Internal gravity waves generated by a turbulent bottom Ekman layer

2007 ◽  
Vol 590 ◽  
pp. 331-354 ◽  
Author(s):  
JOHN R. TAYLOR ◽  
SUTANU SARKAR
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Gravity Waves ◽  
Outer Layer ◽  
Wave Amplitude ◽  
Internal Gravity Waves ◽  
Ekman Layer ◽  
Buoyancy Frequency ◽  
Viscous Effects ◽  
Outer Flow

Internal gravity waves excited by the turbulent motions in a bottom Ekman layer are examined using large-eddy simulation. The outer flow is steady and uniformly stratified while the density gradient is set to zero at the flat lower wall. After initializing with a linear density profile, a mixed layer forms near the wall separated from the ambient stratification by a pycnocline. Two types of internal wave are observed. Waves with frequencies larger than the free-stream buoyancy frequency are seen in the pycnocline, and vertically propagating internal waves are observed in the outer layer with characteristic frequency and wavenumber spectra. Since a signature of the pycnocline waves is observed in the frequency spectrum of the mixed layer, these waves may affect the boundary-layer turbulence. The dominant outer-layer waves have a group velocity directed 35-60° from the vertical axis, which is consistent with previous laboratory studies. The energy flux associated with the radiated waves is small compared to the integrated dissipation in the boundary layer, but is of the same order as the integrated buoyancy flux. A linear model is proposed to estimate the decay in wave amplitude owing to viscous effects. Starting from the observed wave amplitudes at the bottom of the pycnocline, the model prediction for the spectral distribution of the outer layer wave amplitude compares favourably with the simulation results.

Stratification Effects in a Bottom Ekman Layer

2008 ◽  
Vol 38 (11) ◽  
pp. 2535-2555 ◽  
Author(s):  
John R. Taylor ◽  
Sutanu Sarkar
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Outer Layer ◽  
Layer Structure ◽  
Wall Stress ◽  
Ekman Layer ◽  
Length Scale ◽  
Primary Role ◽  
Mean Velocity ◽  
The Mean

Abstract A stratified bottom Ekman layer over a nonsloping, rough surface is studied using a three-dimensional unsteady large eddy simulation to examine the effects of an outer layer stratification on the boundary layer structure. When the flow field is initialized with a linear temperature profile, a three-layer structure develops with a mixed layer near the wall separated from a uniformly stratified outer layer by a pycnocline. With the free-stream velocity fixed, the wall stress increases slightly with the imposed stratification, but the primary role of stratification is to limit the boundary layer height. Ekman transport is generally confined to the mixed layer, which leads to larger cross-stream velocities and a larger surface veering angle when the flow is stratified. The rate of turning in the mixed layer is nearly independent of stratification, so that when stratification is large and the boundary layer thickness is reduced, the rate of veering in the pycnocline becomes very large. In the pycnocline, the mean shear is larger than observed in an unstratified boundary layer, which is explained using a buoyancy length scale, u*/N(z). This length scale leads to an explicit buoyancy-related modification to the log law for the mean velocity profile. A new method for deducing the wall stress based on observed mean velocity and density profiles is proposed and shows significant improvement compared to the standard profile method. A streamwise jet is observed near the center of the pycnocline, and the shear at the top of the jet leads to local shear instabilities and enhanced mixing in that region, despite the fact that the Richardson number formed using the mean density and shear profiles is larger than unity.

The Effect of Internal Gravity Waves on Fluctuations in Meteorological Parameters of the Atmospheric Boundary Layer

2018 ◽  
Vol 54 (2) ◽  
pp. 173-181 ◽  
Author(s):  
D. V. Zaitseva ◽  
M. A. Kallistratova ◽  
V. S. Lyulyukin ◽  
R. D. Kouznetsov ◽  
D. D. Kuznetsov
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Gravity Waves ◽  
Meteorological Parameters ◽  
Internal Gravity Waves

scholarly journals Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory

2005 ◽  
Vol 62 (1) ◽  
pp. 107-124 ◽  
Author(s):  
In-Sun Song ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Spectral Structure ◽  
Two Dimensional ◽  
Resonance Factor ◽  
Flux Spectrum ◽  
Wave Momentum

Abstract The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 2. Coupling with internal gravity waves via topography

2008 ◽  
Vol 595 ◽  
pp. 409-433 ◽  
Author(s):  
XUESONG WU ◽  
JING ZHANG
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Shear Instability ◽  
Acoustic Analogy ◽  
Physical Processes ◽  
Reflected Waves ◽  
Instability Modes ◽  
Viscous Shear ◽  
Incident Waves

The aim of this paper is to show that the viscous shear instability identified in Part 1 is intrinsically coupled with internal gravity waves when a localized surface topography is present within a boundary layer. The coupling involves two aspects: receptivity and radiation. The former refers to excitation of shear instability modes by gravity waves, and the latter to emission of gravity waves by instability modes. Both physical processes are studied using triple-deck theory. In particular, the radiated gravity waves are found to produce a leading-order back action on the source, and this feedback effect, completely ignored in the acoustic analogy type of approach, is naturally taken into account by the triple-deck formalism. A by-product is that for certain incident angles, gravity waves are over-reflected by the boundary layer, i.e. the reflected waves are stronger than the incident waves.

scholarly journals Phase Structure of Internal Gravity Waves in the Ocean with Shear Flows

2021 ◽  
Vol 37 (4) ◽  
Author(s):  
V. V. Bulatov ◽  
Yu. V. Vladimirov ◽  
I. Yu. Vladimirov ◽  
◽  
◽  
...  
Keyword(s):  
Shear Flow ◽  
Spectral Problem ◽  
Gravity Waves ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Flow Profile ◽  
Wave Fields ◽  
Background Shear

Purpose. The description of the internal gravity waves dynamics in the ocean with background fields of shear currents is a very difficult problem even in the linear approximation. The mathematical problem describing wave dynamics is reduced to the analysis of a system of partial differential equations; and while taking into account the vertical and horizontal inhomogeneity, this system of equations does not allow separation of the variables. Application of various approximations makes it possible to construct analytical solutions for the model distributions of buoyancy frequency and background shear ocean currents. The work is aimed at studying dynamics of internal gravity waves in the ocean with the arbitrary and model distributions of density and background shear currents. Methods and Results. The paper represents the numerical and analytical solutions describing the main phase characteristics of the internal gravity wave fields in the stratified ocean of finite depth, both for arbitrary and model distributions of the buoyancy frequency and the background shear currents. The currents are considered to be stationary and horizontally homogeneous on the assumption that the scale of the currents' horizontal and temporal variability is much larger than the characteristic lengths and periods of internal gravity waves. Having been used, the Fourier method permitted to obtain integral representations of the solutions under the Miles – Howard stability condition is fulfilled. To solve the vertical spectral problem, proposed is the algorithm for calculating the main dispersion dependences that determine the phase characteristics of the generated wave fields. The calculations for one real distribution of buoyancy frequency and shear flow profile are represented. Transformation of the dispersion surfaces and phase structures of the internal gravitational waves’ fields is studied depending on the generation parameters. To solve the problem analytically, constant distribution of the buoyancy frequency and linear dependences of the background shear current on depth were used. For the model distribution of the buoyancy and shear flow frequencies, the explicit analytical expressions describing the solutions of the vertical spectral problem were derived. The numerical and asymptotic solutions for the characteristic oceanic parameters were compared. Conclusions. The obtained results show that the asymptotic constructions using the model dependences of the buoyancy frequency and the background shear velocities’ distribution, describe the numerical solutions of the vertical spectral problem to a good degree of accuracy. The model representations, having been applied for hydrological parameters, make it possible to describe qualitatively correctly the main characteristics of internal gravity waves in the ocean with the arbitrary background shear currents.

Can laboratory experiments reach regimes relevant for the oceanic dynamics?

2021 ◽  
Author(s):  
Costanza Rodda ◽  
Clement Savaro ◽  
Antoine Campagne ◽  
Miguel Calpe Linares ◽  
Pierre Augier ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Scaling Laws ◽  
Spatial Scales ◽  
Scaling Law ◽  
Internal Gravity Waves ◽  
Energy Spectra ◽  
Finite Size Effect ◽  
Wave Turbulence ◽  
Common Mechanism ◽  
Buoyancy Frequency

<p>Atmospheric and oceanic energy spectra are characterized by global scaling laws, suggesting a common mechanism driving the energy route to dissipation. Although several possible theories have been proposed, it is not clear yet what the phenomena contributing the most to the energy at the different spatial scales are. One possible scenario is that internal gravity waves, which can be ubiquitously found in the atmosphere and the ocean and play a fundamental role in the energy transfer, cause the observed spectral slopes at the mesoscales in the atmosphere and submesoscales in the oceans. In the context of this open field of investigation, we present an experimental study where internal gravity waves are forced at a given frequency by the oscillating walls of a large pentagonal-shaped domain filled with a stably stratified fluid. The setup is built inside the 13-meters-diameter tank at the Coriolis facility in Grenoble, where geophysical regimes (with high Reynolds number and low Froude) can be achieved and rotation can also be added. The purpose of our investigation is to determine whether it is possible to induce a wave turbulence cascade by forcing internal waves at the large scales. Following a previous study<sup>1</sup>, where instead of the pentagonal a square domain was utilized, we obtained the velocity field employing time-resolved particle image velocimetry and then calculated the energy spectra. The previous study inside a square domain showed some evidence of a cascade, but it was strongly affected by 2D modes that sharpened the spectrum. Therefore, we changed the domain shape to a pentagon to reduce this finite-size effect. When the waves are forced at frequency <em>ω<sub>F</sub>=0.4 N</em>, our data shows that the spectra follow the scaling law <em>ω<sup>-2</sup></em> at frequencies larger than the forcing frequency and extending beyond <em>N</em>. The experimental spectra strikingly resemble the characteristic Garret-Munk spectrum measured in the ocean. As the interaction of weakly non-linear waves dominates the dynamics at frequencies smaller than the buoyancy frequency <em>N</em>, we can conclude that the experimental spectra are generated by weak internal wave turbulence driving the turbulent cascade at the high-frequency end of the spectrum. </p><p> </p><p>1 "<em>Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility", C. Savaro, A. Campagne, M. Calpe Linares, P. Augier, J. Sommeria, T. Valran, S. Viboud, and N. Mordant, PRF 2020</em></p>

scholarly journals Analysis of Gravity Waves Generated at the Top of a Drainage Flow

2010 ◽  
Vol 67 (12) ◽  
pp. 3949-3966 ◽  
Author(s):  
Samuel Viana ◽  
Enric Terradellas ◽  
Carlos Yagüe
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Sonic Anemometer ◽  
Internal Gravity Waves ◽  
Common Source ◽  
Flux Divergence ◽  
Near Surface ◽  
Key Factor ◽  
Stable Atmospheric Boundary Layer ◽  
Drainage Current

Abstract Drainage or katabatic flows are common mesoscale circulations established as a result of differential radiative cooling of near-surface air masses in sloping terrain. The initial irruption of these flows, with sudden shifts in wind speed and direction, may result in vertical displacements of air parcels from their equilibrium position, which prove to be a common source of internal gravity waves. This paper illustrates this mechanism and describes the main features of the oscillations following the study of observational data gathered throughout one night during the Stable Atmospheric Boundary Layer Experiment in Spain 2006 (SABLES2006) field campaign. Pressure differences, measured by microbarometers set at different levels of a tower, help to interpret the evolution of other atmospheric variables, provide a detailed picture of the irruption of a drainage current, and reveal the formation of gravity waves at its top. The main parameters of the waves are derived from wavelet cross correlation of pressure time series, recorded by a surface array of microbarometers. The analysis yields, among other parameters, the horizontal component of the phase and group velocities of the gravity waves, which compare well with the velocity of irruption of the drainage current. Wavelet and other multiresolution techniques are also applied to sonic anemometer records to study the interaction between turbulence and larger-scale motions. The analysis shows evidence of heat flux divergence induced by the gravity waves, which may constitute a key factor for the vertical thermal profile in the nocturnal boundary layer (NBL) in situations of weak turbulence and important wave activity.

The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

2009 ◽  
Vol 619 ◽  
pp. 235-259 ◽  
Author(s):  
KEI SAKAMOTO ◽  
KAZUNORI AKITOMO
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Interfacial Layer ◽  
Rapid Development ◽  
Tidal Mixing ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Rotating Frame ◽  
Three Dimensional Model ◽  
Bottom Boundary

To investigate turbulent properties and the developing mechanisms of the tidally induced bottom boundary layer in the linearly stratified ocean, numerical experiments have been executed with a non-hydrostatic three-dimensional model in the rotating frame, changing the temporal Rossby number Rot = |σ/f|, i.e. the ratio of the tidal frequency σ to the Coriolis parameter f. After the flow transitions to turbulence, the entire water column can be characterized by three layers: the mixed layer where density is homogenized and the flow is turbulent (z < zm); the stratified layer where the initial stratification remains and the flow is laminar (z > zt); and the interfacial layer between them where the flow is turbulent but the stratification remains (zm < z < zt). Turbulence is scaled by the frictional velocity uτ and the mixed-layer thickness zm (uτ and uτ/N where N is the buoyancy frequency) in the mixed (interfacial) layer, and has similarity. The mixed layer is thickened by the process where light water of the upper stratified layer is mixed with the lower unstratified layer water through the interfacial layer. As Rot approaches unity, i.e. near the critical latitude, the mixed layer develops more rapidly according to the following mechanism. As becomes Rot closer to unity, the current shear in the interfacial layer is intensified, since the difference of velocity becomes larger between the lower turbulent mixed and upper laminar stratified layers, and this leads to thickening of the interfacial layer. As a result, density deviation of the water entrained from above becomes larger, and this causes more rapid development of the mixed layer. In terms of the energy conversion from the eddy kinetic energy (EKE) to the potential energy (PE), the efficiency factor β which is the ratio of the conversion rate from EKE to PE to that from the tidal shear to EKE increased from 0.25% for Rot = 0.5 to 3.5% for Rot = 1.05 on average. When the time is normalized by the period required for the mixed layer to be thickened to the unstratified turbulent boundary layer δ = uτ/|f+σ|, the mixed layer development occurred in a similar manner in all cases. This similarity suggests the possibility of universal formulation for the turbulent tidal mixing under stratification.

Anisotropy in internal gravity waves in conditions of a stable nocturnal boundary layer

2009 ◽  
Vol 18 (3) ◽  
pp. 331-337 ◽  
Author(s):  
Anke Kniffka ◽  
Astrid Ziemann ◽  
Igor Chunchuzov ◽  
Sergei Kulichkov ◽  
Vitali Perepelkin
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Nocturnal Boundary Layer

scholarly journals Asymptotics of the Far Fields of Internal Gravity Waves Excited by a Source of Radial Symmetry

2021 ◽  
Vol 56 (5) ◽  
pp. 672-677
Author(s):  
V. V. Bulatov ◽  
Yu. V. Vladimirov
Keyword(s):  
Gravity Waves ◽  
Hankel Transform ◽  
Internal Gravity Waves ◽  
Radial Symmetry ◽  
Wave Mode ◽  
Buoyancy Frequency ◽  
Asymptotic Results ◽  
Model Distribution ◽  
Perturbation Source ◽  
Individual Wave

Abstract— The problem of the far field of internal gravity waves generated by a perturbation source of radial symmetry aroused at an initial instant of time is solved. The constant model distribution of the buoyancy frequency is considered and, using the Fourier–Hankel transform, an analytical solution to the problem is obtained in the form of the sum of wave modes. Asymptotics of the solutions that describe the spatial-temporal characteristics of elevation of the isopycnic lines and the vertical and horizontal velocity components far from the perturbation source are obtained. The asymptotics of the components of the wave field are expressed in terms of the square of the Airy function and its derivatives in the neighborhood of the wave fronts of an individual wave mode. The exact and asymptotic results are compared and it is shown that the asymptotic method makes it possible to calculate effectively the far wave fields at times of the order of ten and more of the Brunt–Väisälä periods.

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