Scattering of long coastal-trapped waves due to bottom irregularities

The topographic scattering of long coastal-trapped waves is considered to see whether or not stratification tends to weaken scattering. Numerical examples show that this is not the case in general. Rather, susceptibility to scattering depends upon the particular example: in some cases it weakens with stratification, and in other it strengthens.     

Turbulence and mixing in the boundary layer generated by shoaling internal waves

Over a range of incidence angles the energy of an internal wave propagating onto a sloping boundary is concentrated in a boundary layer on the slope. As a wave propagates upslope the change in its amplitude and interaction with the downslope flow remaining from previous waves results in the wave breaking and the generation of turbulence and mixing in the boundary layer. Measurements of the overturning and buoyancy scales on the slope show that turbulence is generated and decays during each wave cycle and that much of the energy input to mixing scales is extracted from density inversions generated by the wave-induced mean flow. A comparison with decaying turbulence behind a grid in a stratified water tunnel suggests that the criterion for the extinction of the buoyancy flux is similar in the two cases.     

On the role of criticality in coastal flows over irregular bottom topography

A simple expansion technique is developed for predicting the response of a horizontally sheared oceanic coastal flow over uniform coastal topography to variations in that bottom topography. The technique is illustrated by application to supercritical and subcritical flows. The response of the supercritical flow is local, while that of the subcritical flow extends downstream to be eventually attenuated by frictional damping. However, the response of both flow types is weak unless the flow is nearly critical.     

Experimental observation of strong mixing due to internal wave focusing over sloping terrain

This paper reports on experimental observation of internal waves that are focused due to a sloping topography. A remarkable mixing of the density field was observed. This result is of importance for the deep ocean, where internal waves are believed to play a role in mixing. The experiments were performed on the rotating platform at the Coriolis Laboratory, Grenoble. The rotation, its modulation and density stratification were set to be in the internal wave regime. After applying various data processing techniques we observe internal wave rays, which converge to a limiting state: the wave attractor. At longer time scales we observe a remarkably efficient mixing of the density field, possibly responsible for driving observed sheared mean flows and topographic Rossby waves. We offer the hypothesis that focusing of internal waves to the wave attractor leads to the mixing.     

Boundary-layer flow over topography: Impacts of the Askervein study

One of the objectives of the Askervein Hill Project was to obtain a comprehensive and accurate dataset for verification of models of flow and turbulence over low hills. In the present paper, a retrospective of the 1982 and 1983 Askervein experiments is presented. The field study is described in brief and is related to similar studies conducted in the early 1980s. Data limitations are discussed and applications of numerical and wind-tunnel models to Askervein are outlined. Problems associated with model simulations are noted and model results are compared with the field measurements.     

Numerical simulation of air flow over breaking waves

The air flow above breaking monochromatic Stokes waves is studied using a numerical nonlinear model of the turbulent air flow above waves of finite amplitude. The breaking event (spilling breaker) is parameterized by increasing the local roughness at the downwind slope of the wave, just beyond the crest. Both moderate slope waves and steep waves are considered. Above steep breaking waves, a large increase (typically 100%) in the total wind stress — averaged over the wave profile — is found compared to nonbreaking moderate slope waves. This is due to the drastic increase of the form drag, which arises from the asymmetrical surface pressure pattern above breaking waves. Both increase of wave slope (sharpening of the crest) and increase of local roughness in the spilling breaker area cause this asymmetrical surface pressure pattern. A comparison of the numerical results with the recent experimental measurements of Banner (1990) is carried out and a good agreement is found for the structure of the pressure pattern above breaking waves and for the magnitude of enhanced momentum transfer. Also: Dept. of Applied Physics, Techn. Univ. Delft, Netherlands.     

Some evidence of organized flow over natural waves

Measurements of the flow characteristics at 2 m over unobstructed wave surfaces on Lake Michigan were made using an anemometer-bivane as a velocity sensor. During one 40-min period of measurement, significant energy concentration was observed at the frequency of dominant surface waves in the vertical and cross wind spectra. Cross spectra between the surface elevation and vertical motions in the flow indicate that the surface lags the vertical motions by about 55 ° at the frequency of dominant waves.     

A new model of tropical waves incorporating momentum mixing by cumulus convection

A comparison is made between the magnitudes of observed large-scale weather waves over the tropical Pacific and the magnitudes of the corresponding waves, predicted by wave-CISK theories, which are driven by the observed amount of latent heating (i.e., precipitation). The theoretical wave fields of meridional velocity, vorticity, and temperature rate are shown to exceed the observed quantities by an order of magnitude. An attempt is made to simulate the observed balance between the diabatic heating and adiabatic cooling within the context of the inviscid theories. For a broad class of heating profiles, geometries and basic states, it is found that this compensation without temperature change cannot be satisfactorily modelled, regardless of the vertical shape of the heating, when the vertical wavelength of the disturbance exceeds about 6 km.Scale analysis demonstrates that an important dynamical term has been neglected in the inviscid models, viz., the vertical transport of horizontal momentum by cumulus clouds. When this process is included in the wave model, velocities, relative vorticity, and the time rate of temperature change are all comparable to the observed values. The general behavior of a system where both forcing and cumulus “friction” are proportional to each other has not been previously examined. We find the behavior of such a system to have several novel features. For example, we find that for a wide range of precipitation amplitudes (from 1/4 to 4 times the precipitation amplitudes of waves in the western Pacific) we get essentially constant amplitudes for wind. The implications of this and other features for various aspects of tropical wave modelling are discussed.     

On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)² up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z ₀ ^eff. The form of the varation of z ₀ ^eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.     

A study of gravity waves generated by convective systems in eta model forecasts

Summary Spectral filtering and visualization reveal a multitude of gravity waves in the fine mesh (29 km) Eta model output, extending into the large scale, masking the vertical motions associated with Rossby-modes. The 6 h forecast of the Eta model from 00 UTC 22 December 1994 initialization contains gravity waves recognizable over a broad spectrum of wavelengths as concentric circles radiating outward from centers of model convection. Contamination of the signal is therefore identifiable in any spectral range, as rings. Postprocessing techniques are presented to eliminate gravity wave contamination and to reveal the meteorologically significant signal. Low-pass filtering is found to be an effective means of extracting the Rossby signal, but with loss in Rossby signal that renders the results obtained with a high resolution model no better than what could have been obtained from a coarser resolution model. Time filtering, is suggested as a more effective method for eliminating the effects of fast modes while maintaining mesoscale details of the slow modes.With 9 Figures     

The Ekman boundary-layer stress due to flow over a regular array of hills

The flow of water over a regular array of hills in a rotating laboratory experiment is studied as an analogue of planetary boundary layers. Gaussian-shaped hills of heighth = 1 cm andh = 1/3 cm covered the floor of a 228 cm diam rotating tank. The characteristic depth of the Ekman layer varied fromD = 0.1 cm toD = 0.3 cm and the Reynolds number for the Ekman layer varied up toRe = 150. The integrated boundary-layer stress as a function ofRe andD/h was determined by the rate of spin-up of the water after a small increase of the rotation rate.Selected functional relations were fitted to the empirical data by the method of least squares for the laminar and turbulent regimes of flow. These results indicate maximum non-linear effects of the hills and a minimum transition Reynolds number nearD/h = 0.2. The patterns of flow as indicated by dye tracers are briefly discussed. Peculiar circular bands of dye appear to be caused by the selective ejection of dye from the boundary layer when the circular flow is at a particular angle of incidence with respect to the triangular pattern of hills.The research reported herein was supported in part by the National Science Foundation under Grant NSF GA 4388.     

A non-linear extension of the mixed spectral finite difference model for neutrally stratified turbulent flow over topography

A non-linear extension of the mixed spectral finite difference model for neutrally stratified surface-layer flow over complex terrain is developed. The non-linear terms are treated as additional source terms in the present model. The solution is calculated iteratively in spectral space, while the source terms are evaluated in physical space (at each iteration step) with the help of a Fast Fourier Transform algorithm.Results for simple 2D sinusoidal topography are shown to compare well with full non-linear finite difference results. The method, compared to conventional finite difference methods, has the advantage of rapid convergence and substantial savings in computer time.     

Vertical mixing of passive scalars owing to breaking gravity waves

In this paper, some aspects of dispersion of air pollutants as emitted from aircraft in the lower stratosphere have been investigated. As this part of the atmosphere is always stably stratified, mixing as a result of small-scale turbulence is very slow. Instead, effective vertical mixing can be provided by breaking gravity waves. We have examined the mixing properties of those events by means of a numerical model, which simulates the wave development as well as the dispersion of passive trace substances. From these simulations, an effective diffusion coefficient for the entire event of a breaking gravity wave of about 0.7 m² s⁻¹ was calculated.     

Development of a non-linear mixed spectral finite difference model for turbulent boundary-layer flow over topography

Further development of the non-linear mixed spectral finite difference (NLMSFD) model of turbulent boundary-layer flow over topography is documented. This includes modifications and refinements to the solution procedure, the incorporation of second-order turbulence closures to the model and the three-dimensional extension of the model. Based on these higher order closures, linear limitations, boundary-layer approximation and non-linear effects are discussed. The impact of different turbulence closures on the prediction of the NLMSFD model is also demonstrated. Furthermore, sample results for 3D idealized topography (sinusoidal) are presented. The parameterization of drag over small-scale topography is also addressed.     

A multi-scale simulation of an extreme downslope windstorm over complex topography

Summary A severe localized windstorm, with near-surface winds > 60 ms⁻¹, occurred in an isolated valley within the Alpine mountains (> 1800 m) of central Norway on 31 January 1995. A multi-scale numerical simulation of the event was performed with the Naval Research Laboratory (NRL)’s Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS), configured with four nested grids telescoping down to 1-km horizontal resolution. The windstorm occurred in response to topographic blocking and deformation of a lower-tropospheric warm front and attendant jet (> 35 ms⁻¹ at 2 km). The key findings are: i) mountain wave resonance and amplification arising from the interaction of the surface-based front and jet with complex orography, ii) sensitivity of the wave response to differential diabatic heating (vertical) gradients above the front, and iii) trapped response within the layer of large frontal stratification in the lower troposphere and subsequent amplification consistent with the theoretically-established two-layer windstorm analogue of Durran (1986). Received September 29, 1999 Revised December 30, 1999     

A note on the temporal evolution of taylor columns over topography

The formation of two regions of vorticity, one cyclonic and one anticyclonic, after the initiation of flow is discussed. In particular, the linearized case of elongated topography is examined. The non-linear interaction of the two vortices, once formed, is discussed using a simple model.     

A Laboratory Model for the Flow in Urban Street Canyons Induced by Bottom Heating

Water tank experiments are carried out to investigate the convection flow induced by bottom heating and the effects of the ambient wind on the flow in non-symmetrical urban street canyons based on the PIV (Particle Image Visualization) technique. Fluid experiments show that with calm ambient wind,the flows in the street canyon are completely driven by thermal force, and the convection can reach the upper atmosphere of the street canyon. Horizontal and vertical motions also appear above the roofs of the buildings. These are the conditions which favor the exchange of momentum and air mass between the street canyon and its environment. More than two vortices are induced by the convection, and the complex circulation pattern will vary with time in a wider street canyon. However， in a narrow street canyon， just one vortex appears. With a light ambient wind, the bottom heating and the associated convection result in just one main vortex. As the ambient wind speed increases, the vortex becomes more organized and its center shifts closer to the leeward building.     

The effect of ekman suction on a flow over a shallow topography in the beta plane

The effect of bottom Ekman layer suction on a homogeneous, constant depth, eastwards, low Rossby number flow over a shallow bottom topography in the beta plane is studied. The governing vorticity equation is obtained by expanding the velocities in the continuity and momentum equations in powers of the Rossby number, ?, and matching the vertical velocity with the vertical velocity at the outer edge of the bottom Ekman layer obtained from the Ekman layer solution. The suction effect is then linearized using an Oseen approxiamation and the resulting linear model is solved using Fourier transforms with the requirement that the solution behave like a vortex near the origin which is equivalent to the effect of an isolated bump, i.e., a Green's function solution is obtained. An analytical solution is thus, obtained in integral form and then numerically integrated. The effect of Ekman suction is found to be a damping of the downstream Rossby waves in a distance of order $\text{2√2U/f}{}_0\text{E}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, an increased upstream influence, and a counterclockwise rotation of the closed streamline region about the origin. It is pointed out that the vortex solutions can be superimposed in order to obtain the solution for flow over topographies of finite horizontal text. This technique was used to compute the flow over a right circular cylinder. The results agree favorably with the experimental results of McCartney (1975).     

东亚地区一次切断低压引起的平流层、对流层交换数值模拟研究

用中尺度模式(MM5)模拟研究东亚地区(网格中心45°N,120°E)一次强切断低压过程(2000年4月8日～12日)引起的平流层、对流层交换.用Wei公式计算此次过程由平流层到对流层的净交换量为5.0×1014 kg,平均交换通量为-0.72×10-3 kg m-2 s-1.地面锋与高空锋的相互作用,在急流入口处和高空锋区出现对流层顶折叠,并引起平流层、对流层物质交换,其中空气的水平运动起主要作用.利用历史天气图统计东亚地区(20～70°N,80～180°E)切断低压的年平均个数为60,占北半球极区类型切断低压的52%.由此,推断东亚地区的平流层、对流层交换对整个北半球的平流层、对流层交换贡献很大.