Lateral Eddy Viscosity Research Articles

Parameter sensitivity analysis of the short-range prediction of Kuroshio extension transition processes using an optimization approach

In this study, the optimization parameter sensitivity analysis (OPSA) method is applied to investigate the sensitivity of the short-range prediction of the Kuroshio extension (KE) transition process to parameter uncertainties as simulated with a reduced-gravity shallow water model. The results show that the uncertainties of the model parameters have important impacts on the short-range predictions of the KE transition processes: the predictions are found to be mainly affected by the uncertainties in the reduced-gravity and interfacial friction coefficients. On the contrary, the prediction is insensitive to the wind stress amplitude and the lateral eddy viscosity coefficient. Furthermore, if the sensitive parameters are more accurately estimated, the prediction will be significantly improved. It is therefore suggested that the OPSA method is a useful tool to assess parameter sensitivity for the prediction of the KE transition processes.

Simulation of two-dimensional currents to the depth and suspended sediment concentration in Aceh Besar Waters

Aceh Besar Waters are geographically located at 5.3° - 5.7°N and 95.1° - 95.6°E which border Indian Ocean, Andaman Sea, and Malacca Strait in the West, North, and East, respectively. The purpose of this study was to simulate the circulation of current and suspended sediment transport driven by southwest and northeast monsoon. Model discretization cover 0.5 x 0.5 arcminutes (925 x 925 m) of spatial resolution with time interval of 9 seconds. The parameters of the model are wind friction Cd = 1.285x10−3, bottom friction r = 0.0025, lateral eddy viscosity = 2500 m2/s. The primary data of estuary suspended sediment concentrations were collected in the coastal waters of Lhok Nga, Ulee Lheue, Lampulo, Alue Naga and Krueng Raya as input for the suspended sediment distribution model. The results of the study show that during southwest monsoon, the current in the western part of Aceh Besar Waters move northward and during northeast monsoon in the western and eastern part of the region, the current move toward south and west. Thus, the distribution of suspended sediments follows the direction of the current, where sediment concentrations are reduced when they are away from the coast.

Lateral Shear Layer and Its Velocity Distribution of Flow in Rectangular Open Channels

The lateral velocity distribution of flow in the shear layer of open channel is required to many problems in river and eco-environment engineering, e.g. distribution of pollutant dispersion, sediment transport and bank erosion, and aquatic habitat. It is not well understood about how the velocity varies laterally in the wall boundary layer. This paper gives an analytical solution of lateral velocity distribution in a rectangular open channel based on the depth-averaged momentum equation proposed by Shiono & Knight. The obtained lateral velocity distributions in the wall shear layer are related to the two hydraulic parameters of lateral eddy viscosity (λ) and depth-averaged secondary flow (Γ) for given roughened channels. Preliminary relationships between the above two parameters and the aspect ratio of channel, B/H, are obtained from two sets of experimental data. The lateral width (δ) of the shear layer was investigated and found to relate to the λ and the bed friction factor (f), as described by Equation (26). This study indicates that the lateral shear layer near the wall can be very wide (δ/H = 14.6) for the extreme case (λ = 0.6 and f = 0.01).

The Lateral Eddy Viscosity Derived from the Decay of Oceanic Mesoscale Eddies

The relationship of lateral eddy viscosity depending on length scale is estimated with the decay rate of mesoscale eddies identified from sea level anomaly of satellite observations. The eddy viscosity is expressed in terms of the mesoscale eddy parameters according to vortex dynamics. The census of mesoscale eddies shows, in general, that the eddy numbers obey the e-folding decay laws in terms of their amplitude, area and lifetime. The intrinsic values in the e-folding laws are used to estimate the lateral eddy viscosity. Dislike the previous theory that diffusivities are proportional to the length square, the eddy mixing rates (diffusivity and viscosity) from satellite mesoscale eddy datasets are proportional to rs to power of 1.8 (slightly less than 2), where rs is the radius of eddy with radius larger than the Batchelor scale. Additionally, the extrapolation of the eddy mixing to the molecule scale implies that the above power laws may hold until the value of rs is less than O (1 m). These mixing rates with the new parameterizations are suggested to use in numerical schemes. Finally, the climatological distributions of eddy viscosity are calculated.

Kuroshio Extension Bimodality and the North Pacific Oscillation: A Case of Intrinsic Variability Paced by External Forcing

Abstract A previous North Pacific Ocean circulation model forced by climatological winds is extended here to include a time-dependent North Pacific Oscillation (NPO) forcing. The Kuroshio Extension (KE) decadal bimodal cycle (which is a self-sustained intrinsic relaxation oscillation in the climatologically forced case) is now excited by the NPO forcing. Both the timing of the cycles and the Rossby wave teleconnection mechanism that is found to govern the synchronization from 1993 to 2012 are in good agreement with altimeter observations. Sensitivity numerical experiments are carried out by varying the zonal location and amplitude of the NPO forcing, and the lateral eddy viscosity. The emergence of the KE bimodality with a correct timing is found to be extremely sensitive to changes in the dissipative parameterization; the implications of such sensitivity for deficiencies found in more realistic North Pacific Ocean general circulation models are discussed. The dynamical mechanism that emerges from this study is explained as a case of intrinsic variability in an excitable dynamical system triggered, and therefore paced, by an external forcing.

On the Width of the Equatorial Deep Jets

Abstract The equatorial deep jets (EDJ) are a striking feature of the equatorial ocean circulation. In the Atlantic Ocean, the EDJ are associated with a vertical scale of between 300 and 700 m, a time scale of roughly 4.5 years, and upward energy propagation to the surface. It has been found that the meridional width of the EDJ is roughly 1.5 times larger than expected based on their vertical scale. Here, the authors use a shallow-water model for a high-order baroclinic vertical normal mode to argue that mixing of momentum along isopycnals can explain the enhanced width. A lateral eddy viscosity of 300 m2 s−1 is found to be sufficient to account for the width implied by observations.

Intrinsic low-frequency variability of the Gulf Stream

Abstract. In this paper a process study aimed at analyzing the low-frequency variability of intrinsically oceanic origin of the Gulf Stream (GS) and GS extension (GSE) is presented. An eddy-permitting reduced-gravity nonlinear shallow water model is implemented in an idealized North Atlantic Ocean, with schematic boundaries including the essential geometric features of the coastline and a realistic zonal basin width at all latitudes. The forcing is provided by a time-independent climatological surface wind stress obtained from 41 years of monthly ECMWF fields. The model response yields strong intrinsic low-frequency fluctuations on the interannual to decadal time scales. The modelled time-averaged GS/GSE flows are found to exhibit several features that can also be deduced from satellite altimeter data, such as the Florida Current seaward deflection, the GS separation at Cape Hatteras, and the overall structure of the GSE. The intrinsic low-frequency variability yields two preferred states of the GSE differing in latitudinal location that also have their counterpart in the altimeter data. A preliminary analysis of the variability in terms of dynamical systems theory is carried out by using the lateral eddy viscosity as the control parameter. A complex transition sequence from a steady state to irregular low-frequency variability emerges, in which Hopf and global bifurcations can be identified.

Numerical prediction of morphological change of straight trapezoidal open-channel

This paper presents a numerical model that is capable of simulating the morphological process of the trapezoidal open-channel. The fact that particles on the sloped side bank do not move in the same direction as the flow adds the difficulty in modeling. The lateral distribution model, which distributes the unit discharge over the width, is used for the flow analysis. Vectorial bedload formula by Kovacs and Parker (1994) is used and channel topography is calculated by solving Exner’s equation with the help of sliding algorithm proposed by Menendez et al. (2008). Values of roughness coefficient and lateral eddy viscosity are calibrated using laboratory data sets. Finally, the proposed model is applied to laboratory experiments of Ikeda (1981) and Izumi et al. (1991). Time evolutions of channel cross section and dimensionless shear stress are provided and discussed.

Flow movement and sediment transport in compound channels

There are many studies on the flow movement in compound channels, yet few are concerned with sediment transport. An experimental study on the flow movement and sediment transport in compound channels is presented. The experimental results indicate that the distribution of longitudinal velocity with depth in the main channel and the floodplains has a logarithmic component. The longitudinal velocity with flow depth in the interactive region does not obey a logarithmic distribution, but involves a wake function. In the boundary region, the longitudinal velocity obeys a parabolic distribution. In addition, based on the suspended sediment diffusion equation and the flow interaction between main channel and floodplains, expressions are derived to predict the lateral eddy viscosity and the sediment diffusion coefficients. Finally, an analytical solution for the lateral distribution of the depth-averaged velocity and sediment concentration in a compound channel is obtained. The results from the analytical solution agree well with experimentation.

Numerical simulation of typhoon surges along the coast of Taiwan

A numerical model has been designed to study the storm surge induced by typhoon along the coast of Taiwan. The governing equations have been expressed in spherical coordinate system, and a finite difference method has been used to solve them. In the system of hydrodynamical equations, the nonlinear advection and lateral eddy viscosity terms are prominent in shallow coastal waters. Air pressure gradient and wind stresses are the driving forces in the model of typhoon surge. The model has been verified with storm surges induced by Typhoons Herb in 1996, and by typhoons Kai-Tak and Bilis in 2000.

Zonal discharges and boundary shear in prismatic channels

This paper illustrates a new approach to obtaining analytical stage–discharge formulae for both zonal and total discharges in straight prismatic channels of any shape, based on the concepts of a zero–shear force interface and an analytical solution for the lateral variation of depth-averaged velocity. The analytical solution for velocity is derived from the depth-integrated form of the Navier–Stokes equations, and includes the effects of bed friction, lateral turbulence, and secondary flows/planform vorticity. The analytical formulae for stage discharge are given for both simple and compound trapezoidal channels, together with formulae that permit the boundary shear force to be determined for every linear element on the wetted perimeter. These stage–discharge and shear force formulae depend on the channel geometry and on three hydraulic parameters related to the bed friction factor f, lateral eddy viscosity λ and depth-averaged secondary flow Γ, as required in the original Shiono and Knight method. The analytical results show good agreement with experimental data. Ways of extending this approach to more complex shaped channels are outlined.

A Kuroshio Extension System Model Study: Decadal Chaotic Self-Sustained Oscillations

Abstract A model study of the Kuroshio Extension system, in which forcing is provided by a time-independent climatological wind, yields a mean meandering path and a decadal variability of the jet in significant agreement with in situ and altimetric measurements. A reduced-gravity primitive equation ocean model is implemented in a box spanning the whole North Pacific, including a schematic coastline at the western side, and an analytical wind forcing is determined according to the ECMWF and Comprehensive Ocean–Atmosphere Data Set (COADS) climatologies. The modeled time-averaged Kuroshio Extension shows meanders, northern and southern recirculation regions, and a jet penetration that are in good agreement with the corresponding observed climatological features. This result suggests that intrinsic nonlinear mechanisms are likely to play a major role in determining the meander pattern of the mean flow. The internal low-frequency variability is found to be a chaotic bimodal self-sustained oscillation between an energetic meandering state and a much weaker state with a reduced zonal penetration of the jet. These high and low energy states are found to be very similar to the “elongated” and “contracted” modes of the Kuroshio Extension detected through altimetric measurements; moreover, the characteristic period (of around 10 yr), flow patterns, and transition details of a typical bimodal cycle are found to be in significant agreement with altimeter observations for the period 1992–2004. A complex dynamical mechanism supporting this internal oscillation, and involving the bimodal behavior of the Kuroshio south of Japan, is proposed and discussed. On the basis of these modeling results and of their validation with altimeter data, it is hypothesized that the observed bimodal decadal variability of the Kuroshio Extension is basically due to a self-sustained internal oscillation related to the instability of the Kuroshio south of Japan without any crucial intervention of wind-driven Sverdrup transport fluctuations and of topographic interactions, although such effects certainly play an important role in shaping the finer structure of Kuroshio Extension changes. Finally, in a preliminary analysis of the variability in the framework of nonlinear dynamical systems theory it is suggested that the strange attractor corresponding to the modeled low-frequency variability is associated with a homoclinic orbit produced by a global bifurcation; moreover, transitions between oscillations of different character found for slightly different values of the lateral eddy viscosity and forcing amplitude are conjectured to be due to heteroclinic connections.

Lateral Reynolds Stress and Eddy Viscosity in a Coastal Strait

Abstract The lateral Reynolds stress uυ, representing the transfer of along-strait momentum toward the sides of Juan de Fuca Strait, is measured with an array of ADCPs. The contributions to the stress from a number of frequency bands are analyzed to highlight the roles of different processes. Motion in a frequency band that includes internal waves and Doppler-shifted subinertial eddies gives a Reynolds stress that, when scaled by the observed shear, is consistent with an eddy viscosity of O(10 m2 s−1). This viscosity acts on the tides and the estuarine flow. The tides can also impart a viscous stress upon the low-frequency estuarine flow. These tidal currents, although strong, are largely nondivergent within the area of the array and thus appear to be less important for the cross-strait transfer of momentum. The long-term mean estuarine circulation can be acted upon by meanders of the estuarine flow, defined as features with periods of 3–5 days. These meanders are found to also have a horizontal eddy viscosity of O(10 m2 s−1). The measured Reynolds stress divergences are consistent with both the strongly curved profile of the estuarine mean flow and also the more slablike tidal current profile. This paper represents the first direct calculation of eddy viscosity on the medium-sized scale of the array, O(1 km).

Stage-discharge prediction for rivers in flood applying a depth-averaged model

The prediction of the stage-discharge relationship for rivers in flood is described by a finite element model of depth-averaged turbulent flow, calibrated using (hree hydraulic coefficients governing local bed friction, lateral eddy viscosity and depth-averaged secondary flow. The resulting lateral distributions of depth-averaged velocity are subsequently integrated to yield the stage-discharge relationship. The calibration of the model involves the establishment of simplifying hypotheses for certain coefficients in order to give the correct depth-mean velocity and boundary shear, both across the channel and with stage. Comparisons against some experimental data from the UK Flood Channel Facility, for channels with trapezoidal and compound cross-sections, help develop the calibration philosophy for both inbank and overbank flows. Numerical experiments with the coherence method for a hypothetical river are used to extend the model calibration to rivers with homogeneous and heterogeneous roughness. Applications of the model to simulating the flow in a number of natural valley and mountain rivers serve to test hypotheses and results obtained at a real scale.

Sensitivity of an Equatorial Pacific OGCM to the Lateral Diffusion

An OGCM is used to investigate the importance of lateral mixing in the tropical Pacific Ocean circulation. Horizontal subgrid-scale physics is parameterized by the usual Laplacian operator. Three simulations are performed using three different orders of magnitude for lateral eddy viscosity and diffusivity coefficients: 104, 103, and 102 m2 s−1. The upper layer response is found sensitive to lateral diffusion as well as the rest of the general circulation. Decreasing lateral mixing coefficients raises the mean kinetic energy level and the input of energy by the wind, and enhances the vertical dissipation. This weakens the equatorial meridional cell and induces a reduction of 20 Sv in the transport of the equatorial upwelling. These results are due to the nonlinear interplay between horizontal and vertical diffusion. The nature of the Equatorial Undercurrent (EUC) is found particularly sensitive to the relative importance of the diffusive conditions. Lateral mixing dominates the different regimes of the EUC when the strongest diffusion coefficient is used. Under these conditions, the EUC dynamics is similar to a boundary layer regime where strong meridian and vertical circulation insulates the equatorial dynamics. Conversely, a weakness of horizontal diffusion leads to enhancement of the vertical diffusion role, even in the core of the EUC. In the eastern inertial regime, vertical diffusion can replace horizontal diffusion when dissipation is needed. While the dynamics is severely altered between the simulations, the SST pattern errors with the climatology are found quite similar, in conflict with the results reported by Nevertheless, at the basin scale, lateral mixing conditions affect the meridian heat transport. Similar diffusive and advective heat transport amplitudes are found with the strongest lateral coefficient, while advective meridian heat transport dominates in both other experiments. Moreover, the different terms of the surface heat budget are found sensitive to the lateral diffusion: when lateral diffusion coefficient is sufficiently low, the balance implies the heating by the transient heat transport and the cooling by both monthly mean advection and vertical diffusion. Indeed, in the equatorial cold tongue, vertical diffusion is large enough to distribute heat down to the thermocline below the mixed layer.

The zonal momentum balance in an eddy-resolving general-circulation model of the Southern Ocean

The momentum balance in the zonally unbounded region of the Southern Ocean is examined using an eddy-resolving ocean general-circulation model (namely FRAM). Momentum, which is input at the surface and accelerates the Antarctic Circumpolar Current, is transferred down the water column and removed by topographic form stress. Bottom friction and lateral eddy viscosity are found to be negligible. the poleward flux of eastward momentum has a small effect in redistributing momentum. In spite of this, below the wind-driven surface layer and above the level of topography, the poleward momentum-flux divergence provides the main balance along with the ageostrophic flux of planetary vorticity (although the magnitude of these terms is an order of magnitude smaller than the wind stress). Below the Ekman layer, standing eddies produce a drag on the flow whilst transient eddies accelerate the flow. However, the impact of transient eddies is smaller. the downward transfer of momentum is achieved by interfacial form stress. This can be understood in terms of a poleward density (heat) flux. the main contribution comes from standing eddies, with a smaller contribution from transient eddies. Both contributions assist the transfer. the flux of density (heat) from the neighbouring oceans (to the north and south of the Drake Passage latitudes) influences the depth penetration of zonal momentum, particularly in the upper 1000 m. the Johnson-Bryden theory is generalized to give an additional term which is proportional to the stream function for the residual circulation associated with Eliassen-Palm cross-sections.

The zonal momentum balance in an eddy‐resolving general‐circulation model of the southern ocean

AbstractThe momentum balance in the zonally unbounded region of the Southern Ocean is examined using an eddy‐resolving ocean general‐circulation model (namely FRAM). Momentum, which is input at the surface and accelerates the Antarctic Circumpolar Current, is transferred down the water column and removed by topographic form stress. Bottom friction and lateral eddy viscosity are found to be negligible. the poleward flux of eastward momentum has a small effect in redistributing momentum. In spite of this, below the wind‐driven surface layer and above the level of topography, the poleward momentum‐flux divergence provides the main balance along with the ageostrophic flux of planetary vorticity (although the magnitude of these terms is an order of magnitude smaller than the wind stress). Below the Ekman layer, standing eddies produce a drag on the flow whilst transient eddies accelerate the flow. However, the impact of transient eddies is smaller. the downward transfer of momentum is achieved by interfacial form stress. This can be understood in terms of a poleward density (heat) flux. the main contribution comes from standing eddies, with a smaller contribution from transient eddies. Both contributions assist the transfer. the flux of density (heat) from the neighbouring oceans (to the north and south of the Drake Passage latitudes) influences the depth penetration of zonal momentum, particularly in the upper 1000 m. the Johnson‐Bryden theory is generalized to give an additional term which is proportional to the stream function for the residual circulation associated with Eliassen‐Palm cross‐sections.

Dissipative effects on inertial flows over a sill

Abstract A systematic investigation of the effects of various parametrizations of dissipation, e.g. quadratic and linear frictional drag, harmonic lateral viscosity, and harmonic lateral diffusion on inertial flow over a sill and possible hydraulic control is presented. Rotation effects are ignored and the geometry is assumed to vary only slowly with downstream distance so that the flow may be considered one-dimensional. Results are given both for a single-active layer and for two-active layers with a rigid lid. If the parametrization is only a function of the dependent variables and not of their spatial derivatives, then it may be possible to hydraulically control the flow. A general expression is derived for the possible control point and the two gradients there, which are functions of the slope and possibly of flow rate. Specific energy is irreversibly removed from the flow and non-controlled as well as controlled flows can exhibit significant asymmetry in fluid depth over a sill. The upstream specific energy, and hence depth of the lower layer, of the controlled flow is greater than for an ideal fluid. Frictional effects modify the behaviour of long gravity waves, such that they are dispersive and damped with time. The system will only exhibit hydraulic control if these effects are small. For a viscous single layer of fluid, the gradient in surface elevation is always uniquely defined, so classically defined hydraulic control, as such, cannot exist. However, for values of non-dimensional lateral eddy viscosity coefficient, A M ⪅ 0.1 q 1 3 , where q is the flow rate, there is a narrow band of specific energies centred around that for the control solution in an ideal fluid, E crit , for which the surface elevation, h is very asymmetric over the sill; the solutions resemble the inviscid, hydraulically controlled solutions. Outside this range, either the fluid depth tends to zero, or the surface elevation is almost uniform over the sill. A ‘control’-type solution exists which has the conjugate values of the inviscid equation up- and downstream of the sill, where the gradient in fluid depth, and hence the viscous term, is zero. For larger values of A M , the band of specific energies is much wider, and the upstream specific energy of the ‘control’-type solution is much lower than that for an inviscid fluid. Long gravity waves are dispersive and damped with time. There is a short-wave cut-off, k 2 > h /(4 A M 2 ), above which waves are stationary in the flow. Longer waves, k 2 ⪡ h /(4 A M 2 ), are critical if h ⋍ q 2 3 , as for an ideal fluid. If these waves can propagate significant distances, then any observed asymmetry in h will be due to inertial and not to viscous effects. The behaviour of unidirectional, two-layer flow is similar. The governing equation for viscous, two-layer exchange flow is singular, and typically excludes the ‘control’-type solutions found for unidirectional flows. Establishing the existence and behaviour of steady inertial flows in the presence of lateral diffusion between layers is more difficult. It significantly alters the single-layer solutions once the non-dimensional coefficient A H is large, i.e. A M ⪆ A H ⪆ 0.1 q 1 3 . The flow rate may become zero on the downslope as all the fluid diffuses into the inert, infinitely deep, overlaying layer. The fluid depth is maintained by reverse flow from downstream. In this case, the depth of the active layer tends to zero downstream for all values of specific energy. For two-layer flow, both unidirectional and exchange, the governing equation is such that the lower-layer flow rate and interfacial height return to their upstream values. Motivation for the study is provided by the increasingly fine spatial resolution achievable in large-scale numerical models of the ocean general circulation, and the question of whether they are capable of simulating some form of hydraulic control. Application to modelling oceanic flows over a sill is discussed.

On the Properties of the Free Double Kelvin Wave in a Viscous and Diffusive Fluid

The modifications to the structure and propagation characteristics of the double Kelvin wave due to various parameterizations of dissipative effects; namely, a lateral eddy viscosity and diffusion with coefficients AM, AH, and Rayleigh friction and Newtonian cooling with coefficients rM, rH, are examined. Under the assumption of geostrophy in the alongstep direction, and AM = AH, rM = rH, analytic expressions may be obtained and asymptotic limits derived.

Interannual characteristics of an 80 km resolution diagnostic Arctic ice–ocean model

Seasonal simulations with large-scale coupled ice–ocean models have reproduced many features of the ice and ocean circulation of the Arctic Ocean and the Greenland and Norwegian seas (e.g. Hibler and Bryan, 1987; Semtner, 1987). However, the crude resolution and high lateral eddy viscosity used by these models prevent the simulation of many of the smaller-scale seasonal features and tend to produce sluggish circulation. Similarly, the use of a single year’s atmospheric forcing prevents the simulation of features on an interannual time-scale. As an initial step towards addressing these issues, an 80 km diagnostic Arctic ice–ocean model is constructed and integrated over a three-year period using daily atmospheric forcing to drive the model. To examine the effect of topographic resolution and eddy viscosity on model results, similar simulations were performed with a 160 km-resolution model. The results of these simulations are compared with one another, with buoy drift in the Arctic Basin, and with observed ice-edge variations. The model results proved most sensitive to changes in horizontal resolution. The 80 km results provided a more realistic and robust circulation in most areas of the Arctic and improved the modelled ice edge in the Barents Sea, while also successfully simulating the interannual variation in the region. Although it performed better than the 160 km model, the 80 km model still produced too large an ice extent in the Greenland Sea. No significant improvement in the ice-edge prediction was observed by varying the lateral eddy viscosity. The results indicate that problems remain in the vertical resolution in shallow regions, in treating penetrative convection, and in the simulation of inflow into the Arctic Basin through the Fram Strait.