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- Author or Editor: G. L. Mellor x
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Abstract
The time evolution of an estuary plume and its coastal front over a continental shelf is numerically calculated here using a three-dimensional model with eddy mixing based on the turbulence kinetic energy closure. The plume and front system is found to be unsteady with a natural period of about 5–10 days, during which the plume pulsates and intermittent coastal currents propagate down the coast.
Abstract
The time evolution of an estuary plume and its coastal front over a continental shelf is numerically calculated here using a three-dimensional model with eddy mixing based on the turbulence kinetic energy closure. The plume and front system is found to be unsteady with a natural period of about 5–10 days, during which the plume pulsates and intermittent coastal currents propagate down the coast.
Abstract
The present paper describes a one-dimensional unsteady model of the ocean surface mixed layer. Themodel somewhat resembles the approach of Munk and Anderson in that the differential equations for meanvelocity and temperature are solved. The Richardson-number-dependent stability functions which enterthe model are significantly different, however, as is the fact that we are able to solve problems with realisticboundary conditions. Furthermore, all empirical constants have been determined from neutral turbulentflow experiments.
Comparisons of prediction and data are favorable.
Abstract
The present paper describes a one-dimensional unsteady model of the ocean surface mixed layer. Themodel somewhat resembles the approach of Munk and Anderson in that the differential equations for meanvelocity and temperature are solved. The Richardson-number-dependent stability functions which enterthe model are significantly different, however, as is the fact that we are able to solve problems with realisticboundary conditions. Furthermore, all empirical constants have been determined from neutral turbulentflow experiments.
Comparisons of prediction and data are favorable.
Abstract
In a recent paper by Mellor et al., it was found that, in two-dimensional (x, z) applications with finite horizontal viscosity and zero diffusivity, the velocity error, associated with the evaluation of horizontal density or pressure gradients on a sigma coordinate grid, prognostically disappeared, leaving behind a small and physically insignificant distortion in the density field. The initial error is numerically consistent in that it decreases as the square of the grid increment size. In this paper, we label this error as a sigma error of the first kind.
In three-dimensional applications, the authors have encountered an error that did not disappear and that has not been understood by us or, apparently, others. This is a vorticity error that is labeled a sigma error of the second kind and is a subject of this paper. Although it does not prognostically disappear, it seems to be tolerably small. To evaluate these numerical errors, the authors have adopted the seamount problem initiated by Beckman and Haidvogel. It represents a stringent test case, as evidenced by their paper, wherein the model is initialized with horizontal isopycnals, zero velocity, and no forcing; then, any velocities that develop must be considered errors.
Two appendices are important adjuncts to the paper, the first providing theoretical confirmation and understanding of the numerical results, and the second delving into additional errors related to horizontal or isosigma diffusion. It is, however, shown that satisfactory numerical solutions are obtained with zero diffusivity.
Abstract
In a recent paper by Mellor et al., it was found that, in two-dimensional (x, z) applications with finite horizontal viscosity and zero diffusivity, the velocity error, associated with the evaluation of horizontal density or pressure gradients on a sigma coordinate grid, prognostically disappeared, leaving behind a small and physically insignificant distortion in the density field. The initial error is numerically consistent in that it decreases as the square of the grid increment size. In this paper, we label this error as a sigma error of the first kind.
In three-dimensional applications, the authors have encountered an error that did not disappear and that has not been understood by us or, apparently, others. This is a vorticity error that is labeled a sigma error of the second kind and is a subject of this paper. Although it does not prognostically disappear, it seems to be tolerably small. To evaluate these numerical errors, the authors have adopted the seamount problem initiated by Beckman and Haidvogel. It represents a stringent test case, as evidenced by their paper, wherein the model is initialized with horizontal isopycnals, zero velocity, and no forcing; then, any velocities that develop must be considered errors.
Two appendices are important adjuncts to the paper, the first providing theoretical confirmation and understanding of the numerical results, and the second delving into additional errors related to horizontal or isosigma diffusion. It is, however, shown that satisfactory numerical solutions are obtained with zero diffusivity.
Abstract
Much has been written of the error in computing the horizontal pressure gradient associated with sigma coordinates in ocean or atmospheric numerical models. There also exists the concept of “hydrostatic inconsistency” whereby, for a given horizontal resolution, increasing the vertical resolution may not be numerically convergent.
In this paper, it is shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size. Furthermore, it is shown that the pressure gradient error is advectively eliminated after a long time integration. At the other extreme, it is shown that diagnostic calculations of the North Atlantic Ocean using rather coarse resolution, and where the temperature and salinity and the pressure gradient error are held constant, do not exhibit significant differences when compared to a calculation where horizontal pressure gradients are computed on z-level coordinates. Finally, a way of canceling the error ab initio is suggested.
Abstract
Much has been written of the error in computing the horizontal pressure gradient associated with sigma coordinates in ocean or atmospheric numerical models. There also exists the concept of “hydrostatic inconsistency” whereby, for a given horizontal resolution, increasing the vertical resolution may not be numerically convergent.
In this paper, it is shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size. Furthermore, it is shown that the pressure gradient error is advectively eliminated after a long time integration. At the other extreme, it is shown that diagnostic calculations of the North Atlantic Ocean using rather coarse resolution, and where the temperature and salinity and the pressure gradient error are held constant, do not exhibit significant differences when compared to a calculation where horizontal pressure gradients are computed on z-level coordinates. Finally, a way of canceling the error ab initio is suggested.
Abstract
Rotational effects on turbulence structure and mixing are investigated using a second-moment closure model. Both explicit and implicit Coriolis terms are considered. A general criterion for rotational effects to be small is established in terms of local turbulent Rossby numbers. Characteristic length scales are determined for rotational effects and Monin–Obukhov type similarity theory is developed for rotating stratified flows. A one-dimensional version of the closure model is then applied to simulate oceanic mixed layer evolution. It is shown that the effects of rotation on mixed layer depth tend to be small because of the influence of stable stratification. These findings contradict a hypothesis of Garwood et al. that rotational effects on turbulence are responsible for the disparity in the mixed-layer depths between the eastern and western regions of the equatorial Pacific Ocean. The model is also applied to neutrally stratified flows to demonstrate that rotation can either stabilize or destabilize the flow.
Abstract
Rotational effects on turbulence structure and mixing are investigated using a second-moment closure model. Both explicit and implicit Coriolis terms are considered. A general criterion for rotational effects to be small is established in terms of local turbulent Rossby numbers. Characteristic length scales are determined for rotational effects and Monin–Obukhov type similarity theory is developed for rotating stratified flows. A one-dimensional version of the closure model is then applied to simulate oceanic mixed layer evolution. It is shown that the effects of rotation on mixed layer depth tend to be small because of the influence of stable stratification. These findings contradict a hypothesis of Garwood et al. that rotational effects on turbulence are responsible for the disparity in the mixed-layer depths between the eastern and western regions of the equatorial Pacific Ocean. The model is also applied to neutrally stratified flows to demonstrate that rotation can either stabilize or destabilize the flow.
Abstract
A second-moment, turbulence closure model is applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. In the case of ice moving over a warm, ocean surface layer, melting is intrinsically a transient process; that is, melting is rapid when warm surface water initially contacts the ice. Then the process slows when surface water is insulated from deeper water due to the stabilizing effect of the melt water, and the thermal energy stored in the surface layer is depleted. Effectively, the same process prevails when ocean surface water flows under stationary ice in which case, after an initial rapid increase, the melting process decreases with downstream distance. Accompanying the stabilizing effect of the melt water is a reduction in the ice-seawater interfacial shear stress. This process and model simulators are used to explain field observations wherein ice near the marginal ice zone diverges from the main pack.
When the surface ice layer is made to grow by imposing heat conduction through the ice, the surface ocean layer is destabilized by brine rejection and mixing in the water column is enhanced. The heat flux into the water column is a small percentage of the heat conduction through the ice.
Abstract
A second-moment, turbulence closure model is applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. In the case of ice moving over a warm, ocean surface layer, melting is intrinsically a transient process; that is, melting is rapid when warm surface water initially contacts the ice. Then the process slows when surface water is insulated from deeper water due to the stabilizing effect of the melt water, and the thermal energy stored in the surface layer is depleted. Effectively, the same process prevails when ocean surface water flows under stationary ice in which case, after an initial rapid increase, the melting process decreases with downstream distance. Accompanying the stabilizing effect of the melt water is a reduction in the ice-seawater interfacial shear stress. This process and model simulators are used to explain field observations wherein ice near the marginal ice zone diverges from the main pack.
When the surface ice layer is made to grow by imposing heat conduction through the ice, the surface ocean layer is destabilized by brine rejection and mixing in the water column is enhanced. The heat flux into the water column is a small percentage of the heat conduction through the ice.
Abstract
In an earlier paper, a second-moment turbulence closure model was applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. An overly simplistic parameterization of the molecular sublayers of temperature and salinity within the mixed layer was used. This paper investigates the use of a more recent parameterization by Yaglom and Kader which is supported by laboratory data. A relatively low melt rate results in the case where ice overlays warm water. This agrees with some recent observations in the interior of the marginal ice zone.
A surface heat sink drives the freezing case which, due to the large difference in heat and salt molecular diffusivities, produces a strong supercooling effect. This is converted into an estimate of frazil ice production through a simple scheme. The model results provide an explanation for high frazil ice concentrations observed in the Arctic and Antarctic.
Abstract
In an earlier paper, a second-moment turbulence closure model was applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. An overly simplistic parameterization of the molecular sublayers of temperature and salinity within the mixed layer was used. This paper investigates the use of a more recent parameterization by Yaglom and Kader which is supported by laboratory data. A relatively low melt rate results in the case where ice overlays warm water. This agrees with some recent observations in the interior of the marginal ice zone.
A surface heat sink drives the freezing case which, due to the large difference in heat and salt molecular diffusivities, produces a strong supercooling effect. This is converted into an estimate of frazil ice production through a simple scheme. The model results provide an explanation for high frazil ice concentrations observed in the Arctic and Antarctic.
U.S. Weather Research Program (USWRP) prospectus development teams (PDTs) are small groups of scientists that are convened by the USWRP lead scientist on a one-time basis to discuss critical issues and to provide advice related to future directions of the program. PDTs are a principal source of information for the Science Advisory Committee, which is a standing committee charged with the duty of making recommendations to the Program Office based upon overall program objectives. PDT-1 focused on theoretical issues, and PDT-2 on observational issues; PDT-3 is the first of several to focus on more specialized topics. PDT-3 was convened to identify forecasting problems related to U.S. coastal weather and oceanic conditions, and to suggest likely solution strategies.
There were several overriding themes that emerged from the discussion. First, the lack of data in and over critical regions of the ocean, particularly in the atmospheric boundary layer, and the upper-ocean mixed layer were identified as major impediments to coastal weather prediction. Strategies for data collection and dissemination, as well as new instrument implementation, were discussed. Second, fundamental knowledge of air–sea fluxes and boundary layer structure in situations where there is significant mesoscale variability in the atmosphere and ocean is needed. Companion field studies and numerical prediction experiments were discussed. Third, research prognostic models suggest that future operational forecast models pertaining to coastal weather will be high resolution and site specific, and will properly treat effects of local coastal geography, orography, and ocean state. The view was expressed that the exploration of coupled air-sea models of the coastal zone would be a particularly fruitful area of research. PDT-3 felt that forecasts of land-impacting tropical cyclones, Great Lakes-affected weather, and coastal cyclogenesis, in particular, would benefit from such coordinated modeling and field efforts. Fourth, forecasting for Arctic coastal zones is limited by our understanding of how sea ice forms. The importance of understanding air-sea fluxes and boundary layers in the presence of ice formation was discussed. Finally, coastal flash flood forecasting via hydrologic models is limited by the present accuracy of measured and predicted precipitation and storm surge events. Strategies for better ways to improve the latter were discussed.
U.S. Weather Research Program (USWRP) prospectus development teams (PDTs) are small groups of scientists that are convened by the USWRP lead scientist on a one-time basis to discuss critical issues and to provide advice related to future directions of the program. PDTs are a principal source of information for the Science Advisory Committee, which is a standing committee charged with the duty of making recommendations to the Program Office based upon overall program objectives. PDT-1 focused on theoretical issues, and PDT-2 on observational issues; PDT-3 is the first of several to focus on more specialized topics. PDT-3 was convened to identify forecasting problems related to U.S. coastal weather and oceanic conditions, and to suggest likely solution strategies.
There were several overriding themes that emerged from the discussion. First, the lack of data in and over critical regions of the ocean, particularly in the atmospheric boundary layer, and the upper-ocean mixed layer were identified as major impediments to coastal weather prediction. Strategies for data collection and dissemination, as well as new instrument implementation, were discussed. Second, fundamental knowledge of air–sea fluxes and boundary layer structure in situations where there is significant mesoscale variability in the atmosphere and ocean is needed. Companion field studies and numerical prediction experiments were discussed. Third, research prognostic models suggest that future operational forecast models pertaining to coastal weather will be high resolution and site specific, and will properly treat effects of local coastal geography, orography, and ocean state. The view was expressed that the exploration of coupled air-sea models of the coastal zone would be a particularly fruitful area of research. PDT-3 felt that forecasts of land-impacting tropical cyclones, Great Lakes-affected weather, and coastal cyclogenesis, in particular, would benefit from such coordinated modeling and field efforts. Fourth, forecasting for Arctic coastal zones is limited by our understanding of how sea ice forms. The importance of understanding air-sea fluxes and boundary layers in the presence of ice formation was discussed. Finally, coastal flash flood forecasting via hydrologic models is limited by the present accuracy of measured and predicted precipitation and storm surge events. Strategies for better ways to improve the latter were discussed.
