scholarly journals Deterministic model of the eddy dynamics for a midlatitude ocean model

2021 ◽  
Author(s):  
Takaya Uchida ◽  
Bruno Deremble ◽  
Stephane Popinet
Keyword(s):  
Deterministic Model ◽  
North Atlantic Ocean ◽  
Ocean Model ◽  
Global Ocean ◽  
Mean Flow ◽  
Flux Divergence ◽  
Time Step ◽  
Weather System ◽  
Basin Scale ◽  
The Mean

Mesoscale eddies, the weather system of the oceans, although being on the scales of O(20-100 km), have a disproportionate role in shaping the mean jets such as the separated Gulf Stream in the North Atlantic Ocean, which is on the scale of O(1000 km) in the along-jet direction. With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as mesoscale permitting. It is well known, however, that due to grid-scale numerical viscosity, mesoscale-permitting simulations have less energetic eddies and consequently weaker eddy feedback onto the mean flow. In this study, we run a quasi-geostrophic model at mesoscale-resolving resolution in a double gyre configuration and formulate a deterministic closure for the eddy rectification term of potential vorticity (PV), namely, the eddy PV flux divergence. We successfully reproduce the spatial patterns and magnitude of eddy kinetic and potential energy diagnosed from the model. One novel point about our approach is that we account for non-local eddy feedbacks onto the mean flow by solving the `sub-grid' eddy PV equation prognostically in addition to the mean PV. In return, we are able to parametrize the variability in total (mean+eddy) PV at each time step instead of solely the mean PV. A closure for the total PV is beneficial as we are able to account for both the mean state and extreme events.

scholarly journals Deterministic Model of the Eddy Dynamics for a Midlatitude Ocean Model

2021 ◽  
Author(s):  
Takaya Uchida ◽  
Bruno Deremble ◽  
Stephane Popinet
Keyword(s):  
Deterministic Model ◽  
North Atlantic Ocean ◽  
Ocean Model ◽  
Global Ocean ◽  
Mean Flow ◽  
Flux Divergence ◽  
Time Step ◽  
Weather System ◽  
Basin Scale ◽  
The Mean

Mesoscale eddies, the weather system of the oceans, although being on the scales of O(20-100km), have a disproportionate role in shaping the mean jets such as the separated Gulf Stream in the North Atlantic Ocean, which is on the scale of O(1000km) in the along-jet direction. With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as mesoscale permitting. It is well known, however, that due to grid-scale numerical viscosity, mesoscale permitting simulations have less energetic eddies and consequently weaker eddy feedback onto the mean flow. In this study, we run a quasi-geostrophic model at mesoscale resolving resolution in a double gyre configuration and formulate a deterministic parametrization for the eddy rectification term of potential vorticity (PV), namely, the eddy PV flux divergence. We have moderate success in reproducing the spatial patterns and magnitude of eddy kinetic and potential energy diagnosed from the model. One novel point about our approach is that we account for non-local eddy feedbacks onto the mean flow by solving the eddy PV equation prognostically in addition to the mean flow. In return, we are able to parametrize the variability in total (mean+eddy) PV at each time step instead of solely the mean PV. A closure for the total PV is beneficial as we are able to account for both the mean state and extreme events.

scholarly journals The influence of idealized surface heterogeneity on virtual turbulent flux measurements

2018 ◽  
Vol 18 (7) ◽  
pp. 5059-5074 ◽  
Author(s):  
Frederik De Roo ◽  
Matthias Mauder
Keyword(s):  
Energy Budget ◽  
Turbulent Flux ◽  
Surface Heterogeneity ◽  
Surface Fluxes ◽  
Convective Conditions ◽  
Mean Flow ◽  
Flux Divergence ◽  
Length Scales ◽  
Flux Measurements ◽  
The Mean

Abstract. The imbalance of the surface energy budget in eddy-covariance measurements is still an unsolved problem. A possible cause is the presence of land surface heterogeneity, which affects the boundary-layer turbulence. To investigate the impact of surface variables on the partitioning of the energy budget of flux measurements in the surface layer under convective conditions, we set up a systematic parameter study by means of large-eddy simulation. For the study we use a virtual control volume approach, which allows the determination of advection by the mean flow, flux-divergence and storage terms of the energy budget at the virtual measurement site, in addition to the standard turbulent flux. We focus on the heterogeneity of the surface fluxes and keep the topography flat. The surface fluxes vary locally in intensity and these patches have different length scales. Intensity and length scales can vary for the two horizontal dimensions but follow an idealized chessboard pattern. Our main focus lies on surface heterogeneity of the kilometer scale, and one order of magnitude smaller. For these two length scales, we investigate the average response of the fluxes at a number of virtual towers, when varying the heterogeneity length within the length scale and when varying the contrast between the different patches. For each simulation, virtual measurement towers were positioned at functionally different positions (e.g., downdraft region, updraft region, at border between domains, etc.). As the storage term is always small, the non-closure is given by the sum of the advection by the mean flow and the flux-divergence. Remarkably, the missing flux can be described by either the advection by the mean flow or the flux-divergence separately, because the latter two have a high correlation with each other. For kilometer scale heterogeneity, we notice a clear dependence of the updrafts and downdrafts on the surface heterogeneity and likewise we also see a dependence of the energy partitioning on the tower location. For the hectometer scale, we do not notice such a clear dependence. Finally, we seek correlators for the energy balance ratio in the simulations. The correlation with the friction velocity is less pronounced than previously found, but this is likely due to our concentration on effectively strongly to freely convective conditions.

scholarly journals An automaton model for the cell cycle

2010 ◽  
Vol 1 (1) ◽  
pp. 36-47 ◽  
Author(s):  
Atilla Altinok ◽  
Didier Gonze ◽  
Francis Lévi ◽  
Albert Goldbeter
Keyword(s):  
Cell Cycle ◽  
Steady State ◽  
Deterministic Model ◽  
Initial Conditions ◽  
Cell Number ◽  
Time Step ◽  
M Phase ◽  
Random Manner ◽  
The Mean ◽  
Cell Cycle Phases

We consider an automaton model that progresses spontaneously through the four successive phases of the cell cycle: G1, S (DNA replication), G2 and M (mitosis). Each phase is characterized by a mean duration τ and a variability V . As soon as the prescribed duration of a given phase has passed, the transition to the next phase of the cell cycle occurs. The time at which the transition takes place varies in a random manner according to a distribution of durations of the cell cycle phases. Upon completion of the M phase, the cell divides into two cells, which immediately enter a new cycle in G1. The duration of each phase is reinitialized for the two newborn cells. At each time step in any phase of the cycle, the cell has a certain probability to be marked for exiting the cycle and dying at the nearest G1/S or G2/M transition. To allow for homeostasis, which corresponds to maintenance of the total cell number, we assume that cell death counterbalances cell replication at mitosis. In studying the dynamics of this automaton model, we examine the effect of factors such as the mean durations of the cell cycle phases and their variability, the type of distribution of the durations, the number of cells, the regulation of the cell population size and the independence of steady-state proportions of cells in each phase with respect to initial conditions. We apply the stochastic automaton model for the cell cycle to the progressive desynchronization of cell populations and to their entrainment by the circadian clock. A simple deterministic model leads to the same steady-state proportions of cells in the four phases of the cell cycle.

scholarly journals The Contribution of Striations to the Eddy Energy Budget and Mixing: Diagnostic Frameworks and Results in a Quasigeostrophic Barotropic System with Mean Flow

2015 ◽  
Vol 45 (8) ◽  
pp. 2095-2113 ◽  
Author(s):  
Ru Chen ◽  
Glenn R. Flierl
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Ocean Model ◽  
Invariance Property ◽  
Mean Flow ◽  
Eddy Diffusivities ◽  
Energy Cascades ◽  
The Mean ◽  
Flow Theories ◽  
Noise Forcing

AbstractLow-frequency oceanic motions have banded structures termed “striations.” Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a β-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of β-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations’ contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

scholarly journals Effects of Eddy Vorticity Forcing on the Mean State of the Kuroshio Extension

2015 ◽  
Vol 45 (5) ◽  
pp. 1356-1375 ◽  
Author(s):  
Andrew S. Delman ◽  
Julie L. McClean ◽  
Janet Sprintall ◽  
Lynne D. Talley ◽  
Elena Yulaeva ◽  
...  
Keyword(s):  
Reference Frames ◽  
Model Simulation ◽  
Kuroshio Extension ◽  
Relative Vorticity ◽  
Ocean Model ◽  
Instability Criterion ◽  
Mean Flow ◽  
Vorticity Budget ◽  
The Mean ◽  
The Kuroshio

AbstractEddy–mean flow interactions along the Kuroshio Extension (KE) jet are investigated using a vorticity budget of a high-resolution ocean model simulation, averaged over a 13-yr period. The simulation explicitly resolves mesoscale eddies in the KE and is forced with air–sea fluxes representing the years 1995–2007. A mean-eddy decomposition in a jet-following coordinate system removes the variability of the jet path from the eddy components of velocity; thus, eddy kinetic energy in the jet reference frame is substantially lower than in geographic coordinates and exhibits a cross-jet asymmetry that is consistent with the baroclinic instability criterion of the long-term mean field. The vorticity budget is computed in both geographic (i.e., Eulerian) and jet reference frames; the jet frame budget reveals several patterns of eddy forcing that are largely attributed to varicose modes of variability. Eddies tend to diffuse the relative vorticity minima/maxima that flank the jet, removing momentum from the fast-moving jet core and reinforcing the quasi-permanent meridional meanders in the mean jet. A pattern associated with the vertical stretching of relative vorticity in eddies indicates a deceleration (acceleration) of the jet coincident with northward (southward) quasi-permanent meanders. Eddy relative vorticity advection outside of the eastward jet core is balanced mostly by vertical stretching of the mean flow, which through baroclinic adjustment helps to drive the flanking recirculation gyres. The jet frame vorticity budget presents a well-defined picture of eddy activity, illustrating along-jet variations in eddy–mean flow interaction that may have implications for the jet’s dynamics and cross-frontal tracer fluxes.

scholarly journals Optimal Surface Excitation of the Thermohaline Circulation

2008 ◽  
Vol 38 (8) ◽  
pp. 1820-1830 ◽  
Author(s):  
Laure Zanna ◽  
Eli Tziperman
Keyword(s):  
Surface Temperature ◽  
Time Scale ◽  
General Circulation ◽  
Thermohaline Circulation ◽  
Initial Conditions ◽  
Singular Problem ◽  
Mean Flow ◽  
L2 Norm ◽  
Basin Scale ◽  
The Mean

Abstract The amplification of thermohaline circulation (THC) anomalies resulting from heat and freshwater forcing at the ocean surface is investigated in a zonally averaged coupled ocean–atmosphere model. Optimal initial conditions of surface temperature and salinity leading to the largest THC growth are computed, and so are the structures of stochastic surface temperature and salinity forcing that excite maximum THC variance (stochastic optimals). When the THC amplitude is defined as its sum of squares (equivalent to using the standard L2 norm), the nonnormal linearized dynamics lead to an amplification with a time scale on the order of 100 yr. The optimal initial conditions have a vanishing THC anomaly, and the complex amplification mechanism involves the advection of both temperature and salinity anomalies by the mean flow and of the mean temperature and salinity by the anomaly flow. The L2 characterization of THC anomalies leads to physically interesting results, yet to a mathematically singular problem. A novel alternative characterizing the THC amplitude by its maximum value, as often done in general circulation model studies, is therefore introduced. This complementary method is shown to be equivalent to using the L-infinity norm, and the needed mathematical approach is developed and applied to the THC problem. Under this norm, an amplification occurs within 10 yr explained by the classic salinity advective feedback mechanism. The analysis of the stochastic optimals shows that the character of the THC variability may be very sensitive to the spatial pattern of the surface forcing. In particular, a maximum THC variance and long-time-scale variability are excited by a basin-scale surface forcing pattern, while a significantly higher frequency and to some extent a weaker variability are induced by a smooth and large-scale, yet mostly concentrated in polar areas, surface forcing pattern. Overall, the results suggest that a large THC variability can be efficiently excited by atmospheric surface forcing, and the simple model used here makes several predictions that would be interesting to test using more complex models.

scholarly journals Development of a semi-Lagrangian advection scheme for the NEMO ocean model (3.1)

2020 ◽  
Vol 13 (9) ◽  
pp. 4379-4398
Author(s):  
Christopher Subich ◽  
Pierre Pellerin ◽  
Gregory Smith ◽  
Frederic Dupont
Keyword(s):  
Ocean Circulation ◽  
Fluid Motion ◽  
Ocean Model ◽  
Global Ocean ◽  
Test Case ◽  
Courant Number ◽  
Time Step ◽  
Fluid Properties ◽  
Grid Points ◽  
Lagrangian Advection

Abstract. As resolutions of ocean circulation models increase, the advective Courant number – the ratio between the distance travelled by a fluid parcel in one time step and the grid size – becomes the most stringent factor limiting model time steps. Some atmospheric models have escaped this limit by using an implicit or semi-implicit semi-Lagrangian formulation of advection, which calculates materially conserved fluid properties along trajectories which follow the fluid motion and end at prescribed grid points. Unfortunately, this formulation is not straightforward in ocean contexts, where the irregular, interior boundaries imposed by the shore and bottom orography are incompatible with traditional trajectory calculations. This work describes the adaptation of the semi-Lagrangian method as an advection module for an operational ocean model. We solve the difficulties of the ocean's internal boundaries by calculating parcel trajectories using a time-exponential formulation, which ensures that all parcel trajectories remain inside the ocean domain despite strong accelerations near the boundary. Additionally, we derive this method in a way that is compatible with the leapfrog time-stepping scheme used in the NEMO-OPA (Nucleus for European Modelling of the Ocean, Océan Parallélisé) ocean model, and we present simulation results for a simplified test case of flow past a model island and for 10-year free runs of the global ocean on the quarter-degree ORCA025 grid.

Near-inertial waves modulated by background flow in realistic global ocean simulations

2021 ◽  
Author(s):  
Keshav Raja ◽  
Maarten Buijsman ◽  
Oladeji Siyanbola ◽  
Miguel Solano ◽  
Jay Shriver ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Normal Modes ◽  
Deep Ocean ◽  
Ocean Model ◽  
Global Ocean ◽  
Inertial Waves ◽  
Flux Divergence ◽  
Large Wave ◽  
Wind Input ◽  
Anticyclonic Eddies

<p>Wind generated near-inertial waves (NIWs) are a major source of energy for deep-ocean mixing by transmitting wind energy from the ocean surface into the interior. Recently, it has been established that the NIW energy transmission to ocean depths is significantly modulated by background mesoscale vorticity. Thus, understanding NIW energetics in the presence of mesoscale eddies on a global scale is crucial.</p><p>We study the generation, propagation and dissipation of NIWs in global 1/25<sup>o</sup> Hybrid Coordinate Ocean Model (HYCOM) simulations with realistic tidal forcing. The model has 41 layers with uniform vertical coordinates in the mixed layer and isopycnal coordinates in the ocean interior. The model is forced by 1/3hr wind from the NAVGEM atmospheric model. We analyze one month of model data for May-June 2019. The 3D HYCOM fields are projected on vertical normal modes to compute the wind input, wave kinetic energy (KE), flux divergence and dissipation per mode.</p><p>We find that the globally integrated wind input in surface near-inertial motions is 0.21 TW for the 30-day period and is consistent with previous studies. The sum of the wind input to the first 5 modes accounts to only 31% of the total wind input while the sum of the NIW kinetic energy in the first 5 modes adds up to 60% of the total NIW KE. The difference in the fraction of the total between the wind input and NIW KE (31% and 60%) suggests that a significant portion of wind-induced near-inertial motions is dissipated close to the surface without being projected onto modes. We also find that NIW horizontal fluxes diverge from areas with cyclonic vorticity and converge in areas with anticyclonic vorticity, i.e., anticyclonic eddies are a sink for NIW energy in the global ocean.</p><p>The residual NIW KE that does not project onto modes is found to be largely trapped in anticyclonic eddies. In a next step, we will study the fate of this energy, which most likely propagate downward as beam-like features with large wave numbers. We will compute the near-inertial wave energy balance for fixed subsurface layers and consider the energy exchange between these layers to understand the vertical structure of NIW energy dissipation. We find that the downward NIW radiation to the ocean interior at 500 m depth is 19% of the surface near-inertial wind input for the 30-day period.</p>

A global coupled atmosphere-ocean model

1989 ◽  
Vol 329 (1604) ◽  
pp. 263-273 ◽  
Keyword(s):  
Water Flux ◽  
Coupled Model ◽  
Ocean Model ◽  
Global Ocean ◽  
Max Planck ◽  
Weather Forecasts ◽  
Medium Range ◽  
Climate Drift ◽  
The Mean ◽  
Atmosphere Model

A low-resolution version of the European Centre for Medium Range Weather Forecasts global atmosphere model has been coupled to a global ocean model developed at the Max Planck Institut in Hamburg. The atmosphere model is driven by the sea surface temperature and the ice thickness calculated by the ocean model, which, in turn, is driven by the wind stress, the heat flux and the fresh-water flux diagnosed by the atmosphere model. Even though each model reaches stationarity when integrated on its own, the coupling of both creates problems, because the fields calculated by each model are not consistent with those the other model has to have to stay stationary, as some of the fluxes are not balanced. In the coupled experiment the combined ocean-atmosphere system drifts towards a colder state. To counteract this problem a flux correction has been applied, which balances the mean biases of each model. This method makes the climate drift of the coupled model smaller, but additional work has to be done to perfect this method.

The dissipation of the internal tide inferred from a global ocean model, altimetry, and in-situ observations

2020 ◽  
Author(s):  
Maarten Buijsman ◽  
Harpreet Kaur ◽  
Zhongxiang Zhao ◽  
Amy Waterhouse ◽  
Caitlin Whalen
Keyword(s):  
Correction Factor ◽  
Internal Tide ◽  
Horizontal Resolution ◽  
Ocean Model ◽  
Internal Tides ◽  
Global Ocean ◽  
Flux Divergence ◽  
Data Set ◽  
Tidal Dissipation ◽  
Dissipation Rates

<p>In this presentation we combine several model and observational data sets to better understand the dissipation of the diurnal and semidiurnal internal tide in the global ocean, which is relevant for maintaining the global overturning circulation. We compute depth-integrated internal tide dissipation rates from a realistically-forced global HYbrid Coordinate Ocean Model (HYCOM) simulation with a horizontal resolution of 4 km (1/25 degrees) and 41 layers. We also compute dissipation rates from altimetry in two ways: 1) from the low-mode flux divergence away from topography and 2) by fitting exponential decay curves along low-mode internal tide beams. The internal-tide sea-surface height amplitude is computed with a least-squares harmonic analysis over a 20+ year altimetry data set. Hence, the altimetry-inferred dissipation rates both reflect the tidal dissipation and the energy scattered from the stationary to the nonstationary internal tide. To account for the dissipation of the nonstationary tide, we apply a spatially-varying correction factor to the stationary dissipation inferred from altimetry.  This correction factor is computed from a global 8-km HYCOM simulation with a duration of 6 years, from which the stationary and nonstationary internal tides can be easily isolated. We compare the simulated and the corrected altimetry-inferred dissipation rates with dissipation rates from finescale and microstructure observations. Preliminary results show that the simulated dissipation is up to a factor of two larger than the depth-integrated dissipation rates inferred from finescale methods, but smaller than the dissipation rates from microstructure.</p>

Sign in / Sign up

Export Citation Format

Share Document