scholarly journals Lagrangian transport by vertically confined internal gravity wavepackets

2019 ◽  
Vol 864 ◽  
pp. 348-380 ◽  
Author(s):  
T. S. van den Bremer ◽  
H. Yassin ◽  
B. R. Sutherland
Keyword(s):  
Group Velocity ◽  
Phase Speed ◽  
Stable Stratification ◽  
Stokes Drift ◽  
Near Surface ◽  
Lagrangian Transport ◽  
Special Cases ◽  
Induced Flow ◽  
Boussinesq Fluid ◽  
Exponential Stratification

We examine the flows induced by horizontally modulated, vertically confined (or guided), internal wavepackets in a stratified, Boussinesq fluid. The wavepacket induces both an Eulerian flow and a Stokes drift, which together determine the Lagrangian transport of passive tracers. We derive equations describing the wave-induced flows in arbitrary stable stratification and consider four special cases: a two-layer fluid, symmetric and asymmetric piecewise constant (‘top-hat’) stratification and, more representative of the ocean, exponential stratification. In a two-layer fluid, the Stokes drift is positive everywhere with the peak value at the interface, whereas the Eulerian flow is negative and uniform with depth for long groups. Combined, the net depth-integrated Lagrangian transport is zero. If one layer is shallower than the other, the wave-averaged interface displaces into that layer making the Eulerian flow in that layer more negative and the Eulerian flow in the opposite layer more positive so that the depth-integrated Eulerian transports are offset by the same amount in each layer. By contrast, in continuous stratification the depth-integrated transport due to the Stokes drift and Eulerian flow are each zero, but the Eulerian flow is singular if the horizontal phase speed of the induced flow equals the group velocity of the wavepacket, giving rise to a single resonance in uniform stratification (McIntyre, J. Fluid Mech., vol. 60, 1973, pp. 801–811). In top-hat stratification, this single resonance disappears, being replaced by multiple resonances occurring when the horizontal group velocity of the wavepacket matches the horizontal phase speed of higher-order modes. Furthermore, if the stratification is not vertically symmetric, then the Eulerian induced flow varies as the inverse squared horizontal wavenumber for shallow waves, the same as for the asymmetric two-layer case. This ‘infrared catastrophe’ also occurs in the case of exponential stratification suggesting significant backward near-surface transport by the Eulerian induced flow for modulated oceanic internal modes. Numerical simulations are performed confirming these theoretical predictions.

scholarly journals Turbulence-Induced Anti-Stokes Flow and the Resulting Limitations of Large-Eddy Simulation

2018 ◽  
Vol 48 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Brodie Pearson
Keyword(s):  
Stokes Flow ◽  
Energy Production ◽  
Surface Wind ◽  
Stokes Drift ◽  
Near Surface ◽  
Eddy Simulation ◽  
Surface Wind Stress ◽  
Planetary Rotation ◽  
Large Eddy ◽  
Anti Stokes

AbstractThis study shows that the presence of Stokes drift us in the turbulent upper ocean induces a near-surface Eulerian current that opposes the Stokes drift. This current is distinct from previously studied anti-Stokes currents because it does not rely on the presence of planetary rotation or mean lateral gradients. Instead, the anti-Stokes flow arises from an interaction between the Stokes drift and turbulence. The new anti-Stokes flow is antiparallel to us near the ocean surface, is parallel to us at depth, and integrates to zero over the depth of the boundary layer. The presence of Stokes drift in large-eddy simulations (LES) is shown to induce artificial energy production caused by a combination of the new anti-Stokes flow and LES numerics. As a result, care must be taken when designing and interpreting simulations of realistic wave forcing, particularly as rotation becomes weak and/or us becomes perpendicular to the surface wind stress. The mechanism of the artificial energy production is demonstrated for a generalized LES subgrid scheme.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

Model and Experimental Estimates of Vertical Mixing Intensity in the Sea Upper Homogeneous Layer

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
A. M. Chukharev ◽  
M. I. Pavlov ◽  
◽  
Keyword(s):  
Experimental Data ◽  
Turbulence Intensity ◽  
Multiscale Model ◽  
Turbulent Exchange ◽  
Stokes Drift ◽  
Homogeneous Layer ◽  
Depth Range ◽  
Near Surface ◽  
Langmuir Circulations ◽  
Turbulence Generation

Purpose. The study is aimed at qualitative and quantitative analysis (based on the updated previously proposed multiscale model) of the experimental data on turbulence intensity and their comparison with theoretical and semi-empirical relationships for the purpose of describing the contributions of various turbulence sources. Methods and Results. A comparative analysis of experimental data and model calculations of turbulence characteristics near the sea surface was performed. The methods of theoretical assessing generation of turbulence in the near-surface sea layer by various physical processes are considered. The results of calculations by the well-known models of turbulent exchange were compared with the experimental data collected by the scientists of the Turbulence Department of MHI, RAS, using the specialized equipment. The analysis results made it possible to determine the possibility of applying the considered models for calculating turbulence intensity under different hydrometeorological conditions. At light winds, none of the models yielded the results which matched the measurement data. At moderate winds, the simulation results showed quite satisfactory agreement with the experiment data; and for strong winds, the multiscale model results were the best. This model was modified to assess the contributions of two other mechanisms of turbulence generation: the Stokes drift and the Langmuir circulations. Conclusions. Objective assessment of the turbulent exchange intensity requires taking into account of three main mechanisms of turbulence generation, namely flow velocity shear, wave motions and wave breaking. Depending on the hydrometeorological situation, each of these mechanisms can dominate in a certain depth range. The calculations performed using the updated model showed that the Stokes drift added 2–17 % to the total dissipation in the upper 30-meter layer, whereas the contribution of the Langmuir circulations calculated through dependence of the vertical velocity of kinetic energy transfer upon the Langmuir number, can reach 15 % for small Langmuir numbers.

scholarly journals The Phase Speed of a Travelling Disturbance in the F Region of the Ionosphere and its Comparison with Group Velocity

1961 ◽  
Vol 14 (4) ◽  
pp. 481 ◽  
Author(s):  
LH Heisler ◽  
JD Whitehead
Keyword(s):  
Group Velocity ◽  
Phase Speed ◽  
Theoretical Explanation ◽  
F Region

Three methods of measuring the phase speed of a disturbance in the F region, that is, the speed of a peak or trough in the isoionic contours, are given using ionograms records from one station. The analysis has been applied to one such disturbance whose group velocity was known to be 10 km/min. All three methods gave the phase speed to be about half of this. The theoretical explanation of this observation is discussed.

scholarly journals Mutual Interaction between Surface Waves and Langmuir Circulations Observed in Wave-Resolving Numerical Simulations

2020 ◽  
Vol 50 (8) ◽  
pp. 2323-2339
Author(s):  
Yasushi Fujiwara ◽  
Yutaka Yoshikawa
Keyword(s):  
Surface Waves ◽  
Friction Velocity ◽  
Phase Speed ◽  
Mutual Interaction ◽  
Stokes Drift ◽  
Horizontal Shear ◽  
Budget Analysis ◽  
Vorticity Budget ◽  
Langmuir Circulations ◽  
The Waves

AbstractWave-resolving simulations of monochromatic surface waves and Langmuir circulations (LCs) under an idealized condition are performed to investigate the dynamics of wave–current mutual interaction. When the Froude number (the ratio of the friction velocity of wind stress imposed at the surface and wave phase speed) is large, waves become refracted by the downwind jet associated with LCs and become amplitude modulated in the crosswind direction. In such cases, the simulations using the Craik–Leibovich (CL) equation with a prescribed horizontally uniform Stokes drift profile are found to underestimate the intensity of LCs. Vorticity budget analysis reveals that horizontal shear of Stokes drift induced by the wave modulation tilts the wind-driven vorticity to the downwind direction, intensifying the LCs that caused the waves to be modulated. Such an effect is not reproduced in the CL equation unless the Stokes drift of the waves modulated by LCs is prescribed. This intensification mechanism is similar to the CL1 mechanism in that the horizontal shear of the Stokes drift plays a key role, but it is more likely to occur because the shear in this interaction is automatically generated by the LCs whereas the shear in the CL1 mechanism is retained only when a particular phase relation between two crossing waves is kept locked for many periods.

scholarly journals Equatorial Waves in Opposite QBO Phases

2011 ◽  
Vol 68 (4) ◽  
pp. 839-862 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian J. Hoskins ◽  
Julia M. Slingo
Keyword(s):  
Group Velocity ◽  
Lower Stratosphere ◽  
Phase Speed ◽  
Kelvin Waves ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Vertical Wavelength ◽  
Quasi Biennial Oscillation ◽  
Zonal Wavenumber ◽  
The Waves

Abstract A methodology for identifying equatorial waves is used to analyze the multilevel 40-yr ECMWF Re-Analysis (ERA-40) data for two different years (1992 and 1993) to investigate the behavior of the equatorial waves under opposite phases of the quasi-biennial oscillation (QBO). A comprehensive view of 3D structures and of zonal and vertical propagation of equatorial Kelvin, westward-moving mixed Rossby–gravity (WMRG), and n = 1 Rossby (R1) waves in different QBO phases is presented. Consistent with expectation based on theory, upward-propagating Kelvin waves occur more frequently during the easterly QBO phase than during the westerly QBO phase. However, the westward-moving WMRG and R1 waves show the opposite behavior. The presence of vertically propagating equatorial waves in the stratosphere also depends on the upper tropospheric winds and tropospheric forcing. Typical propagation parameters such as the zonal wavenumber, zonal phase speed, period, vertical wavelength, and vertical group velocity are found. In general, waves in the lower stratosphere have a smaller zonal wavenumber, shorter period, faster phase speed, and shorter vertical wavelength than those in the upper troposphere. All of the waves in the lower stratosphere show an upward group velocity and downward phase speed. When the phase of the QBO is not favorable for waves to propagate, their phase speed in the lower stratosphere is larger and their period is shorter than in the favorable phase, suggesting Doppler shifting by the ambient flow and a filtering of the slow waves. Tropospheric WMRG and R1 waves in the Western Hemisphere also show upward phase speed and downward group velocity, with an indication of their forcing from middle latitudes. Although the waves observed in the lower stratosphere are dominated by “free” waves, there is evidence of some connection with previous tropical convection in the favorable year for the Kelvin waves in the warm water hemisphere and WMRG and R1 waves in the Western Hemisphere, which is suggestive of the importance of convective forcing for the existence of propagating coupled Kelvin waves and midlatitude forcing for the existence of coupled WMRG and R1 waves.

scholarly journals Ground surface-temperature reconstruction based on data from a deep borehole in permafrost at Janssonhaugen, Svalbard

2000 ◽  
Vol 31 ◽  
pp. 287-294 ◽  
Author(s):  
Ketil Isaksen ◽  
Daniel Vonder Mühll ◽  
Hansueli Gubler ◽  
Thomas Kohl ◽  
Johan Ludvig Sollid
Keyword(s):  
Surface Temperature ◽  
Phase Speed ◽  
Ground Surface ◽  
Temperature Reconstruction ◽  
Geothermal Gradient ◽  
Temperature History ◽  
Deep Borehole ◽  
Near Surface ◽  
Ground Surface Temperature ◽  
Average Value

AbstractAnalyses of the geothermal gradient in permafrost areas constitute a key signal of the ground-surface temperature history. Permafrost temperatures in selected areas are particularly well suited to reconstructing past surface-temperature changes, mainly because there is no thermal disturbance due to circulating groundwater. One year of temperature data from an instrumented 102 m deep borehole in permafrost on Janssonhaugen, Svalbard, is presented. Ground thermal properties are calculated. The average value for the thermal conductivity is 1.85 ±0.05 W m–1 K–1 , and the average value for the thermal diffusivity is 1.1m2 s–1, which gives a phase speed for the annual wave of 5.65 × KT2 m d–1. The depth of zero annual amplitude is 18 m The permafrost thickness is estimated as approximately 220 m. Analysis of the temperatures reveals an increasing temperature gradient with depth. Using a heat-conduction inversion model, a palaeoclimatic reconstruction is presented, showing a warming of the surface temperature over the last 60–80 years. The temperature profile represents a regional signal on Svalbard, which shows an inflection associated with near-surface warming of 1.5 ± 0.5°C in the 20th century.

Strong Cross-Barrier Flow under Stable Conditions Producing Intense Winter Orographic Precipitation: A Case Study over the Subtropical Central Andes

2009 ◽  
Vol 24 (4) ◽  
pp. 1009-1031 ◽  
Author(s):  
Maximiliano Viale ◽  
Federico A. Norte
Keyword(s):  
Heavy Precipitation ◽  
Stable Stratification ◽  
Central Andes ◽  
Precipitation Event ◽  
Windward Side ◽  
Orographic Precipitation ◽  
Near Surface ◽  
Low Level ◽  
Precipitation Enhancement ◽  
Subtropical Central Andes

Abstract The most intense orographic precipitation event over the subtropical central Andes (36°–30°S) during winter 2005 was examined using observational data and a regional model simulation. The Eta-Programa Regional de Meteorología (PRM) model forecast was evaluated and used to explore the airflow structure that generated this heavy precipitation event, with a focus on orographic influences. Even though the model did not realistically reproduce any near-surface variables, nor the precipitation shadow in the leeside lowlands, its reliable forecast of heavy precipitation over the windward side and the wind fields suggests that it can be used as a valuable forecasting tool for such events in the region. The synoptic flow of the 26–29 August 2005 storm responded to a well-defined dipole from low to upper levels with anomalous low (high) geopotential heights at midlatitudes (subtropical) latitudes located off the southeast Pacific coast, resulting in a large meridional geopotential height gradient that drove a strong anomalous cross-barrier flow. Precipitation enhancement in the Andes was observed during the entire event; however, the highest rates were in the prefrontal sector under the low-level stable stratification and cross-barrier winds exceeding 2.5 standard deviations (σ) from the climatological monthly mean. The combination of strong cross-mountain winds with the stable stratification in the air mass of a frontal system, impinging on the high Andes range, appears to be the major factor in determining the flow structure that produced the pattern of precipitation enhancement, with uplift maximized near mountaintops and low-level blocking upwindleading to the formation of a low-level along-barrier jet. Additionally, only the upstream wind anomalies for the 15 heaviest events over a 10-yr (1967–76) period were investigated. They exhibited strong anomalous northwesterly winds for 14 of the 15 events, whereas for the remaining event there were no available observations to evaluate. Thus, these anomalies may also be exploited for forecasting capabilities.

scholarly journals Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation

2020 ◽  
Vol 637 ◽  
pp. A65 ◽  
Author(s):  
C. Damiani ◽  
R. H. Cameron ◽  
A. C. Birch ◽  
L. Gizon
Keyword(s):  
Perturbation Theory ◽  
Radial Force ◽  
Force Balance ◽  
Surface Boundary ◽  
Pressure Perturbation ◽  
Uniform Rotation ◽  
Near Surface ◽  
Depth Dependence ◽  
Special Cases ◽  
Inviscid Case

Context. Large-scale Rossby waves have recently been discovered based on measurements of horizontal surface and near-surface solar flows. Aims. We are interested in understanding why it is only equatorial modes that are observed and in modelling the radial structure of the observed modes. To this aim, we have characterised the radial eigenfunctions of r modes for slowly rotating polytropes in uniform rotation. Methods. We followed Provost et al. (1981, A&A, 94, 126) and considered a linear perturbation theory to describe quasi-toroidal stellar adiabatic oscillations in the inviscid case. We used perturbation theory to write the solutions to the fourth order in the rotational frequency of the star. We numerically solved the eigenvalue problem, concentrating on the type of behaviour exhibited where the stratification is nearly adiabatic. Results. We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density, r modes can only exist for ℓ = m spherical harmonics in the inviscid case and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification, the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales as rm. For all r modes, except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance. Conclusions. The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the need for both horizontal and radial force balance. In the absence of super- or sub-adiabatic stratification and viscosity, both the horizontal and radial parts of the force balance independently determine the pressure perturbation. The only quasi-toroidal cases in which these constraints on the pressure perturbation are consistent are the special cases where ℓ = m and the horizontal displacement scales with rm.

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