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.

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 Mesoscale-dependent near-inertial internal waves and microscale turbulence in the Tsushima Warm Current

2021 ◽  
Author(s):  
Yusuke Kawaguchi ◽  
Taku Wagawa ◽  
Itsuka Yabe ◽  
Daiki Ito ◽  
Tomoharu Senjyu ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Internal Waves ◽  
Theoretical Perspective ◽  
Relative Vorticity ◽  
Tsushima Warm Current ◽  
Vertical Shear ◽  
Easterly Wind ◽  
Warm Current ◽  
Mesoscale Structure ◽  
Honshu Island

AbstractThis study examined characteristics of near-inertial internal waves (NIWs) associated with the background mesoscale field near the Tsushima Warm Current. Observational stations off Sado Island were visited recurrently to assess spatiotemporal changes of fine-scale and microscale properties of seawater. Also, NIWs were inspected in terms of relative vorticity and total strain in surface geostrophic motion. During summer expeditions in 2019, current and hydrographic surveys at the rim of an anticyclonic eddy provided clear evidence of downward-travelling NIWs, which were most amplified near the depth of lower pycnocline. The amplification of NIW coincided with elevation in the dissipation rates of turbulent kinetic energy (TKE) and microscale variation of temperature. The fall 2019 expedition found details of wave and turbulence properties associated with the mesoscale structure of paired vortices, where a cyclone and anticyclone were, respectively, adjacent to the east and west. Amplified signals of NIW-related vertical shear and TKE dissipation were found at isopycnals between the dipole cores. From the theoretical perspective of internal wave, the baroclinic term attributable to vertical shear of geostrophic current was interpreted as inducing downward travel of NIW through the lower pycnoclines between the dipole cores. It is also noted that cyclones, passing through the central part of Sea of Japan, can deliver kinetic energy into 10-km scale internal waves as a consequence of interaction between easterly wind and mountainous topography in the Honshu Island.

scholarly journals The Life Cycle of Spontaneously Generated Internal Waves

2018 ◽  
Vol 48 (2) ◽  
pp. 343-359 ◽  
Author(s):  
Callum J. Shakespeare ◽  
Andrew McC. Hogg
Keyword(s):  
Internal Waves ◽  
Vertical Shear ◽  
Spontaneous Generation ◽  
Net Energy ◽  
Mean Flow ◽  
Ocean Energy ◽  
Energy Transfers ◽  
The Mean ◽  
Internal Wave Generation ◽  
The Individual

AbstractRecent numerical modeling studies have suggested significant spontaneous internal wave generation near the ocean surface and energy transfers to and from these waves in the ocean interior. Spontaneous generation is the emission of waves by unbalanced, large Rossby number flows in the absence of direct forcing. Here, the authors’ previous work is extended to investigate where and how these waves exchange energy with the nonwave (mean) flow. A novel double-filtering technique is adopted to separate first the wave and nonwave fields, then the individual upward- and downward-propagating wave fields, and thereby identify the pathways of energy transfer. These energy transfers are dominated by the interaction of the waves with the vertical shear in the mean flow. Spontaneously generated waves are found to be oriented such that the downward-propagating wave is amplified by the mean shear. The internal waves propagate through the entire model depth while dissipating energy and reflect back upward. The now-upward-propagating waves have the opposite sign interaction with the mean shear and decay, losing most of their energy to the nonwave flow in the upper 500 m. Overall, in the simulations described here, approximately 30% of the wave energy is dissipated, and 70% is returned to the mean flow. The apparent preferential orientation of spontaneous generation suggests a potentially unique role for these waves in the ocean energy budget in uniformly drawing net energy from mean flow in the upper-ocean interior and transporting it to depth.

scholarly journals Generalized Hough Modes: The Structure of Damped Global-Scale Waves Propagating on a Mean Flow with Horizontal and Vertical Shear

2005 ◽  
Vol 62 (8) ◽  
pp. 2674-2683 ◽  
Author(s):  
David A. Ortland
Keyword(s):  
Wave Structure ◽  
Global Scale ◽  
Vertical Shear ◽  
Order Effects ◽  
Horizontal Shear ◽  
Mean Flow ◽  
Background Flow ◽  
Vertical Scale ◽  
Tidal Theory ◽  
The Mean

Abstract The technique of classical tidal theory in which linear disturbances to a background flow at rest are expanded in terms of Hough modes is generalized for damped disturbances to a general zonal mean state under the assumption that the vertical scale of the background flow is longer than the vertical scale of the disturbance. Generalized Hough modes provide an alternative to the concept of mode coupling between classical modes as a means of describing how the mean flow and damping affect the wave structure. Generalized modes take into account the horizontal shear of the mean flow and damping at lowest order. Effects of vertical shear in the mean flow only arise as first-order corrections, and hence generalized modes provide exact modal solutions to the linearized primitive equations when the mean flow only varies with latitude.

Nonlinear interactions between convection, rotation and flows with vertical shear

1986 ◽  
Vol 164 ◽  
pp. 91-105 ◽  
Author(s):  
David H. Hathaway ◽  
Richard C. J. Somerville
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Rotation Vector ◽  
Vertical Shear ◽  
Nonlinear Interactions ◽  
Mean Flow ◽  
Rotation Vectors ◽  
Convective Motions

A three-dimensional and time-dependent numerical model is used to study the nonlinear interactions between thermal convective motions, rotation, and imposed flows with vertical shear. All cases have Rayleigh numbers of 104 and Prandtl numbers of 1.0. Rotating cases have Taylor numbers of 104.For the non-rotating cases, the effects of the shear on the convection produce longitudinal rolls aligned with the shear flow and a downgradient flux of momentum. The interaction between the convection and the shear flow decreases the shear in the interior of the fluid layer while adding kinetic energy to the convective motions. For unit Prandtl number the dimensionless flux of momentum is equal to the dimensionless flux of heat.For rotating cases with vertical rotation vectors, the shear flow favours rolls aligned with the shear and produces a downgradient flux of momentum. However, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. As in the non-rotating cases, the convective motions become more energetic by extracting energy from the mean flow. For Richardson numbers larger than about − 1.0, the dominant source of eddy kinetic energy is the shear flow rather than buoyancy.For rotating cases with tilted rotation vectors the results depend upon the direction of the shear. For weak shear, convective rolls aligned with the rotation vector are favoured. When the shear flow is directed to the east along the top, the rolls become broader and the convection weaker. For large shear in this direction, the convective motions are quenched by the competition between the shear flow and the tilted rotation vector. When the shear flow is directed to the west along the top, strong shear produces rolls aligned with the shear. The heat and momentum fluxes become large and can exceed those found in the absence of a tilted rotation vector. Countergradient fluxes of momentum can also be produced.

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.

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 Divergent versus Nondivergent Instabilities of Piecewise Uniform Shear Flows on the f Plane

2009 ◽  
Vol 39 (7) ◽  
pp. 1685-1699
Author(s):  
Nathan Paldor ◽  
Yona Dvorkin ◽  
Eyal Heifetz
Keyword(s):  
Numerical Solutions ◽  
Delta Function ◽  
Relative Vorticity ◽  
Linear Instability ◽  
Large Radius ◽  
Mean Flow ◽  
Uniform Shear ◽  
Linear Shear ◽  
The Mean ◽  
Inner Region

Abstract The linear instability of a piecewise uniform shear flow is classically formulated for nondivergent perturbations on a 2D barotropic mean flow with linear shear, bounded on both sides by semi-infinite half-planes where the mean flows are uniform. The problem remains unchanged on the f plane because for nondivergent perturbations the instability is driven by vorticity gradient at the edges of the inner, linear shear region, whereas the vorticity itself does not affect it. The instability of the unbounded case is recovered when the outer regions of uniform velocity are bounded, provided that these regions are at least twice as wide as the inner region of nonzero shear. The numerical calculations demonstrate that this simple scenario is greatly modified when the perturbations’ divergence and the variation of the mean height (which geostrophically balances the mean flow) are retained in the governing equations. Although a finite deformation radius exists on the shallow water f plane, the mean vorticity gradient that governs the instability in the nondivergent case remains unchanged, so it is not obvious how the instability is modified by the inclusion of divergence in the numerical solutions of the equations. The results here show that the longwave instability of nondivergent flows is recovered by the numerical solution for divergent flows only when the radius of deformation is at least one order of magnitude larger than the width of the inner uniform shear region. Nevertheless, even at this large radius of deformation both the amplitude of the velocity eigenfunction and the distribution of vorticity and divergence differ significantly from those of nondivergent perturbations and vary strongly in the cross-stream direction. Whereas for nondivergent flows the vorticity and divergence both have a delta-function structure located at the boundaries of the inner region, in divergent flows they are spread out and attain their maximum away from the boundaries (either in the inner region or in the outer regions) in some range of the mean shear. In contrast to nondivergent flows for which the mean shear is merely a multiplicative factor of the growth rates, in divergent flows new unstable modes exist for sufficiently large mean shear with no shortwave cutoff. This unstable mode is strongly affected by the sign of the mean shear (i.e., the sign of the mean relative vorticity).

scholarly journals Enhanced Diapycnal Mixing due to Near-Inertial Internal Waves Propagating through an Anticyclonic Eddy in the Ice-Free Chukchi Plateau

2016 ◽  
Vol 46 (8) ◽  
pp. 2457-2481 ◽  
Author(s):  
Yusuke Kawaguchi ◽  
Shigeto Nishino ◽  
Jun Inoue ◽  
Katsuhisa Maeno ◽  
Hiroki Takeda ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Arctic Ocean ◽  
Internal Waves ◽  
Relative Vorticity ◽  
Anticyclonic Eddy ◽  
The Arctic ◽  
Buoyancy Frequency ◽  
Energy Propagation ◽  
Microstructure Observation ◽  
Chukchi Plateau

AbstractThe Arctic Ocean is known to be quiescent in terms of turbulent kinetic energy (TKE) associated with internal waves. To investigate the current state of TKE in the seasonally ice-free Chukchi Plateau, Arctic Ocean, this study performed a 3-week, fixed-point observation (FPO) using repeated microstructure, hydrographic, and current measurements in September 2014. During the FPO program, the microstructure observation detected noticeable peaks of TKE dissipation rate ε during the transect of an anticyclonic eddy moving across the FPO station. Particularly, ε had a significant elevation in the lower halocline layer, near the critical level, reaching the order of 10−8 W kg−1. The ADCP-measured current displayed energetic near-inertial internal waves (NIWs) propagating via the stratification at the top and bottom of the anticyclone. According to spectral analyses of horizontal velocity, the waves had almost downward energy propagation, and its current amplitude reached ~10 cm s−1. The WKB scaling, incorporating vertical variations of relative vorticity, suggests that increased wave energy near the two pycnoclines was associated with diminishing group velocity at the corresponding depths. The finescale parameterization using observed near-inertial velocity and buoyancy frequency successfully reproduced the characteristics of observed ε, supporting that the near-inertial kinetic energy can be effectively dissipated into turbulence near the critical layer. According to a mixed layer slab model, a rapidly moving storm that has passed over in the first week likely delivered the bulk of NIW kinetic energy, eventually captured by the vortex, into the surface water.

scholarly journals On the Annual Earth’s Rotation

1980 ◽  
Vol 56 ◽  
pp. 187-190
Author(s):  
Angelo Poma ◽  
Edoardo Proverbio
Keyword(s):  
Kinetic Energy ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Show Evidence

AbstractA number of works have presented evidence that the seasonal terms of the Earth’s rotation are variables from year to year. In this paper, introducing a parameter associated to a mean seasonal kinetic energy we show evidence of about 4 year and 7 yr periodicity. This result is briefly discussed.

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