scholarly journals Complex EOF Analysis as a Method to Separate Barotropic and Baroclinic Velocity Structure in Shallow Water

2008 ◽  
Vol 25 (5) ◽  
pp. 808-821 ◽  
Author(s):  
Catherine R. Edwards ◽  
Harvey E. Seim
Keyword(s):  
Boundary Layer ◽  
Shallow Water ◽  
Internal Structure ◽  
Internal Tide ◽  
Tidal Currents ◽  
Tidal Dynamics ◽  
Bottom Boundary ◽  
Bottom Boundary Layers ◽  
Baroclinic Modes ◽  
Ceof Analysis

Abstract Defining the vertical depth average of measured currents to be barotropic is a widely used method of separating barotropic and baroclinic tidal currents in the ocean. Away from the surface and bottom boundary layers, depth-averaging measured velocity is an excellent estimate of barotropic tidal flow, and internal tidal dynamics can be well represented by the difference between the measured currents and their depth average in the vertical. However, in shallow and/or energetic tidal environments such as the shelf of the South Atlantic Bight (SAB), bottom boundary layers can occupy a significant fraction of the water column, and depth averaging through the bottom boundary layer can overestimate the barotropic current by several tens of centimeters per second near bottom. The depth-averaged current fails to capture the bottom boundary layer structure associated with the barotropic tidal signal, and the resultant estimate of baroclinic tidal currents can mimic a bottom-trapped internal tide. Complex empirical orthogonal function (CEOF) analysis is proposed as a method to retain frictional effects in the estimate of the barotropic tidal currents and allow an improved determination of the baroclinic currents. The method is applied to a midshelf region of the SAB dominated by tides and friction to quantify the effectiveness of CEOF analysis to represent internal structure underlying a strong barotropic signal in shallow water. Using examples of synthesized and measured data, EOF estimates of the barotropic and baroclinic modes of motion are compared to those made using depth averaging. The estimates of barotropic tidal motion using depth-averaging and CEOF methods produce conflicting predictions of the frequencies at which there is meaningful baroclinic variability. The CEOF method preserves the frictional boundary layer as part of the barotropic tidal current structure in the gravest mode, providing a more accurate representation of internal structure in higher modes. The application of CEOF techniques to isolate internal structure co-occurring with highly energetic tidal dynamics in shallow water is a significant test of the method. Successful separation of barotropic and baroclinic modes of motion suggests that, by fully capturing the effects of friction associated with the barotropic tide, CEOF analysis is a viable technique to facilitate examination of the internal tide in similar environments.

scholarly journals NUMERICAL MODELING OF A TURBULENT BOTTOM BOUNDARY LAYER UNDER SOLITARY WAVES ON A SMOOTH SURFACE

2018 ◽  
pp. 26
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Solitary Waves ◽  
Bottom Boundary Layer ◽  
Stream Velocity ◽  
Bottom Boundary ◽  
Sediment Movement ◽  
Bottom Boundary Layers ◽  
Turbulent Models

A number of studies on bottom boundary layers under sinusoidal and cnoidal waves were carried out in the past owing to the role of bottom shear stress on coastal sediment movement. In recent years, the bottom boundary layers under long waves have attracted considerable attention due to the occurrence of huge tsunamis and corresponding sediment movement. In the present study two-equation turbulent models proposed by Menter(1994) have been applied to a bottom boundary layer under solitary waves. A comparison has been made for cross-stream velocity profile and other turbulence properties in x-direction.

scholarly journals Boundary Layer Forcing of a Semidiurnal, Cross-Channel Seiche

2005 ◽  
Vol 35 (9) ◽  
pp. 1518-1537 ◽  
Author(s):  
Wayne Martin ◽  
Parker MacCready ◽  
Richard Dewey
Keyword(s):  
Boundary Layer ◽  
Numerical Models ◽  
Internal Tide ◽  
Tidal Currents ◽  
Tidal Mixing ◽  
Bottom Boundary Layer ◽  
Salt Balance ◽  
Juan De Fuca ◽  
Similar Mode ◽  
Northern Side

Abstract The outer Strait of Juan de Fuca is a stratified, tidal channel about 100 km long, 20 km wide, and 200 m deep. Tidal currents of O(0.5 m s−1) occur at both diurnal and semidiurnal periods and there is a pronounced spring–neap variation in the stratification due to changes in tidal mixing. Vertical isotherm excursions of O(50 m) have previously been observed along the northern side of the channel that appear to be phase locked to the tidal currents. Analyses of recent ADCP and thermistor chain data confirm the isotherm excursions and find that they are accompanied by distinctive baroclinic structures in the horizontal currents that persist across spring–neap cycles, and from year to year. The authors find that the phase of the semidiurnal signal does not vary along the channel, as would be expected of an along-channel internal tide. Instead, comparison of the semidiurnal measurements with two-dimensional analytical and numerical models indicate that much of the baroclinic structure can be explained as a cross-channel, internal seiche that is locally driven by reversing Ekman forcing in the bottom boundary layer. Near the bottom, the vertical motions are kinematic, resulting primarily from cross-channel flow on the side slopes. In the middepths, the seiche appears to explain part but not all of the vertical motions. The seiche appears to persist and to maintain a similar mode shape across large, O(2), changes in stratification. In Juan de Fuca, it is expected that these motions affect the overall salt balance of the system by enhancing mixing between the upper and lower layers of the estuary.

Non linear shallow water modelling of bore-driven swash: Description of the bottom boundary layer

2011 ◽  
Vol 58 (6) ◽  
pp. 463-477 ◽  
Author(s):  
Riccardo Briganti ◽  
Nicholas Dodd ◽  
Dubravka Pokrajac ◽  
Tom O'Donoghue
Keyword(s):  
Boundary Layer ◽  
Shallow Water ◽  
Bottom Boundary Layer ◽  
Bottom Boundary ◽  
Non Linear

scholarly journals Turbulence Asymmetries in Bottom Boundary Layer Velocity Pulses Associated with Onshore-Propagating Nonlinear Internal Waves

2020 ◽  
Vol 50 (8) ◽  
pp. 2373-2391 ◽  
Author(s):  
Johannes Becherer ◽  
James N. Moum ◽  
John A. Colosi ◽  
James A. Lerczak ◽  
Jacqueline M. McSweeney
Keyword(s):  
Internal Waves ◽  
Residence Time ◽  
Surf Zone ◽  
Internal Tide ◽  
Inner Shelf ◽  
Bottom Boundary ◽  
Nonlinear Internal Waves ◽  
Leading Role ◽  
Bottom Boundary Layers ◽  
Shelf Region

AbstractThe inner shelf is a region inshore of that part of the shelf that roughly obeys Ekman dynamics and offshore of the surf zone. Importantly, this is where surface and bottom boundary layers are in close proximity, overlap, and interact. The internal tide carries a substantial amount of energy into the inner shelf region were it eventually dissipates and contributes to mixing. A part of this energy transformation is due to a complex interaction with the bottom, where distinctions between nonlinear internal waves of depression and elevation are blurred, indeed, where polarity reversals of incoming waves take place. From an intensive set of measurements over the inner shelf off central California, we identify salient differences between onshore pulses from waves with properties of elevation waves and offshore pulses from shallowing depression waves. While the velocity structures and amplitudes of on/offshore pulses 1 m above the seafloor are not detectably different, onshore pulses are both more energetically turbulent and carry more sediments than offshore pulses. Their turbulence is also oppositely skewed: onshore pulses slightly to the leading edges, offshore pulses to the trailing edges of the pulses. We consider in turn three independent mechanisms that may contribute to the observed asymmetry: propagation in adverse pressure gradients and the resultant inflection point instability, residence time of a fluid parcel in the pulse, and turbulence suppression by stratification. The first mechanism may largely explain higher turbulence in the trailing edge of offshore pulses. The extended residence time may be responsible for the high and more uniform turbulence distribution across onshore compared to offshore pulses. Stratification does not play a leading role in turbulence modification inside of the pulses 1 m above the bed.

scholarly journals MODELING TURBULENT BOTTOM BOUNDARY LAYER DYNAMICS

1986 ◽  
Vol 1 (20) ◽  
pp. 110 ◽  
Author(s):  
Y.P. Sheng
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Boundary Layers ◽  
Turbulent Transport ◽  
Complex Problem ◽  
Comprehensive Model ◽  
Bottom Boundary ◽  
Bottom Boundary Layers ◽  
Dimensional Boundary ◽  
Boundary Layer Dynamics

This paper presents a modeling approach aimed at solving a complete hierarchy of turbulent bottom boundary layers which are often encountered in practical coastal and oceanographic engineering problems. The practical problem is extremely complex due to the presence and interaction of competing processes. A comprehensive model is thus needed to first provide fundamental understanding of a variety of turbulent bottom boundary layers before any simple model for the complex problem can be meaningfully constructed. This paper presents a comprehensive second-order closure model of turbulent transport and in addition, discusses some applications of the model to wave boundary layer, wave-current boundary layer, sediment-laden boundary layer and two-dimensional boundary layer. Example is provided to show how such a comprehensive model may be used to guide the development of a simple model.

Overturning and Dissipation Caused by Baroclinic Tidal Flow near the Sill of a Fjord Basin

2009 ◽  
Vol 39 (9) ◽  
pp. 2156-2174 ◽  
Author(s):  
Lars Arneborg ◽  
Bengt Liljebladh
Keyword(s):  
Boundary Layer ◽  
Time Series ◽  
Large Fraction ◽  
Internal Tide ◽  
Bottom Layer ◽  
Internal Tides ◽  
Bottom Boundary Layer ◽  
Transitional Flow ◽  
Mixing Efficiency ◽  
Bottom Boundary

Abstract Dissipation time series and moored velocity and density time series on the inner slopes of the Gullmar Fjord sill showed that the internal tides generated at the sill radiated to the head of the fjord, were reflected, and then radiated back to the sill, where they dissipated their energy mainly below sill level. A large amount of the dissipation was caused by a transitional flow at a particular phase of the internal tide, when the bottom layer descended down the sill slope and had to pass a constriction set up by a submarine hill. The inward, baroclinic bottom-layer flow transformed into a supercritical bottom jet, which separated from the bottom just downstream of the constriction. A large fraction of the dissipation took place in the successive rebounding region (the hydraulic jump) above the bottom jet, where overturns of the same size as the vertical extent of the rebounding region were observed. More than half of the dissipation was happening in the bottom boundary layer below the jet. During the transitional flow, there were clear pulsations of the jet with periods of about 15 min. The amount of diapycnal mixing caused by the turbulence was reduced by the large fraction of dissipation within the bottom boundary layer and perhaps also by the high-buoyancy Reynolds numbers within the rebounding region. When using a relatively new parameterization of mixing, the mixing was significantly reduced compared to using the traditional constant mixing efficiency method.

Langmuir turbulence in shallow water. Part 2. Large-eddy simulation

2007 ◽  
Vol 576 ◽  
pp. 63-108 ◽  
Author(s):  
A. E. TEJADA-MARTÍNEZ ◽  
C. E. GROSCH
Keyword(s):  
Boundary Layer ◽  
Shallow Water ◽  
Reynolds Stress ◽  
Bottom Boundary Layer ◽  
Reynolds Stresses ◽  
Component Structure ◽  
Bottom Boundary ◽  
Eddy Simulation ◽  
Shear Current ◽  
Anisotropy Tensor

Results of large-eddy simulation (LES) of Langmuir circulations (LC) in a wind-driven shear current in shallow water are reported. The LC are generated via the well-known Craik–Leibovich vortex force modelling the interaction between the Stokes drift, induced by surface gravity waves, and the shear current. LC in shallow water is defined as a flow in sufficiently shallow water that the interaction between the LC and the bottom boundary layer cannot be ignored, thus requiring resolution of the bottom boundary layer. After the introduction and a description of the governing equations, major differences in the statistical equilibrium dynamics of wind-driven shear flow and the same flow with LC (both with a bottom boundary layer) are highlighted. Three flows with LC will be discussed. In the first flow, the LC were generated by intermediate-depth waves (relative to the wavelength of the waves and the water depth). The amplitude and wavelength of these waves are representative of the conditions reported in the observations of A. E. Gargett & J. R. Wells in Part 1 (J. Fluid Mech. vol .000, 2007, p. 00). In the second flow, the LC were generated by shorter waves. In the third flow, the LC were generated by intermediate waves of greater amplitude than those in the first flow. The comparison between the different flows relies on visualizations and diagnostics including (i) profiles of mean velocity, (ii) profiles of resolved Reynolds stress components, (iii) autocorrelations, (iv) invariants of the resolved Reynolds stress anisotropy tensor and (v) balances of the transport equations for mean resolved turbulent kinetic energy and resolved Reynolds stresses. Additionally, dependencies of LES results on Reynolds number, subgrid-scale closure, size of the domain and grid resolution are addressed.In the shear flow without LC, downwind (streamwise) velocity fluctuations are characterized by streaks highly elongated in the downwind direction and alternating in sign in the crosswind (spanwise) direction. Forcing this flow with the Craik–Leibovich force generating LC leads to streaks with larger characteristic crosswind length scales consistent with those recorded by observations. In the flows with LC, in the mean, positive streaks exhibit strong intensification near the bottom and near the surface leading to intensified downwind velocity ‘jets’ in these regions. In the flow without LC, such intensification is noticeably absent. A revealing diagnostic of the structure of the turbulence is the depth trajectory of the invariants of the resolved Reynolds stress anisotropy tensor, which for a realizable flow must lie within the Lumley triangle. The trajectory for the flow without LC reveals the typical structure of shear-dominated turbulence in which the downwind component of the resolved normal Reynolds stresses is greater than the crosswind and vertical components. In the near bottom and surface regions, the trajectory for the flow with LC driven by wave and wind forcing conditions representative of the field observations reveals a two-component structure in which the downwind and crosswind components are of the same order and both are much greater than the vertical component. The two-component structure of the Langmuir turbulence predicted by LES is consistent with the observations in the bottom third of the water column above the bottom boundary layer.

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