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     

Some aspects of internal gravity waves in the multicell-type convective system

Summary Some aspects of internal gravity waves in the multicell-type convective system are examined using a linear theory and a nonlinear numerical model. The basic-state wind is assumed to increase linearly with height and then remain constant.In the theoretical part, the two-dimensional, linear, steady-state response of a stably stratified atmosphere to specified cooling representing the evaporative cooling of falling precipitation in the subcloud layer is analytically considered. It is shown that there exist an updraft on the upstream side of the cooling and a downdraft on the downstream side. As the wind shear increases enough, the magnitude of the updraft decreases. This is because a large portion of the specified cooling is used to compensate for the positive vorticity associated with the positive wind shear and accordingly the effective cooling necessary to produce perturbations is reduced.In the numerical part, a two-dimensional version of the ARPS (Advanced Regional Prediction System) that is a nonhydrostatic, compressible model with detailed physical processes is employed. Results from the dry simulation, in which the steady cooling is specified in the model, show that the simulated quasi-steady field resembles the linear, steady-state solution field because the nonlinearity factor of thermally-induced waves in this case is small. For the moist simulation, the quasi-steady perturbations obtained from the dry simulation are used as initial conditions. It is shown that gravity waces can effectively initiate convection even with small amplitude and that updraft at the head of the density current somewhat resembles the linear, steady-state response of a stably straified flow to the specified cooling. The updraft, that is, forced internal gravity waves, at the head of the density current is responsible for the initiation of consecutive convective cells that move downstream and develop as a main convective cell. This study suggests that internal gravity waves play a major role in the initiation of consecutive convective cells in the multicell-type convective system and hence in its maintenance.     

Particle dispersion and mixing induced by breaking internal gravity waves

The purpose of this paper is to analyze diapycnal mixing induced by the breaking of an internal gravity wave — the primary wave — either standing or propagating. To achieve this aim we apply two different methods. The first method consists of a direct estimate of vertical eddy diffusion from particle dispersion while the second method relies upon potential energy budgets [Winters, K.B., Lombard, P.N., Riley, J.J., D’Asaro, E.A., 1995. J. Fluid Mech. 289, 115–128; Winters, K.B., D’Asaro, E.A., 1996. J. Fluid Mech. 317, 179–193]. The primary wave we consider is of small amplitude and is statically stable, a case for which the breaking process involves two-dimensional instabilities. The dynamics of the waves have been previously analyzed by means of two-dimensional direct numerical simulations [Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1995. J. Fluid Mech. 285, 265–301; Bouruet-Aubertot, P., Sommeria, J., Staquet, C., 1996. Dyn. Atmos. Oceans 29, 41–63; Koudella, C., Staquet, C., 1998. In: Davis, P. (Ed.), Proceedings of the IMA Conference on Mixing and Dispersion on Stably-stratified Flows, Dundee, September 1996. IMA Publication]. High resolution three-dimensional calculations of the same wave are also reported here [Koudella, C., 1999].A local estimate of mixing is first inferred from the time evolution of sets of particles released in the flow during the breaking regime. We show that, after an early evolution dominated by shear effects, a diffusion law is reached and the dispersion coefficient is fairly independent of the initial seeding location of the particles in the flow.The eddy diffusion coefficient, K, is then estimated from the diapycnal diffusive flux. A good agreement with the value inferred from particle dispersion is obtained. This finding is of particular interest regarding the interpretation of in situ estimates of K inferred either from tracer dispersion or from microstructure measurements. Computation of the Cox number, equal to the ratio of eddy diffusivity to molecular diffusivity, shows that the Cox number varies within the interval [9, 262], which corresponds to the range of vertical eddy diffusivity measured in the interior of the ocean. The Cox number is found to depend on the turbulent Froude number squared.We show eventually that mixing results in a weak distortion of the initial density profile and we relate this result to observations made at small scale in the ocean.Comparisons between the analysis of the two-dimensional and high resolution (256³) three-dimensional direct numerical simulations of the primary wave were also conducted. We show that the energetics and the amount of mixing are very close when the primary wave is of small amplitude. This results from the fact that, for a statically stable wave, the dynamics of the initially two-dimensional primary wave remains mostly two-dimensional even after the onset of wavebreaking.     

Generation of oceanic internal gravity waves by a cyclonic surface stress disturbance

Atmospheric cyclones with strong winds significantly impact ocean circulation, regional sea surface temperature, and deep water formation across the global oceans. Thus they are expected to play a key role in a variety of energy transport mechanisms. Even though wind-generated internal gravity waves are thought to contribute significantly to the energy balance of the deep ocean, their excitation mechanisms are only partly understood.The present study investigates the generation of internal gravity waves during a geostrophic adjustment process in a Boussinesq model with axisymmetric geometry. The atmospheric disturbance is set by an idealized pulse of cyclonic wind stress with a Rankine vortex structure. Strength, radius and duration of the forcing are varied. The effect upon wave generation of stratification with variable mixed-layer depth is also examined.Results indicate that internal gravity waves are generated after approximately one inertial period. The outward radial energy flux is dominated by waves having structure close to vertical mode-1 and with frequency close to the inertial frequency. Less energetic higher mode waves are observed to be generated close to the sea floor underneath the storm. The total radiated energy corresponds to approximately 0.02% of the wind input. Deeper mixed-layer conditions as well as weaker stratification reduce this fraction.The low energy transfer rates suggest that other processes that drive vertical motion like surface heat fluxes, turbulent motion, mixed region collapse and storm translation are essential for significant energy extraction by internal gravity waves to occur.     

A study of gravity waves in the planetary boundary layer by acoustic sounding

Gravity waves associated with stably stratified layers were observed in the planetary boundary layer at two locations in France. Using an array of three monostatic Doppler acoustic sounders, the wave speeds and directions were found. A quantitative study of the waves has been performed to determine their physical characteristics. Based on their dynamics, a classification into three types was possible. Most were found to be trapped beneath a critical level.     

A study of internal waves in a wind tunnel

The combined use of a stratified flow wind tunnel and of periodic sampling methods in low Reynolds number flows allows the recovery of the instantaneous dynamics of internal waves. Several detailed examples are given of the thermal structure of large propagating and breaking internal waves and Kelvin-Hemholtz waves. Preliminary measurements of the stability of finite waves as a function of Richardson number are also reported.     

Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves

An ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler–Boussinesq equations. For flows with zero mean potential vorticity, a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length. Stationary scaling solutions of this equation are found for almost vertically propagating waves. The resulting spectra are anisotropic in vertical and horizontal wave numbers. For flows with small but non-zero mean potential vorticity, under the same statistical hypothesis applied to the wave part of the flow, it is shown that the vortex part and the wave part decouple. The vortex part obeys a limiting slow dynamics equation exhibiting vertical collapse and layering which may contaminate the wave-part spectra. Relation of these results to the in situ atmospheric measurements and previous work on oceanic gravity waves is discussed.     

Influence of internal gravity waves on sound propagation in the lower atmosphere

Summary The effects of internal waves on the propagation of acoustic pulses in the lower atmosphere were studied theoretically and by acoustic pulse sounding of the stable atmospheric boundary layer. Due to a control in the experiments of the stratification and time variations of meteorological parameters, such as wind speed, temperature and atmospheric pressure, we were able to observe the influence of the variations of these parameters on a pulse wave form, travel time and time duration. For the travel time and wind speed variations we obtained statistical characteristics (variances, frequency spectra and coherences) in the range of periods from 1 min to 1h and found several dominant periods, which are inherent to the trapped internal waves in the lower atmosphere. Using a nonlinear model of internal wave spectrum in the atmosphere described here we have made the calculations of variances, frequency spectra and structure functions of travel time fluctuations, which allowed us to interpret some of the observed data.     

Generation mechanisms of convectively induced internal gravity waves in a three-dimensional framework

The generation mechanisms of convective gravity waves in the stratosphere are investigated in a three-dimensional framework by conducting numerical simulations of four ideal storms under different environmental conditions: one un-sheared and three constant low-level sheared basic-state winds with the depth of the shear layer of 6 km and the surface wind speeds (U_s) of 8, 18, and 28 m s^?1, using the Advanced Regional Prediction System (ARPS) model. The storms simulated under the un-sheared (U_s = 0 m s^?1), weakly sheared (U_s = 8 and 18ms^?1), and strongly sheared (U_s = 28ms^?1) basicstate winds are classified into single-cell, multicell, and supercell storms, respectively. For each storm, the wave perturbations in a control simulation, including nonlinearity and microphysical processes, are compared with those in quasi-linear dry simulations forced by diabatic forcing and nonlinear forcing that are obtained from the control simulation. The gravity waves generated by the two forcing terms in the quasi-linear dry simulations are out of phase with each other for all of the storms. The gravity waves in the control simulation are represented by a linear sum of the wave perturbations generated by the nonlinear forcing and diabatic forcing. This result is consistent with the results of previous studies in a two-dimensional framework. This implies that both forcing mechanisms are important for generating the convective gravity waves in the three-dimensional framework as well. The characteristics of the three-dimensional gravity waves in the stratosphere were determined by the spectral combination of the forcing terms and the wave-filtering and resonance factor that is determined from the basic-state wind and stability as well as the vertical structure of the forcing.     

地球流体惯性重力内波的波作用量与稳定性

本文首先导出了地球流体中惯性重力内波的波能密度和波作用量;然后,用WKB方法和多尺度方法建立了波作用量方程,并讨论了惯性重力内波的稳定性;最后,定义惯性重力内波的广义波作用量,并在非均匀介质中论证了它的守恒性.     

On generation of internal waves by turbulence in the mixed layer

Turbulent fluctuations in active mixed layers can excite internal waves in stably stratified fluid regions adjoining them. Expressions are derived for the energy and momentum fluxes radiated away by internal waves from an oceanic mixed layer, in terms of the spectrum of the static pressure fluctuations imposed at the base of the mixed layer by the turbulent eddies. The role of these internal wave fluxes in questions such as the determination of the rate of deepening of the layer due to an applied surface stress and the origin of internal waves in the deep ocean is discussed.     

The observed generation and breaking of atmospheric internal gravity waves over the ocean

Observations are presented for internal gravity waves and their breaking at a height of 23.5 m over the ocean in surface-based inversions which are formed because of the advection of warm air over cold water. The spectral and cospectral analyses of velocity and temperature fluctuations were made to establish the characteristic features of the waves. Flow visualization photographs of smoke released during the breaking of a wave are also presented. Comparison between the turbulent energies present during and after breaking of a wave indicates enormous mixing and dispersion occurring during breaking.This research was performed under Contract No. EY-76-C-02-0016 with the United States Energy Research and Development Administration.     

A case of persistent breaking of internal gravity waves in the atmospheric surface layer over the ocean

Formation and breaking of internal gravity waves contributing to a very significant increase in turbulence in the atmospheric surface layer over the Atlantic Ocean off Long Island, New York are reported. Contrary to the bursts that are characteristically of short duration, this increase in turbulence lasted for more than one hour and was typical of what one would observe during unstable atmospheric conditions. However, mean temperature profiles indicated strong stable conditions.This research was performed under the auspices of the United States Department of Energy Under Contract No. EY-76-C-02-0016.     

Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves

Summary In this study, the response of a dynamically unstable shear flow with a critical level to periodic forcing is presented. An energy argument is proposed to explain the upshear tilt of updrafts associated with disturbances in two-dimensional stably stratified flows. In a dynamically unstable flow, the energy equation requires an upshear tilt of the perturbation streamfunction and vertical velocity whereU _z is positive. A stability model is constructed using an iteration method. An upshear tilt of the vertical velocity and the streamfunction fields is evident in a dynamically unstable flow, which is required by energy conversion from the basic shear to the growing perturbation wave energy according to the energy argument. The momentum flux profile indicates that the basic flow is decreased (increased) above (below) the critical level. Thus, the shear instability tends to smooth the shear layer. Following the energy argument, a downshear tilt of the updraft is produced in an unstably stratified flow since the perturbation wave energy is negative. The wave energy budget indicates that the disturbance is caused by a thermal instability modified by a shear flow since the potential energy grows faster than the kinetic energy.With 4 Figures     

On the breakdown into turbulence of propagating internal waves

The breakdown of propagating internal waves is studied using linear stability analysis and direct numerical simulations. Sinusoidal wave trains in a uniformly stratified, non-rotating environment are considered. Cases are addressed with differing wave amplitudes and directions of propagation. For large-amplitude waves it is found that the primary instabilities are both two- and three-dimensional. It is also found that there is no qualitative difference in the breakdown process for waves with amplitude slightly below or slightly above the amplitude of incipient overturning. For the parameter regimes considered, the breakdown process could not be attributed to convective or shear instability alone, but a combination of the two. Owing to the growth of instabilities, local patches of statically unstable fluid and also of intense shear form, leading ultimately to local patches of turbulence.     

On the influence of variations in Monin-Obukhov length on horizontal roll vortices in an inversion-capped planetary boundary layer

Observations of the planetary boundary layer under conditions with strong or moderate winds often show the large-scale boundary-layer motions to be highly elongated in a direction close to that of the geostrophic wind. The properties of such large-scale motions are examined by means of a two-dimensional numerical model. The small-scale turbulence is parameterized using a buoyancy-dependent mixing-length hypothesis. The objective is to understand how the properties and dynamics of such rolls depend upon the relative importance of shear and buoyancy forces.     

Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves part II: Nonlinear response

Summary The nonlinear response of a dynamically unstable shear flow with critical level to an initial temperature anomaly is investigated using a nonlinear numerical model. Both nonconstant and constant shear profiles of the basic flow are considered. Effects of the solid lower boundary on the dynamically unstable, nonlinear flow are also studied. It is found that in a dynamically unstable, linear flow with a hyperbolic tangent wind profile, the updraft is tilted upshear. The result in consistent with that of a linear stability model (LC). The upshear tilt can be explained by the Orr mechanism (1907) and the energy argument proposed by LC. In a dynamically unstable, nonlinear flow, the updrafts produced by a sinusoidal initial temperature perturbation are stronger in the lower layer and are more compact and located further apart compared to the corresponding linear flow. In addition, the perturbed wave energy is slightly smaller than the linear case. It is found that the growth rate is smaller during the early stage and much larger during the later stage. For a localized initial temperature perturbation in a dynamically unstable flow, a stronger updraft with two compensated downdrafts are produced. Gravity waves are produced in a dynamically stable flow with both a hyperbolic tangent wind profile and a linear wind profile. For a linear shear flow with Richardson number less than 1/4, the disturbance grows in the early stage and then decays algebraically at later times, similar to that found in other linear theoretical studies. The influence of the solid lower boundary is to suppress the shear instability in a nonlinear flow with a hyperbolic tangent wind profile ofRi<1/4.With 9 Figures