Submesoscale baroclinic instability in the balance equations

2014 ◽  
Vol 762 ◽  
pp. 256-272 ◽  
Author(s):  
Ian Grooms
Keyword(s):  
Baroclinic Instability ◽  
Ocean Dynamics ◽  
Vertical Shear ◽  
Buoyancy Frequency ◽  
Balance Equations ◽  
Instability Problem ◽  
Geostrophic Shear ◽  
Momentum Fluxes ◽  
Perturbation Energy ◽  
Shear Production

AbstractOcean submesoscale baroclinic instability is studied in the framework of the balance equations. These equations are an intermediate model that includes balanced ageostrophic effects with higher accuracy than the quasigeostrophic approximation, but rules out unbalanced wave motions. As such, the balance equations are particularly suited to the study of baroclinic instability in submesoscale ocean dynamics. The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. It is found that non-quasigeostrophic effects appear only for perturbations with cross-front variation, and that perturbation energy can be generated through both baroclinic production and shear production. The Eady problem is solved analytically in the balance equation framework. Ageostrophic effects are shown to increase the range of unstable modes and the growth rate of the instability for perturbations with cross-front variation. The increased level of instability is attributed to both ageostrophic baroclinic production and shear production of perturbation energy; these results are verified in the primitive equations. Finally, submesoscale baroclinic instability is examined in a case where the buoyancy frequency increases rapidly near the bottom boundary, mimicking the increase of stratification at the base of the oceanic mixed layer. The qualitative results of the Eady problem are repeated in this case, with increased growth rates attributed to the production of perturbation energy by the ageostrophic velocity. The results show that submesoscale baroclinic instability acts to reduce lateral buoyancy gradients and their associated geostrophic shear simultaneously through lateral buoyancy fluxes and vertical momentum fluxes.

scholarly journals Revisiting the Charney Baroclinic Instability Problem and Point-jet Barotropic Instability Problem, Part II: Matched Asymptotic Expansions & Overreflection Without Delta-Functions

2018 ◽  
Vol 4 (1) ◽  
pp. 79-103
Author(s):  
John P. Boyd
Keyword(s):  
Hypergeometric Functions ◽  
Numerical Solutions ◽  
Baroclinic Instability ◽  
Ocean Dynamics ◽  
Effective Theory ◽  
Barotropic Instability ◽  
Third Order ◽  
Confluent Hypergeometric Functions ◽  
Instability Problem ◽  
Delta Functions

Abstract Baroclinic instability generates the cyclones and anticyclones of midlatitude weather. Charney developed the first effective theory for the infancy of this cyclogenesis in 1947. His linear eigenproblem is analytically solvable by confluent hypergeometric functions. It is also, with extension of the domain of the coordinate from [0,∞] to [−∞,∞] by reflection about the origin, the point-jet model of barotropic instability, important for tropical cyclogenesis. (Note that the coordinate is height z in the Charney model, but latitude y for the point-jet bartropic instability. It is a great simplification that the Charney and point-jet instability problems are mathematically identical, but it also is confusing that the mathematical analysis in y also applies to the Charney problem with the substitution of z for y.) Unfortunately, the theory is full of distributions like the Dirac delta-function and the reflected Charney eigenfunction has a discontinuous first derivative at y = 0. Here we regularize the Charney problem by replacing a linear mean current, U = |y|, by either U = є log(cosh(y/є)) or U = є y erf(y/є), followed by matched asymptotic perturbation expansions in powers of the small regularization parameter є. The series is carried to third order because the lowest nonzero correction to the phase speed is O(є2) and this correction is determined simultaneously with the third order approximation to the eigenfunction. The result is both an explicit, analytic regularization of a problem important in atmospheric and ocean dynamics, but also a good school problem because the series is explicit with nothing worse than polylogarithms and confluent hypergeometric functions. The primary meteorological conclusion is that the delta functions in the Charney problem are harmless as demonstrated both by third order perturbation theory and by spectrally-accurate numerical solutions. The physics of the regularized Charney problem is not significantly changed from that of the original Charney problem.

scholarly journals Mesoscale cascades and the conundrum of energy transfer from large to dissipation scales in an adiabatic ocean

2017 ◽  
Author(s):  
Mikhail S. Dubovikov
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Mesoscale Eddy ◽  
Ocean Dynamics ◽  
Buoyancy Frequency ◽  
Rossby Number ◽  
Mean Flow ◽  
Small Scales ◽  
The Mean

Abstract. A well-known conundrum in ocean dynamics has been expressed as follows: How does the energy of the general circulation cascade from the large climate scales, where most of it is generated, to the small scales, where all of it is dissipated? In particular, how is the dynamical transition made from an anisotropic, 2D-like, geostrophic cascade at large scales-with its strong inhibition of down-scale energy flux-to 3D-like, down-scale cascades at small scales. (Muller, McWilliams and Molemaker, 2002). To study this as yet unsolved problem, we introduce in the analysis a dynamical consideration based on the mesoscale model developed by Dubovikov (2003) and Canuto and Dubovikov (2005) within which in a quasi-adiabatic ocean interior the large scale baroclinic instability generates mesoscale eddy potential energy (EPE) at scales of the Rossby deformation radius ~ rd. Since at those scales the mesoscale Rossby number is small, the generated EPE cannot convert into eddy kinetic energy (EKE) and cascades to smaller scales at which the spectral Rossby number Ro(k) increases until at some horizontal scales ~ ℓ it reaches Ro(1 / ℓ)~ 1. Under this condition, EPE converts into EKE and thus the cascade of the former terminates while the inverse EKE cascade begins. At scales ~ rd the inverse EKE cascade terminates and reinforces the EPE cascade produced by the large scale baroclinic instability thus closing the mesoscale energy cycle. If the flow were exactly adiabatic, i.e. eddy energy were not dissipated, the latter would increase unlimitedly at the expense of the permanent production of the total eddy energy (TEE) by the mean flow. However, at the same scales ~ ℓ where the EPE cascade terminates and the inverse EKE cascade begins, the vertical eddy shear reaches the value of the buoyancy frequency N that gives rise to the Kelvin-Helmholtz instability. The latter generates the stratified turbulence which finally dissipates EKE. A steady state regime sets in when the dissipation balances the TEE production by the mean flow.

scholarly journals Stability Analysis of the Labrador Current

2014 ◽  
Vol 44 (2) ◽  
pp. 445-463 ◽  
Author(s):  
Sören Thomsen ◽  
Carsten Eden ◽  
Lars Czeschel
Keyword(s):  
Stability Analysis ◽  
Growth Rates ◽  
Baroclinic Instability ◽  
Cross Flow ◽  
Vertical Shear ◽  
Maximal Growth ◽  
Phase Velocities ◽  
Labrador Current ◽  
Lateral Mixing ◽  
Weak Stratification

Abstract Mooring observations and model simulations point to an instability of the Labrador Current (LC) during winter, with enhanced eddy kinetic energy (EKE) at periods between 2 and 5 days and much less EKE during other seasons. Linear stability analysis using vertical shear and stratification from the model reveals three dominant modes of instability in the LC: 1) a balanced interior mode with along-flow wavelengths of about 30–45 km, phase velocities of 0.3 m s−1, maximal growth rates of 1 day−1, and surface-intensified but deep-reaching amplitudes; 2) a balanced shallow mode with along-flow wavelengths of about 0.3–1.5 km, phase velocities of 0.55 m s−1, about 3 times larger growth rates, but amplitudes confined to the mixed layer (ML); and 3) an unbalanced symmetric mode with the largest growth rates, vanishing phase speeds, and along-flow structure, and very small cross-flow wavelengths, also confined to the ML. Both balanced modes are akin to baroclinic instability but operate at moderate-to-small Richardson numbers Ri with much larger growth rates as for the quasigeostrophic limit of Ri ≫ 1. The interior mode is found to be responsible for the instability of the LC during winter. Weak stratification and enhanced vertical shear due to local buoyancy loss and the advection of convective water masses from the interior result in small Ri within the LC and up to 3 times larger growth rates of the interior mode in March compared to summer and fall conditions. Both the shallow and the symmetric modes are not resolved by the model, but it is suggested that they might also play an important role for the instability in the LC and for lateral mixing.

scholarly journals Instabilities of continuously stratified zonal equatorial jets in a periodic channel model

2002 ◽  
Vol 20 (5) ◽  
pp. 729-740 ◽  
Author(s):  
S. Masina
Keyword(s):  
Channel Model ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Maximum Velocity ◽  
Equatorial Region ◽  
Eastern Pacific ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Vertical Scale ◽  
Surface Jet

Abstract. Several numerical experiments are performed in a nonlinear, multi-level periodic channel model centered on the equator with different zonally uniform background flows which resemble the South Equatorial Current (SEC). Analysis of the simulations focuses on identifying stability criteria for a continuously stratified fluid near the equator. A 90 m deep frontal layer is required to destabilize a zonally uniform, 10° wide, westward surface jet that is symmetric about the equator and has a maximum velocity of 100 cm/s. In this case, the phase velocity of the excited unstable waves is very similar to the phase speed of the Tropical Instability Waves (TIWs) observed in the eastern Pacific Ocean. The vertical scale of the baroclinic waves corresponds to the frontal layer depth and their phase speed increases as the vertical shear of the jet is doubled. When the westward surface parabolic jet is made asymmetric about the equator, in order to simulate more realistically the structure of the SEC in the eastern Pacific, two kinds of instability are generated. The oscillations that grow north of the equator have a baroclinic nature, while those generated on and very close to the equator have a barotropic nature.  This study shows that the potential for baroclinic instability in the equatorial region can be as large as at mid-latitudes, if the tendency of isotherms to have a smaller slope for a given zonal velocity, when the Coriolis parameter vanishes, is compensated for by the wind effect.Key words. Oceanography: general (equatorial oceanography; numerical modeling) – Oceanography: physics (fronts and jets)

Interannual Variability of the North Pacific Subtropical Countercurrent and Its Associated Mesoscale Eddy Field

2010 ◽  
Vol 40 (1) ◽  
pp. 213-225 ◽  
Author(s):  
Bo Qiu ◽  
Shuiming Chen
Keyword(s):  
North Pacific ◽  
Southern Oscillation ◽  
North Pacific Ocean ◽  
Baroclinic Instability ◽  
Mesoscale Eddy ◽  
Vertical Shear ◽  
North Equatorial Current ◽  
Altimeter Data ◽  
Subtropical Countercurrent ◽  
Eddy Field

Abstract Interannual changes in the mesoscale eddy field along the Subtropical Countercurrent (STCC) band of 18°–25°N in the western North Pacific Ocean are investigated with 16 yr of satellite altimeter data. Enhanced eddy activities were observed in 1996–98 and 2003–08, whereas the eddy activities were below average in 1993–95 and 1999–2002. Analysis of repeat hydrographic data along 137°E reveals that the vertical shear between the surface eastward-flowing STCC and the subsurface westward-flowing North Equatorial Current (NEC) was larger in the eddy-rich years than in the eddy-weak years. By adopting a 2½-layer reduced-gravity model, it is shown that the increased eddy kinetic energy level in 1996–98 and 2003–08 is because of enhanced baroclinic instability resulting from the larger vertical shear in the STCC–NEC’s background flow. The cause for the STCC–NEC’s interannually varying vertical shear can be sought in the forcing by surface Ekman temperature gradient convergence within the STCC band. Rather than El Niño–Southern Oscillation signals as previously hypothesized, interannual changes in this Ekman forcing field, and hence the STCC–NEC’s vertical shear, are more related to the negative western Pacific index signals.

scholarly journals Maintenance of mid-latitude oceanic fronts by mesoscale eddies

2020 ◽  
Vol 6 (31) ◽  
pp. eaba7880 ◽  
Author(s):  
Zhao Jing ◽  
Shengpeng Wang ◽  
Lixin Wu ◽  
Ping Chang ◽  
Qiuying Zhang ◽  
...  
Keyword(s):  
Heat Transport ◽  
Baroclinic Instability ◽  
Mesoscale Eddies ◽  
Vertical Shear ◽  
Western Boundary ◽  
Boundary Current ◽  
Surface Cooling ◽  
Surface Ocean ◽  
Oceanic Fronts ◽  
Ocean Carbon

Oceanic fronts associated with strong western boundary current extensions vent a vast amount of heat into the atmosphere, anchoring mid-latitude storm tracks and facilitating ocean carbon sequestration. However, it remains unclear how the surface heat reservoir is replenished by ocean processes to sustain the atmospheric heat uptake. Using high-resolution climate simulations, we find that the vertical heat transport by ocean mesoscale eddies acts as an important heat supplier to the surface ocean in frontal regions. This vertical eddy heat transport is not accounted for by the prevailing inviscid and adiabatic ocean dynamical theories such as baroclinic instability and frontogenesis but is tightly related to the atmospheric forcing. Strong surface cooling associated with intense winds in winter promotes turbulent mixing in the mixed layer, destructing the vertical shear of mesoscale eddies. The restoring of vertical shear induces an ageostrophic secondary circulation transporting heat from the subsurface to surface ocean.

scholarly journals Dynamics of Singular Vectors in the Semi-Infinite Eady Model: Nonzero β but Zero Mean PV Gradient

2006 ◽  
Vol 63 (2) ◽  
pp. 547-564 ◽  
Author(s):  
H. de Vries ◽  
J. D. Opsteegh
Keyword(s):  
Kinetic Energy ◽  
Potential Temperature ◽  
Vertical Shear ◽  
Buoyancy Frequency ◽  
Resonant Level ◽  
Frequency Profile ◽  
First Case ◽  
State Potential ◽  
Surface Buoyancy ◽  
Pv Gradient

Abstract A nonmodal approach based on the potential vorticity (PV) perspective is used to compute the singular vector (SV) that optimizes the growth of kinetic energy at the surface for the β-plane Eady model without an upper rigid lid. The basic-state buoyancy frequency and zonal wind profile are chosen such that the basic-state PV gradient is zero. If the f-plane approximation is made, the SV growth at the surface is dominated by resonance, resulting from the advection of basic-state potential temperature (PT) by the interior PV anomalies. This resonance generates a PT anomaly at the surface. The PV unshielding and PV–PT unshielding contribute less to the final kinetic energy at the surface. The general conclusion of the present paper is that surface cyclogenesis (of the 48-h SV) is stronger if β is included. Three cases have been considered. In the first case, the vertical shear of the basic state is modified in order to retain the zero basic-state PV gradient. The increased shear enhances SV growth significantly first because of a lowering of the resonant level (enhanced resonance), and second because of a more rapid PV unshielding process. Resonance is the most important contribution at optimization time. In the second case, the buoyancy frequency of the basic state is modified. The surface cyclogenesis is stronger than in the absence of β but less strong than if the shear is modified. It is shown that the effect of the modified buoyancy frequency profile is that PV unshielding occurs more efficiently. The contribution from resonance to the SV growth remains almost the same. Finally, the SV is calculated for a more realistic buoyancy frequency profile based on observations. In this experiment the increased value of the surface buoyancy frequency reduces the SV growth significantly as compared to the case in which the surface buoyancy frequency takes a standard value. All growth mechanisms are affected by this change in the surface buoyancy frequency.

Bounds on the eigenvalues of the planetary-scale baroclinic instability problem

1988 ◽  
Vol 12 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Fabio Cavallini ◽  
Fulvio Crisciani ◽  
Renzo Mosetti
Keyword(s):  
Baroclinic Instability ◽  
Planetary Scale ◽  
Instability Problem

scholarly journals Estuarine Boundary Layer Mixing Processes: Insights from Dye Experiments*

2007 ◽  
Vol 37 (7) ◽  
pp. 1859-1877 ◽  
Author(s):  
Robert J. Chant ◽  
Wayne R. Geyer ◽  
Robert Houghton ◽  
Elias Hunter ◽  
James Lerczak
Keyword(s):  
Boundary Layer ◽  
Richardson Number ◽  
Flood Tide ◽  
Buoyancy Flux ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Diapycnal Mixing ◽  
Bottom Boundary ◽  
Shear Production

Abstract A series of dye releases in the Hudson River estuary elucidated diapycnal mixing rates and temporal variability over tidal and fortnightly time scales. Dye was injected in the bottom boundary layer for each of four releases during different phases of the tide and of the spring–neap cycle. Diapycnal mixing occurs primarily through entrainment that is driven by shear production in the bottom boundary layer. On flood the dye extended vertically through the bottom mixed layer, and its concentration decreased abruptly near the base of the pycnocline, usually at a height corresponding to a velocity maximum. Boundary layer growth is consistent with a one-dimensional, stress-driven entrainment model. A model was developed for the vertical structure of the vertical eddy viscosity in the flood tide boundary layer that is proportional to u2*/N∞, where u* and N∞ are the bottom friction velocity and buoyancy frequency above the boundary layer. The model also predicts that the buoyancy flux averaged over the bottom boundary layer is equal to 0.06N∞u2* or, based on the structure of the boundary layer equal to 0.1NBLu2*, where NBL is the buoyancy frequency across the flood-tide boundary layer. Estimates of shear production and buoyancy flux indicate that the flux Richardson number in the flood-tide boundary layer is 0.1–0.18, consistent with the model indicating that the flux Richardson number is between 0.1 and 0.14. During ebb, the boundary layer was more stratified, and its vertical extent was not as sharply delineated as in the flood. During neap tide the rate of mixing during ebb was significantly weaker than on flood, owing to reduced bottom stress and stabilization by stratification. As tidal amplitude increased ebb mixing increased and more closely resembled the boundary layer entrainment process observed during the flood. Tidal straining modestly increased the entrainment rate during the flood, and it restratified the boundary layer and inhibited mixing during the ebb.

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