius of deformation. The eddy amplitudes and momentum fluxes are also examined. The case that best applies to the atmosphere is also discussed. 相似文献
14.
Daniel G. Wright 《大气与海洋》2013,51(3):225-241
Abstract In this note some aspects of the dynamics involved in the process of baroclinic instability are discussed using simple physical arguments. In particular, the connection between the requirement for unstable perturbations to release potential energy from the mean state and the conservation of potential vorticity is examined. It is shown how the conservation of potential vorticity results in perturbation phase propagation relative to the mean flow, which is a necessity for potential energy to be released from the mean state. Eady's (1949) problem is discussed as an illustrative example. 相似文献
15.
Glenn R. Flierl 《Dynamics of Atmospheres and Oceans》1979,3(1):15-38
A model for the structure and motion of baroclinic solitary waves in the atmosphere or ocean is presented. Like gravity wave solitons, these planetary wave solutions are both weakly nonlinear and weakly dispersive. The dispersion effects, induced by β, are small because the scale of the wave is large compared to the deformation radius. The steepening effects are provided by the interaction of the wave with exterior mean shear flow, which may be either barotropic or baroclinic. The solutions have two properties which suggest that such theories may be useful in modelling solitary disturbances in the atmosphere or ocean: radial symmetry and fluid speeds which exceed the phase speed of the wave itself. As an example, we apply the model to Gulf Stream Rings. 相似文献
16.
The effect of barotropic shear in the basic flow on baroclinic instability is investigated using a linear multilevel quasi-geostrophic β-plane channel model and a nonlinear spherical primitive equation model. Barotropic shear has a profound effect on baroclinic instability. It reduces the growth rates of normal modes by severely restricting their structure, confirming earlier results with a two-layer model. Dissipation, in the form of Ekman pumping and Newtonian cooling, does not change the main characteristics of the effect of the shear on normal mode instability.Barotropic shear in the basic state, characterized by large shear vorticity with small horizontal curvature, also effects the nonlinear development of baroclinic waves. The shear limits the energy conversion from the zonal available potential energy to eddy energy, reducing the maximum eddy kinetic energy level reached by baroclinic waves. Barotropic shear, which controls the level of eddy activity, is a major factor which should be considered when parameterizing the eddy temperature and momentum fluxes induced by baroclinic waves in a climate model. 相似文献
17.
M. J. Manton 《Boundary-Layer Meteorology》1974,6(3-4):487-504
Equations of motion, valid for a water droplet or a dust particle less than about 50Μm in radius moving through the air, are derived. Thus, the behaviour of a particle in some simple nonuniform fluid flows is discussed. In particular, it is found that a particle may follow an approximately closed trajectory in an axisymmetric flow about a horizontal axis. Thus, it is argued that turbulence should cause particles to fall at a much slower rate than their terminal velocity, even in the absence of a mean updraft. 相似文献
18.
利用斜压两层模式研究了赤道平面近似下的低纬热带大气适应过程。指出低纬斜压大气适应过程主要受重力惯性内波控制。通过重力惯性内波对初始非地转能量的频散，使纬向运动达到地转平衡，而经向维持非地转运动，正压模式下称为半地转平衡，斜压模式下称为半热成风平衡。通过对垂直运动方程的求解，可知，垂直运动只与重力惯性内波相联系，其产生与初始斜压位涡度无关，而只与初始时刻的垂直运动和垂直运动倾向有关，半地转适应使运动趋向水平运动。讨论了半热成风平衡的建立及其物理机制，指出由于重力惯性内波激发出垂直运动，与垂直运动相联系的水平辐合辐散调整流场和温度场之间的关系，使温压场最终达到半热成风平衡。通过对适应过程终态的分析，指出平均温度场和切变流场之间的适应方向决定于初始非半地转扰动的尺度与斜压Ｒｏｓｓｂｙ变形半径有关的特征尺度的比值，当比值大于１时，切变流场向平均温度场适应；当比值小于１时，平均温度场向切变流场适应 相似文献
19.
《Dynamics of Atmospheres and Oceans》2005,40(3):209-236
Recent advances in observational technology have led to a more detailed knowledge of the low-level flow in hurricanes. In particular, quasi-streamwise rolls on a variety of scales have been observed. Some of these rolls have radial wavelengths of 4–10 km, which is comparable to rolls associated with instabilities inherent to Ekman-type boundary layers.The evolution and stability of the swirling boundary layer underneath a hurricane-like vortex is studied using both a nonlinear model and linearized stability analysis. The nonlinear model is an axisymmetric model of incompressible fluid flow, which is used to simulate the development of boundary layers underneath vortices with hurricane-like wind profiles. Axisymmetric rolls appear in these boundary layers, which have some similarities to the observed rolls in hurricanes. The axisymmetric flow is also used as the basic-state for a linearized stability analysis. The analysis technique allows for arbitrary variation in the radial and vertical directions for both the basic-state flow and the perturbations. Thus, the strong radial variations and curvature effects common to strong vortices are part of the analysis. The analysis finds both symmetric and asymmetric instabilities that are similar to those in the nonlinear simulations and in observations. The instabilities acquire some of their energy from the vertical shear associated with a reversal of the radial inflow at the top of the boundary layer, and some of their energy from vertical shear of the azimuthal flow. The radial flow energy conversion tends to increase for flows with less inertial stability and for modes oriented across the low-level shear; the azimuthal flow conversion increases for larger inertial stability and for modes aligned with the low-level shear. 相似文献
20.
In 2004–2007 and 2011–2013, oceanography sections with the high spatial resolution were carried out on the shelf and continental slope of the Commonwealth Sea and in the Prydz Bay in the Antarctic. In combination with a fine vertical resolution, this provides an advanced interpretation of the obtained data. It becomes possible to analyze the local thermohaline structure of the baroclinic Antarctic slope front (the ASF) and to investigate its stability. The reliable determination of the ASF characteristics enables to apply the parameterizations and criteria obtained during laboratory experiments for analysis of its stability. The ASF instability is preceded by the local vertical dramatic intensification of the front, where the ASF approaches the pure baroclinic state. Therefore, the local baroclinic instability in the ASF area prevails over the barotropic one at the significant mutual impact of layers (δ = H ASF/H b ≈ ≈ 0.3–0.6, H b is the total depth) and accompanied with the hydrostatic instability. Instability conditions in the frontal zone with a width of ～(1–2)Rd L (Rd L is local baroclinic deformation radius) relative to the wide ASF (L ASF ≈ (3–5)Rd L ) coincide with those of the narrow (intensified) ASF (L ASF ≈ Rd L* ). In the case of the runoff of dense Antarctic shelf water, on the shelf edge the realization is possible of the self-oscillatory mechanism of the ASF instability caused by the topographic beta-effect as well as the periodic generation of baroclinic vortices. 相似文献