scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

scholarly journals Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part II: Energetics Arguments and Turbulence Simulations

2015 ◽  
Vol 45 (10) ◽  
pp. 2522-2543 ◽  
Author(s):  
Alberto Scotti
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Turbulent Flows ◽  
Companion Paper ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Ozmidov Scale ◽  
Thorpe Scale ◽  
The Mean ◽  
Shear Driven Flows

AbstractThis paper uses the energetics framework developed by Scotti and White to provide a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles. This study shows that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component that ought to be used to diagnose mixing and dissipation. In general, the energetics of mixing in an overall stably stratified flow involves potentially complex exchanges among the available potential energy and kinetic energy associated with the mean and turbulent components of the flow. The author considers two limiting cases: shear-driven mixing, where mixing comes at the expense of the mean kinetic energy of the flow, and convective-driven mixing, which taps the available potential energy of the mean flow to drive mixing. In shear-driven flows, the rms of the Thorpe displacement, known as the Thorpe scale is shown to be equivalent to the turbulent component of the displacement. In this case, the Thorpe scale approximates the Ozmidov scale, or, which is the same, the Thorpe scale is the appropriate scale to diagnose mixing and dissipation. However, when mixing is driven by the available potential energy of the mean flow (convective-driven mixing), this study shows that the Thorpe scale is (much) larger than the Ozmidov scale. Using the rms of the Thorpe displacement overestimates dissipation and mixing, since the amount of turbulent available potential energy (measured by the turbulent displacement) is only a fraction of the total available potential energy (measured by the Thorpe scale). Corrective measures are discussed that can be used to diagnose mixing from knowledge of the Thorpe displacement. In a companion paper, Mater et al. analyze field data and show that the Thorpe scale can indeed be much larger than the Ozmidov scale.

scholarly journals The Stability of Short Symmetric Internal Waves on Sloping Fronts: Beyond the Traditional Approximation

2012 ◽  
Vol 42 (3) ◽  
pp. 459-475 ◽  
Author(s):  
Alain Colin de Verdière
Keyword(s):  
Kinetic Energy ◽  
Internal Waves ◽  
Relative Vorticity ◽  
Rotation Vector ◽  
Vertical Shear ◽  
Earth’S Rotation ◽  
Horizontal Shear ◽  
Mean Flow ◽  
Earth's Rotation ◽  
The Mean

Abstract The interaction of internal waves with geostrophic flows is found to be strongly dependent upon the background stratification. Under the traditional approximation of neglecting the horizontal component of the earth’s rotation vector, the well-known inertial and symmetric instabilities highlight the asymmetry between positive and negative vertical components of relative vorticity (horizontal shear) of the mean flow, the former being stable. This is a strong stratification limit but, if it becomes too low, the traditional approximation cannot be made and the Coriolis terms caused by the earth’s rotation vector must be kept in full. A new asymmetry then appears between positive and negative horizontal components of relative vorticity (vertical shear) of the mean flow, the latter becoming more unstable. Particularly conspicuous at low latitudes, this new asymmetry does not require vanishing stratification to occur as it operates readily for rotation/stratification ratios 2Ω/N as small as 0.25 (the stratification still dominates over rotation) for realistic vertical shears. Given that such ratios are easily found in ocean–atmosphere boundary layers or in the deep ocean, such ageostrophic instabilities may be important for the routes to dissipation of the energy of the large-scale motions. The energetics show that, depending on the orientation of the internal wave crests with respect to the mean isopycnal surfaces, the unstable motions can draw their energy either from the kinetic energy or from the available potential energy of the mean flow. The kinetic energy source is usually the leading contribution when the growth rates reach their maxima.

Energetics and mixing in buoyancy-driven near-bottom stratified flow

2019 ◽  
Vol 869 ◽  
pp. 214-237
Author(s):  
Pranav Puthan ◽  
Masoud Jalali ◽  
Vamsi K. Chalamalla ◽  
Sutanu Sarkar
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Loss ◽  
Convective Instability ◽  
Mixing Efficiency ◽  
Time Interval ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Long Time ◽  
The Mean

Turbulence and mixing in a near-bottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zero-slope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zero-velocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing  $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the non-sloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slope-parallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.

scholarly journals Energetics of Eddy–Mean Flow Interactions in the Gulf Stream Region

2015 ◽  
Vol 45 (4) ◽  
pp. 1103-1120 ◽  
Author(s):  
Dujuan Kang ◽  
Enrique N. Curchitser
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gulf Stream ◽  
Mean Flow ◽  
Available Potential Energy ◽  
Flow Energy ◽  
Flow Interaction ◽  
The Mean ◽  
Eddy Field ◽  
Coast Region

AbstractA detailed energetics analysis of the Gulf Stream (GS) and associated eddies is performed using a high-resolution multidecadal regional ocean model simulation. The energy equations for the time-mean and time-varying flows are derived as a theoretical framework for the analysis. The eddy–mean flow energy components and their conversions show complex spatial distributions. In the along-coast region, the cross-stream and cross-bump variations are seen in the eddy–mean flow energy conversions, whereas in the off-coast region, a mixed positive–negative conversion pattern is observed. The local variations of the eddy–mean flow interaction are influenced by the varying bottom topography. When considering the domain-averaged energetics, the eddy–mean flow interaction shows significant along-stream variability. Upstream of Cape Hatteras, the energy is mainly transferred from the mean flow to the eddy field through barotropic and baroclinic instabilities. Upon separating from the coast, the GS becomes highly unstable and both energy conversions intensify. When the GS flows into the off-coast region, an inverse conversion from the eddy field to the mean flow dominates the power transfer. For the entire GS region, the mean current is intrinsically unstable and transfers 28.26 GW of kinetic energy and 26.80 GW of available potential energy to the eddy field. The mesoscale eddy kinetic energy is generated by mixed barotropic and baroclinic instabilities, contributing 28.26 and 9.15 GW, respectively. Beyond directly supplying the barotropic pathway, mean kinetic energy also provides 11.55 GW of power to mean available potential energy and subsequently facilitates the baroclinic instability pathway.

scholarly journals Characteristics, Energetics, and Origins of Agulhas Current Meanders and Their Limited Influence on Ring Shedding

2015 ◽  
Vol 45 (9) ◽  
pp. 2294-2314 ◽  
Author(s):  
Shane Elipot ◽  
Lisa M. Beal
Keyword(s):  
Kinetic Energy ◽  
Single Mode ◽  
Cyclonic Circulation ◽  
Recent Analysis ◽  
Altimeter Data ◽  
Western Boundary ◽  
Mean Flow ◽  
Current Time ◽  
Agulhas Current ◽  
The Mean

AbstractThe Agulhas Current intermittently undergoes dramatic offshore excursions from its mean path because of the downstream passage of mesoscale solitary meanders or Natal pulses. New observations and analyses are presented of the variability of the current and its meanders using mooring observations from the Agulhas Current Time-Series Experiment (ACT) near 34°S. Using a new rotary EOF method, mesoscale meanders and smaller-scale meanders are differentiated and each captured in a single mode of variance. During mesoscale meanders, an onshore cyclonic circulation and an offshore anticyclonic circulation act together to displace the jet offshore, leading to sudden and strong positive conversion of kinetic energy from the mean flow to the meander via nonlinear interactions. Smaller meanders are principally represented by a single cyclonic circulation spanning the entire jet that acts to displace the jet without extracting kinetic energy from the mean flow. Synthesizing in situ observations with altimeter data leads to an account of the number of mesoscale meanders at 34°S: 1.6 yr−1 on average, in agreement with a recent analysis by Rouault and Penven (2011) and significantly less than previously understood. The links between meanders and the arrival of Mozambique Channel eddies or Madagascar dipoles at the western boundary upstream are found to be robust in the 20-yr altimeter record. Yet, only a small fraction of anomalies arriving at the western boundary result in meanders, and of those, two-thirds can be related to ring shedding. Most Agulhas rings are shed independently of meanders.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
V. S. Travkin ◽  
◽  
T. V. Belonenko ◽  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Positive Trend ◽  
Barotropic Instability ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Order Of Magnitude ◽  
The Mean ◽  
Mean Kinetic Energy

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

scholarly journals Intraseasonal Modulation of the Surface Cooling in the Gulf of Guinea

2013 ◽  
Vol 43 (2) ◽  
pp. 382-401 ◽  
Author(s):  
Julien Jouanno ◽  
Frédéric Marin ◽  
Yves du Penhoat ◽  
Jean-Marc Molines
Keyword(s):  
Mixed Layer ◽  
Gravity Waves ◽  
Heat Budget ◽  
Vertical Shear ◽  
Upper Ocean ◽  
Equatorial Waves ◽  
Gulf Of Guinea ◽  
The Core ◽  
Mixed Layer Heat Budget ◽  
Inertia Gravity Waves

Abstract A regional numerical model of the tropical Atlantic Ocean and observations are analyzed to investigate the intraseasonal fluctuations of the sea surface temperature at the equator in the Gulf of Guinea. Results indicate that the seasonal cooling in this region is significantly shaped by short-duration cooling events caused by wind-forced equatorial waves: mixed Rossby–gravity waves within the 12–20-day period band, inertia–gravity waves with periods below 11 days, and equatorially trapped Kelvin waves with periods between 25 and 40 days. In these different ranges of frequencies, it is shown that the wave-induced horizontal oscillations of the northern front of the mean cold tongue dominate the variations of mixed layer temperature near the equator. But the model mixed layer heat budget also shows that the equatorial waves make a significant contribution to the mixed layer heat budget through modulation of the turbulent cooling, especially above the core of the Equatorial Undercurrent (EUC). The turbulent cooling variability is found to be mainly controlled by the intraseasonal modulation of the vertical shear in the upper ocean. This mechanism is maximum during periods of seasonal cooling, especially in boreal summer, when the surface South Equatorial Current is strongest and between 2°S and the equator, where the presence of the EUC provides a background vertical shear in the upper ocean. It applies for the three types of intraseasonal waves. Inertia–gravity waves also modulate the turbulent heat flux at the equator through vertical displacement of the core of the EUC in response to equatorial divergence and convergence.

scholarly journals Climatologies and long-term changes in mesospheric wind and wave measurements based on radar observations at high and mid latitudes

2019 ◽  
Vol 37 (5) ◽  
pp. 851-875 ◽  
Author(s):  
Sven Wilhelm ◽  
Gunter Stober ◽  
Peter Brown
Keyword(s):  
Kinetic Energy ◽  
Gravity Waves ◽  
Lower Thermosphere ◽  
Atmospheric Parameters ◽  
Amplitude Response ◽  
Wave Measurements ◽  
Long Term Changes ◽  
The Mean ◽  
Mesosphere And Lower Thermosphere

Abstract. We report on long-term observations of atmospheric parameters in the mesosphere and lower thermosphere (MLT) made over the last 2 decades. Within this study, we show, based on meteor wind measurement, the long-term variability of winds, tides, and kinetic energy of planetary and gravity waves. These measurements were done between the years 2002 and 2018 for the high-latitude location of Andenes (69.3∘ N, 16∘ E) and the mid-latitude locations of Juliusruh (54.6∘ N, 13.4∘ E) and Tavistock (43.3∘ N, 80.8∘ W). While the climatologies for each location show a similar pattern, the locations differ strongly with respect to the altitude and season of several parameters. Our results show annual wind tendencies for Andenes which are toward the south and to the west, with changes of up to 3 m s−1 per decade, while the mid-latitude locations show smaller opposite tendencies to negligible changes. The diurnal tides show nearly no significant long-term changes, while changes for the semidiurnal tides differ regarding altitude. Andenes shows only during winter a tidal weakening above 90 km, while for the Canadian Meteor Orbit Radar (CMOR) an enhancement of the semidiurnal tides during the winter and a weakening during fall occur. Furthermore, the kinetic energy for planetary waves showed strong peak values during winters which also featured the occurrence of sudden stratospheric warming. The influence of the 11-year solar cycle on the winds and tides is presented. The amplitudes of the mean winds exhibit a significant amplitude response for the zonal component below 82 km during summer and from November to December between 84 and 95 km at Andenes and CMOR. The semidiurnal tides (SDTs) show a clear 11-year response at all locations, from October to November.

scholarly journals Gravity waves observed from the Equatorial Wave Studies (EWS) campaign during 1999 and 2000 and their role in the generation of stratospheric semiannual oscillations

2006 ◽  
Vol 24 (10) ◽  
pp. 2481-2491 ◽  
Author(s):  
V. Deepa ◽  
G. Ramkumar ◽  
B. V. Krishna Murthy
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Propagation Characteristics ◽  
Mean Flow ◽  
Vertical Wavelength ◽  
Flow Acceleration ◽  
Equatorial Wave ◽  
The Mean ◽  
Phase Propagation ◽  
Rayleigh Lidar

Abstract. The altitude profiles of temperature fluctuations in the stratosphere and mesosphere observed with the Rayleigh Lidar at Gadanki (13.5° N, 79.2° E) on 30 nights during January to March 1999 and 21 nights during February to April 2000 were analysed to bring out the temporal and vertical propagation characteristics of gravity wave perturbations. The gravity wave perturbations showed periodicities in the 0.5–3-h range and attained large amplitudes (4–5 K) in the mesosphere. The phase propagation characteristics of gravity waves with different periods showed upward wave propagation with a vertical wavelength of 5–7 km. The mean flow acceleration computed from the divergence of momentum flux of gravity waves is compared with that calculated from monthly values of zonal wind obtained from RH-200 rockets flights. Thus, the contribution of gravity waves towards the generation of Stratospheric Semi Annual Oscillation (SSAO) is estimated.

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