流体涡旋中螺旋波不稳定发展的理论研究

文章利用柱坐标下的流体涡度方程,通过求初始时刻的解析解,研究了螺旋波的不稳定发展问题.结论是：涡旋中螺旋波动之间可以通过基本流耦合相互作用,出现共振不稳定增长.其增长率大小与初始扰动的波数相关,数值计算结果也表明：波动在发展过程中,螺旋带状结构将越来越明显,螺旋角越来越小.     

Wind-induced baroclinic response of Lake Constance

We present results of various circulation scenarios for the wind-induced three-dimensional currents in Lake Constance, obtained with the aid of a semi-spectral semi-implicit finite difference code developed in Haidvogel et al. and Wang and Hutter. Internal Kelvin and Poincaré-type oscillations are demonstrated in the numerical results, whose periods depend upon the stratification and the geometry of the basin and agree well with measured data. By solving the eigenvalue problem of the linearized shallow water equations in the two-layered stratified Lake Constance, the interpretation of the oscillations as Kelvin and Poincaré-type waves is corroborated.     

A laboratory study of baroclinic instability

Abstract

Experimental and theoretical results are presented for a simple system which exhibits baroclinic instability. We consider the motion of two immiscible fluids with densities ρ ₁ and ρ ₂ contained in a cylinder rotating with angular frequency ω. The motion is driven by a contact lid rotating with frequency ω + ω. In this paper ω, ω, 2(ρ ₂ – ρ ₁)/(ρ ₂ + ρ ₁), and the geometry are such that the interface does not intersect the “ground” (e.g. an almost horizontal boundary). The motions are described by two-layer quasi-geostrophic equations which are identical, except perhaps for the presence of interfacial friction and tension, with those used in meteorology and oceanography. For small enough internal Froude number F = 4ω² L ²/(g(Δρ/ρ)H) or small enough Rossby number ? = ω/2ω the flow is steady and axisymmetric, the velocity field in each layer being determined primarily by frictional effects in top, bottom, and interfacial Ekman layers. For certain (F, ?) the flow becomes non-axisymmetric. The transition points for the case where the basic potential vorticity gradient is due to interface slope alone have been carefully measured and are in very good agreement with a linear instability theory which neglects sidewall effects. Some preliminary observations of supercritical motion, which include repeatable amplitude and wavenumber vacillation, are reported.     

Nonlinear stability of baroclinic flows over topography

Abstract

A new nonlinear stability criterion is derived for baroclinic flows over topography in spherical geometry. The stability of a wide class of exact three-dimensional nonlinear steady state solutions subject to arbitrary disturbances is established. The resonance condition, at the highest total wavenumber, for the steady state solutions and the stability criteria for baroclinic flow in the absence of topography provide the boundaries of the regions of stability in the presence of topography. The analogous results for flow on periodic or infinite beta planes incorporating non-orthogonal function large scale flows are also discussed.     

The symmetric baroclinic instability of an equatorial current

Abstract

The stability of a baroclinic zonal current to symmetric perturbations on an equatorial β-plane is considered. The fluid is assumed to be Boussinesq, inviseid, adiabatic, hydrostatic, and stably stratified. The solutions exhibit the same stability properties as those on an f-plane: instability occurs whenever Ri < 1/(1 + d), where Ri is the Richardson number and d is a measure of the horizontal shear of the current; the most unstable motions tend to parallel the isotherms of potential temperature; and they have infinitely small scales of variation perpendicular to the isotherms. The variation of Coriolis parameter leads to one important difference in the structure of the eigenfunctions: the rapidly growing modes are concentrated in high latitudes, and the slowly growing ones in low latitudes.

The suggestion that the symmetric cloud bands observed at low latitudes in Jupiter's atmosphere are caused by symmetric instabilities is re-examined in the light of these results. These cloud bands would have to be associated with the slowly-growing, low-latitude modes. These modes consist of small scale motions parallel to the isotherms, with the magnitude of the motions having a large scale modulation as a function of latitude. The time scales of these modes and the latitude scales of their modulation agree qualitatively with the observations of Jupiter's cloud bands, so long as Ri is not very close to zero or to its critical value.     

Convective and absolute instability of baroclinic eddies

Abstract

The long time response to an arbitrary unstable disturbance in a two layer model on an f-plane is sought. It has been found that depending on the ratio of the shear to the average speed of the mean flow two types of baroclinic instabilities exist: convective and absolute. When the system supports convective instabilities the long time response to an initial pulse excitation decreases with time at a fixed point in space. When such a system is excited by a wave maker the steady state frequency of response of the system corresponds to a spatially amplifying wave oscillating with the frequency of the wave maker. If the dispersion relation yields a saddle point of the frequency in the wave number complex plane with positive imaginary part of the frequency the system supports absolute instabilities. The response of the system at any point in space excited by an arbitrary signal grows exponentially with time at a rate determined by the properties of the system at the saddle point. This response is different from that of unstable normal modes. It is conjectured that absolute instability may be responsible for local cyclogenesis activity in certain geographical regions.     

On the development of baroclinic waves influenced by friction and heating

Summary The influence of surface skin friction and a specific type of heating on the stability of baroclinic waves in a two-level, quasi-geostrophic model is investigated. It is found that the effect of friction alone changes the neutral stability curve in such a way that a broader band of wavelengths are unstable for a given value of the vertical windshear. The neutral stability curve is independent of the intensity of friction in this case. The effect of heating is to make all waves longer than a certain critical wave length unstable, but the amplification rate is very small for large values of the wavelength. The combined effect of friction and heating will in general tend to stabilize the waves. The amplification rate is investigated in all cases.Numerical integrations of the linearized equations show that the flow in the stable case will reach a steady state characterized by vanishing dissipation and heat transport, but with a certain wave length dependent ratio between the kinetic energy of the vertical shear flow and the vertical mean flow. It is shown that this ratio can be predicted from the steady state solutions in the adiabatic, frictionless case. A comparison is made between the predictions of the energetics of the waves in the model and observational studies.Research supported by the Section on Atmospheric Sciences, National Science Foundation, GP-2561.Contribution No. 99 from the Department of Meteorology and Oceanography, University of Michigan.     

Observation of baroclinic eddies southeast of Okinawa Island

In the region southeast of Okinawa, during May to July 2001, a cyclonic and an anticyclonic eddy were observed from combined measurements of hydrocasts, an upward-looking moored acoustic Doppler current profiler (MADCP), pressure-recording inverted echo sounders (PIESs), satellite altimetry, and a coastal tide gauge. The hydrographic data showed that the lowest/highest temperature (T) and salinity (S) anomalies from a 13-year mean for the same season were respectively -3.0/ 2.5℃ and -0.20/ 0.15 psu at 380/500 dbar for the cyclonic/anticyclonic eddies. From the PIES data, using a gravest empirical mode method, we estimated time-varying surface dynamic height (D) anomaly referred to 2000 dbar changing from -20 to 30 cm, and time-varying T and S anomalies at 500 dbar ranging through about ±2 ℃ and ±0.2 psu, respectively. The passage of the eddies caused variations of both satellite-measured sea surface height anomaly (SSHA) and tide-gauge-measured sea level anomaly to change from about –20 to 30 cm, consistent with the D anomaly from the PIESs. Bottom pressure sensors measured no variation related to these eddy activities, which indicated that the two eddies were dominated by baro-clinicity. Time series of SSHA map confirmed that the two eddies, originating from the North Pacific Subtropical Countercurrent region near 20°―30°N and 150°―160°E, traveled about 3000 km for about 18 months with mean westward propagation speed of about 6 cm/s, before arriving at the region southeast of Okinawa Island.     

一个三维斜压水动力模型的建立及其在日本琵琶湖中的应用

水温的空间分布对很多湖泊水文现象关系甚大,本文建立了日本琵琶湖的三维斜压水动力数值模式。模拟计算结果表明：１）在不同风速驱动下,湖的上、下两层可形成不同的环流型;２）除形成环流处外,其它部分流速、流向在上、下层表现出明显的垂直切变;３）闭合式温度场储存位能,即使在无风和初始静止流场情况下,也可驱动湖流并形成若干环流特征;４）风对水的驱动作用是形成北湖北部稳定环流的决定性因子,并且本身可构造出温度场     

Barotropic and baroclinic processes in the transport variability of the Antarctic Circumpolar Current

Synoptic scale variability of the Southern Ocean wind field in the high-frequency range of barotropic Rossby waves results in transport variations of the Antarctic Circumpolar Current (ACC), which are highly coherent with the bottom pressure field all around the Antarctic continent. The coherence pattern, in contrast to the steady state ACC, is steered by the geostrophic f/h contours passing through Drake Passage and circling closely around the continent. At lower frequencies, with interannual and decadal periods, the correlation with the bottom pressure continues, but baroclinic processes gain importance. For periods exceeding a few years, variations of the ACC transport are in geostrophic balance with the pressure field associated with the baroclinic potential energy stored in the stratification, whereas bottom pressure plays a minor role. The low-frequency variability of the ACC transport is correlated with the baroclinic state variable in the entire Southern Ocean, mediated by baroclinic topographic–planetary Rossby waves that are not bound to f/h contours. To clarify the processes of wave dynamics and pattern correlation, we apply a circulation model with simplified physics (the barotropic–baroclinic-interaction model BARBI) and use two types of wind forcing: the National Centers for Environmental Prediction (NCEP) wind field with integrations spanning three decades and an artificial wind field constructed from the first three empirical orthogonal functions of NCEP combined with a temporal variability according to an autoregressive process. Experiments with this Southern Annular Mode type forcing have been performed for 1,800 years. We analyze the spin-up, trends, and variability of the model runs. Particular emphasis is placed on coherence and correlation patterns between the ACC transport, the wind forcing, the bottom pressure field and the pressure associated with the baroclinic potential energy. A stochastic dynamical model is developed that describes the dominant barotropic and baroclinic processes and represents the spectral properties for a wide range of frequencies, from monthly periods to hundreds of years.     

Rossby-Haurwitz's equation for the conservation of vertical vorticity component in the baroclinic atmosphere

Summary It is shown that the conservation equation of potential vorticity in the barotropic atmosphere holds good, even in the baroclinic atmosphere, if it is permissible to introduce the isentropic and mass-conservation approximations.     

Linear baroclinic instability in the presence of heat inflow from the lower boundary

A linear Eady model with a parameterization of heat influx from the lower boundary is studied analytically in order to obtain the characteristics of baroclinic normal modes modified by this non-adiabatic source. The results display a secondary maximum of growth rate at high wave numbers and a range of absolutely unstable waves, thus suggesting that the property observed among mid-latitude explosive cyclones of being near-stationary in the phase of maximum growth may be captured by this representation of the air-sea energy exchange.     

Delayed baroclinic response of the Antarctic circumpolar current to surface wind stress

The Antarctic Circumpolar Current (ACC) responds to the surface windstress via two processes, i.e., the instant barotropic process and the delayed baroclinic process. This study focuses on the baroclinic instability mechanism in ACC, which was less reported in the literatures. Results show that the strengthening of surface zonal windstress causes the enhanced tilting of the isopycnal surface, leading to more intense baroclinic instability. Simultaneously, the mesoscale eddies resulting from the baro- clinic instability facilitate the transformation of mean potential energy to eddy energy, which causes the remarkable decrease of the ACC volume transport with the 2-year lag time. This delayed negative cor- relation between the ACC transport and the zonal windstress may account for the steadiness of the ACC transport during last two decades.     

Anticipation of ENSO: what teach us the resonantly forced baroclinic waves

The El Niño-Southern Oscillation (ENSO) is characterized based on the date the events are mature. Their time lag defined relative to the central value of successive intervals of 4 years length, e.g. 01/1868–01/1872, 01/1872–01/1876 …, 01/1996–01/2000 … affects their evolution and, for a given amplitude, their variability. It specifies the dynamics of the quadrennial Quasi-Stationary Wave (QSW) in the tropical Pacific since ENSO always occurs at the end of the eastward phase propagation of that QSW. A third of events are unlagged with very low variability, SST anomalies being nearly concomitant between the extreme eastern and the central-eastern Pacific. A third of events are weakly lagged, in phase with the annual QSW, whose variability is much greater. Several months may elapse between the maximum SST anomalies east of the basin and along its equatorial central part. The last third of the events exhibits considerable variability, whether they are out of phase with the annual QSW or strongly lagged. The SST anomaly between 5°N and 20°N plays a key role in the maturation of the events out of phase. The events in phase (10% of the total population) are characterized by a negative SST anomaly in the central-eastern Pacific that reverses just before the maturation stage of ENSO. Sea water temperature 125 m deep in the central-eastern Pacific carries the earliest relevant information with a lead time of one year for forecasting the amplitude of unlagged ENSO while reporting how SST anomalies will develop until ENSO is fully developed. Besides, long-term forecast of the resumption of La Niña can be achieved accurately when weakly lagged events in phase with the annual QSW occur. The well differentiated typology of events vs. their time lag is the best clue to prove the leading role of the quadrennial QSW in the genesis of ENSO, while the related dynamic of the atmosphere ensues.     

On the meridional form of baroclinic waves in a two-layer quasi-geostrophic model

Summary It is shown that in laterally bounded two-layer models of the atmosphere the only permissible meridional variation of the wave solutions is of the form sin(/D) whereD is the lateral width.     

Variability of baroclinic tidal currents on the Mackenzie Shelf,the Southeastern Beaufort Sea

Semidiurnal tidal currents on the outer shelf of the Mackenzie Shelf in the Beaufort Sea were found to be strongly influenced by the locally generated baroclinic tide. Two primary factors are involved in this process: (1) the sharp shelf break along the northeastern Mackenzie Shelf, promoting the generation of vigorous internal tidal waves; and (2) the proximity to critical latitudes for M₂ and N₂ motions locking these waves and preventing them from leaving the source region. As a result, internal tides are resonantly trapped between the shelf and critical latitudes. The physical properties and temporal variations of tidal motions were examined using current meter measurements obtained from 1987–1988 at four sites (SS1, SS2, SS3, and SS4) offshore of the shelf break at depths of ∼200 m. Each mooring had Aanderaa RCM4s positioned at ∼35 m below the surface and ∼50 m above the bottom. Complex demodulation was used to compute the envelopes (amplitude modulation) of these components. A striking difference in the variability of clockwise (CW) and counterclockwise (CCW) tidal currents was found. The CW tides are highly variable, have greater amplitude, exhibit a burst-like character associated with wind events and contain about 80% of the total energy of the semidiurnal tidal currents. In contrast, the CCW components have a more regular temporal regime with distinct monthly, fortnightly and 10-day modulation at astronomical periodicities associated with frequency differences M₂–N₂ (0.03629 cpd), S₂–M₂ (0.06773 cpd), and S₂–N₂ (0.10402 cpd). Significant horizontal correlation of the CW current envelopes was found only between stations near the northeast Mackenzie Shelf, indicating this to be the main area of baroclinic internal wave generation.     

On the generation of baroclinic rossby waves in the presence of a semi-circular boundary

Abstract

An analytical model is constructed for the generation of baroclinic Rossby waves by a vorticity source in the presence of a semi-circular boundary. The vorticity source is used to represent the effect of the Agulhas retroflection to the south of Southern Africa. The displacement of the interface between the two layers of the model ocean consists of quantized waves near the coast and a train of Rossby waves drifting westward further offshore.