Wind effects on the water in a narrow two-layered lake. Part I. Theoretical analysis. Part II. Analysis of observations from Windermere. Part III. Application of the theory to Windermere

1966 ◽  
Vol 259 (1102) ◽  
pp. 391-430 ◽  
Keyword(s):  
Wind Stress ◽  
Water Surface ◽  
Water Movement ◽  
Lower Layer ◽  
Longitudinal Section ◽  
Bottom Friction ◽  
Bottom Current ◽  
Numerical Application ◽  
Warm Surface Water ◽  
Temperature Observations

This paper presents a theoretical study of water movement in a long narrow lake subject to wind action during the summer season of thermal stratification. A model basin of uniform depth and width, consisting of two homogeneous layers of slightly different density, is considered. The motion of the water is assumed to be two dimensional in the vertical longitudinal section; geostrophic effects are ignored. The top and bottom layers in the model respectively represent the relatively warm surface water and the colder bottom water in the natural lake. Hydrodynamical equations are formulated in terms of the currents in the upper and lower layers, the elevation of the interface between the layers, and the elevation of the water surface. Solutions are sought to determine the dynamic response of the basin to an instantaneous rise in the wind stress applied tangentially over the surface. Three cases are considered corresponding to different frictional conditions at the bottom of the basin: (i) bottom friction zero, (ii) bottom friction proportional to the depth mean of the horizontal current in the lower layer, (iii) bottom current zero. It is assumed that internal friction is zero at the interface between the layers (this interface corresponds to the thermocline boundary in reality). Results obtained show that in the motion of the water there are ordinary and internal seiches characteristic of the two-layered model, together with a wind-driven circulation in the top layer. The theory is applied to determine vertical oscillations of the thermocline in an actual lake (Windermere) at one station, in response to a succession of wind pulses representing actual wind conditions over the lake. The oscillations thus obtained from theory compare satisfactorily with those derived from temperature observations taken in the lake. Depth-mean currents in the lake are deduced from theory, but there are no current measurements against which these values may be tested. The paper is divided into three parts. Part I deals with the development of the theory. Part II gives an account of actual physical conditions in Windermere, describing the analysis of temperature observations taken in the lake (yielding thermocline movements) and the analysis of wind records (yielding corresponding values of wind stress over the water surface). Part III is concerned with the numerical application of the theory to Windermere (under conditions described in part II), and gives general conclusions resulting from the entire work.

On the Role of Bottom Pressure Torques in Wind-Driven Gyres

2021 ◽  
Vol 51 (5) ◽  
pp. 1441-1464
Author(s):  
Andrew L. Stewart ◽  
James C. McWilliams ◽  
Aviv Solodoch
Keyword(s):  
Wind Stress ◽  
Bottom Friction ◽  
Bottom Pressure ◽  
Wind Stress Curl ◽  
Previous Theory ◽  
Model Experiments ◽  
Basin Scale ◽  
Vorticity Budget ◽  
Gyre Circulation

AbstractPrevious studies have concluded that the wind-input vorticity in ocean gyres is balanced by bottom pressure torques (BPT), when integrated over latitude bands. However, the BPT must vanish when integrated over any area enclosed by an isobath. This constraint raises ambiguities regarding the regions over which BPT should close the vorticity budget, and implies that BPT generated to balance a local wind stress curl necessitates the generation of a compensating, nonlocal BPT and thus nonlocal circulation. This study aims to clarify the role of BPT in wind-driven gyres using an idealized isopycnal model. Experiments performed with a single-signed wind stress curl in an enclosed, sloped basin reveal that BPT balances the winds only when integrated over latitude bands. Integrating over other, dynamically motivated definitions of the gyre, such as barotropic streamlines, yields a balance between wind stress curl and bottom frictional torques. This implies that bottom friction plays a nonnegligible role in structuring the gyre circulation. Nonlocal bottom pressure torques manifest in the form of along-slope pressure gradients associated with a weak basin-scale circulation, and are associated with a transition to a balance between wind stress and bottom friction around the coasts. Finally, a suite of perturbation experiments is used to investigate the dynamics of BPT. To predict the BPT, the authors extend a previous theory that describes propagation of surface pressure signals from the gyre interior toward the coast along planetary potential vorticity contours. This theory is shown to agree closely with the diagnosed contributions to the vorticity budget across the suite of model experiments.

Laboratory studies of wind–wave interactions

1968 ◽  
Vol 34 (1) ◽  
pp. 91-111 ◽  
Author(s):  
Jin Wu
Keyword(s):  
Surface Roughness ◽  
Wind Stress ◽  
Water Surface ◽  
Wind Wave ◽  
Wave Drag ◽  
Average Height ◽  
Drift Current ◽  
Stress Coefficient ◽  
Wide Range ◽  
Wind Velocities

The present study consists of wind profile surveys, drift current measurements and water surface observations for a wide range of wind velocities in a wind–wave tank. It is confirmed that the velocity distribution essentially follows the logarithmic law near the water surface and the velocity-defect law toward the outer edge of the boundary layer. The wind stresses and surface roughnesses calculated from these distributions are divided into two groups separated by the occurrence of the wave-breaking phenomenon. For low wind velocities the surface roughness is dictated by ripples, and the wind-stress coefficient varies with U0−½, where U0 is the free-stream wind velocity. The surface roughness is proportional to the average height of the basic gravity wave at higher wind velocities; the stress coefficient is then proportional to U0. In addition, it is found that Charnock's expression (k ∝ u*2/g) holds only at high wind velocities, and that the constant of proportionality determined from the present experiment correlates very well with field observations. A new technique, involving the use of various-sized surface floats to determine the drift current gradient and the surface drift current, has been developed. A good agreement is shown between the gradients obtained from the measured currents and those determined from the wind stresses. Finally, the wind-stress coefficient is shown to be larger than the friction coefficient for turbulent flow along a solid rough surface; the difference is shown to be the wave drag of the wind over the water surface.

On the Cushioning of Water Impact by Entrapped Air

1968 ◽  
Vol 12 (02) ◽  
pp. 116-130 ◽  
Author(s):  
Grant Lewison ◽  
W. M. Maclean
Keyword(s):  
Free Surface ◽  
Flat Plate ◽  
Water Surface ◽  
Peak Pressure ◽  
Water Movement ◽  
Theoretical Work ◽  
Two Dimensional ◽  
Water Impact ◽  
Entrapped Air

Impact between a rigid flat plate and the free surface of water has been investigated experimentally and theoretically. Under two-dimensional conditions, the experiments give values of peak pressure of the same order as those recorded on ships slamming at sea, but very much smaller than would be expected from existing theories. New theoretical work is presented which takes account of the air trapped between the model and the water surface, and of both compressible and incompressible water movement. This shows good general agreement with the experiments, though further work is needed to confirm some of the assumptions made.

Effects of the sea state in the momentum flux over the ocean atmosphere interface

2020 ◽  
Author(s):  
Diego Larios ◽  
Francisco J. Ocampo-Torres ◽  
Pedro Osuna
Keyword(s):  
Wind Stress ◽  
Momentum Flux ◽  
Roughness Length ◽  
Lower Layer ◽  
Wind Waves ◽  
Surface Wind ◽  
Direct Interaction ◽  
Sea State ◽  
Surface Wind Stress ◽  
Wind Sea

<p>The sea surface wind stress is relevant in processes of different scales of space and time such as the exchange of gases and heat, the surface currents, the depth of the mixed layer, the turbulence injection into the ocean. The wind waves are the key component in the coupling of the lower layer of the the atmosphere and the surface layer of the ocean, and various studies have shown the direct and indirect effects on the surface wind stress. In the present study, we present the measurements of the momentum flux and the results meteorological variables at the interface between the ocean and the atmosphere, by using and Oceanographic and Marine Meteorology Buoy (BOMM1) between November 2017 and February 2018. The analysis of the results during moderate wind conditions (U<sub>10N</sub> > 8 ms<sup>-1</sup>) in which mixed sea state conditions occur (swell that interacts with locally generated wind waves) we found a decrease of the roughness length (z<sub>0</sub>), related to developing waves with higher steepness (<em>ak</em>), the data suggest that the presence of swell alters the wind sea part of the spectrum, which leads a reduction of the energy level of the wind-generated waves, hence reducing the wind sea associated roughness. For well developed waves conditions, the roughness length is greater than the parametrization proposed by Drennan <em>al</em>., (2003) for pure wind sea conditions, the data suggest that this is due direct interaction of the wind airflow and swell with higher steepness.  The data of this work suggests that during these conditions (U<sub>10N</sub> > 8 ms<sup>-1</sup>) , the mechanism of reduction of the drag of the wind sea due to the presence of swell, and the increase of the wind stress by direct interaction of swell with the airflow causes the net effect of wave field to behave as expected under pure wind sea conditions, and there seems to be no swell effect.</p>

Nonlinear and time-dependent equivalent-barotropic flows

2019 ◽  
Vol 871 ◽  
pp. 925-951 ◽  
Author(s):  
Luis Zavala Sansón
Keyword(s):  
Wind Stress ◽  
Vertical Structure ◽  
Fluid Velocity ◽  
Bottom Topography ◽  
Bottom Friction ◽  
Time Dependent ◽  
Western Slope ◽  
Topographic Effects ◽  
Specific Level ◽  
Variable Topography

Some oceanic and atmospheric flows may be modelled as equivalent-barotropic systems, in which the horizontal fluid velocity varies in magnitude at different vertical levels while keeping the same direction. The governing equations at a specific level are identical to those of a homogeneous flow over an equivalent depth, determined by a pre-defined vertical structure. The idea was proposed by Charney (J. Met., vol. 6 (6), 1949, pp. 371–385) for modelling a barotropic atmosphere. More recently, steady, linear formulations have been used to study oceanic flows. In this paper, the nonlinear, time-dependent model with variable topography is examined. To include nonlinear terms, we assume suitable approximations and evaluate the associated error in the dynamical vorticity equation. The model is solved numerically to investigate the equivalent-barotropic dynamics in comparison with a purely barotropic flow. We consider three problems in which the behaviour of homogeneous flows has been well established either experimentally, analytically or observationally in past studies. First, the nonlinear evolution of cyclonic vortices around a topographic seamount is examined. It is found that the vortex drift induced by the mountain is modified according to the vertical structure of the flow. When the vertical structure is abrupt, the model effectively isolates the surface flow from both inviscid and viscous topographic effects (due to the shape of the bottom and Ekman friction, respectively). Second, the wind-driven flow in a closed basin with variable topography is studied (for a flat bottom this is the well-known Stommel problem). For a zonally uniform, negative wind-stress curl in the homogeneous case, a large-scale, anticyclonic gyre is formed and displaced southward due to topographic effects at the western slope of the basin. The flow reaches a steady state due to the balance between topographic,$\unicode[STIX]{x1D6FD}$, wind-stress and bottom friction effects. However, in the equivalent-barotropic simulations with abrupt vertical structure, such an equilibrium cannot be reached because the forcing effects at the surface are enhanced, while bottom friction effects are reduced. As a result, the unsteady flow is decomposed as a set of planetary waves. A third problem consists of performing simulations of the wind-driven flow over realistic bottom topography in the Gulf of Mexico. The formation of the so-called Campeche gyre is explored. It is found that such circulation may be consistent with the equivalent-barotropic dynamics.

The Injection of Zonal Momentum by Buoyancy Forcing in a Southern Ocean Model

2015 ◽  
Vol 45 (1) ◽  
pp. 259-271 ◽  
Author(s):  
Emma Howard ◽  
Andrew McC. Hogg ◽  
Stephanie Waterman ◽  
David P. Marshall
Keyword(s):  
Southern Ocean ◽  
Wind Stress ◽  
Volume Transport ◽  
Ocean Model ◽  
Bottom Friction ◽  
Meridional Overturning Circulation ◽  
Overturning Circulation ◽  
Buoyancy Forcing ◽  
Momentum Budget ◽  
Zonal Momentum

AbstractAn overturning circulation, driven by prescribed buoyancy forcing, is used to set a zonal volume transport in a reentrant channel ocean model with three isopycnal layers. The channel is designed to represent the Southern Ocean such that the forced overturning resembles the lower limb of the meridional overturning circulation (MOC). The relative contributions of wind and buoyancy forcing to the zonal circulation are examined. It is found that the zonal volume transport is strongly dependent on the buoyancy forcing and that the eddy kinetic energy is primarily set by wind stress forcing. The zonal momentum budget integrated over each layer is considered in the buoyancy-forced, wind-forced, and combined forcing case. At equilibrium, sources and sinks of momentum are balanced, but the transient spinup reveals the source of momentum for the current. In the buoyancy-forced case, the forcing creates a baroclinic shear with westward flow in the lower layer, allowing topographic form stress and bottom friction to act as the initial sources of eastward momentum, with bottom friction acting over a longer time frame. In the wind-forced and combined forcing cases, the surface wind stress dominates the initial momentum budget, and the time to reach equilibration is shorter in the combined forcing simulation. These results imply that future changes in the rate of formation of Antarctic Bottom Water may alter the volume transport of the Antarctic Circumpolar Current.

A two-layer model of Gulf Stream separation

1969 ◽  
Vol 39 (3) ◽  
pp. 511-528 ◽  
Author(s):  
A. T. Parsons
Keyword(s):  
Wind Stress ◽  
Gulf Stream ◽  
Stream Flow ◽  
Lower Layer ◽  
Western Boundary ◽  
Boundary Current ◽  
Layer Model ◽  
Layer Depth ◽  
Boundary Currents ◽  
Two Layer Model

A study is made of the wind-driven circulation of a two-layer ocean within a square basin, with a view to describing the observed separation of western boundary currents. The lower layer is allowed to surface and the line along which the upper-layer depth vanishes is interpreted as the region of the surfacing thermocline. For a representative wind stress the theory predicts the gross features of the Gulf Stream flow, the region adjacent to the surfacing line containing the separated boundary current. By assuming that the effects of friction and inertia are confined to regions of a boundary-layer character, the position of a separated current is shown to depend only on the degree of stratification and certain integral properties of the applied wind stress.

STUDIES ON THE RELATIONSHIP BETWEEN WATER MOVEMENT AND WATER CHEMISTRY IN MIRES

1966 ◽  
Vol 44 (6) ◽  
pp. 747-758 ◽  
Author(s):  
J. H. Sparling
Keyword(s):  
Water Chemistry ◽  
Oxygen Concentration ◽  
Flow Rate ◽  
Water Surface ◽  
Water Movement ◽  
Simple Diffusion ◽  
Flow Rates ◽  
Acidic Conditions ◽  
The Relationship ◽  
Iron And Manganese

Fifty-four sites were selected in a number of mires in Ontario, and rates of water movement were measured on a number of occasions. The rates of water movement ranged from less than 0.1 cm sec−1 to over 8 cm sec−1. The oxygen concentration of the mire waters increased with increasing flow rate, approaching saturation at rates over 1 cm sec−1. From a model it was shown that at a flow rate of less than 0.3–0.4 cm sec−1 the diffusion of oxygen into the water would be similar to simple diffusion into a stationary water surface, and because of the respiration of roots and microorganisms in the peat, the oxygen would tend to be depleted. Above flow rates of 0.4 cm sec−1 the water is agitated, and is continually replenished with oxygen from the atmosphere. Reduced states of iron and manganese were shown to be in solution at concentrations greater than 0.1 mg/1 only at low rates of water flow. The pH was also shown to increase with faster rates of water movement, the increase depending on the base status of the mire. Aluminium is in solution only in situations of low water movement where more acidic conditions are prevalent.

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