scholarly journals Estuarine Boundary Layer Mixing Processes: Insights from Dye Experiments*

2007 ◽  
Vol 37 (7) ◽  
pp. 1859-1877 ◽  
Author(s):  
Robert J. Chant ◽  
Wayne R. Geyer ◽  
Robert Houghton ◽  
Elias Hunter ◽  
James Lerczak
Keyword(s):  
Boundary Layer ◽  
Richardson Number ◽  
Flood Tide ◽  
Buoyancy Flux ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Diapycnal Mixing ◽  
Bottom Boundary ◽  
Shear Production

Abstract A series of dye releases in the Hudson River estuary elucidated diapycnal mixing rates and temporal variability over tidal and fortnightly time scales. Dye was injected in the bottom boundary layer for each of four releases during different phases of the tide and of the spring–neap cycle. Diapycnal mixing occurs primarily through entrainment that is driven by shear production in the bottom boundary layer. On flood the dye extended vertically through the bottom mixed layer, and its concentration decreased abruptly near the base of the pycnocline, usually at a height corresponding to a velocity maximum. Boundary layer growth is consistent with a one-dimensional, stress-driven entrainment model. A model was developed for the vertical structure of the vertical eddy viscosity in the flood tide boundary layer that is proportional to u2*/N∞, where u* and N∞ are the bottom friction velocity and buoyancy frequency above the boundary layer. The model also predicts that the buoyancy flux averaged over the bottom boundary layer is equal to 0.06N∞u2* or, based on the structure of the boundary layer equal to 0.1NBLu2*, where NBL is the buoyancy frequency across the flood-tide boundary layer. Estimates of shear production and buoyancy flux indicate that the flux Richardson number in the flood-tide boundary layer is 0.1–0.18, consistent with the model indicating that the flux Richardson number is between 0.1 and 0.14. During ebb, the boundary layer was more stratified, and its vertical extent was not as sharply delineated as in the flood. During neap tide the rate of mixing during ebb was significantly weaker than on flood, owing to reduced bottom stress and stabilization by stratification. As tidal amplitude increased ebb mixing increased and more closely resembled the boundary layer entrainment process observed during the flood. Tidal straining modestly increased the entrainment rate during the flood, and it restratified the boundary layer and inhibited mixing during the ebb.

Entrainment and mixing in stratified shear flows

2001 ◽  
Vol 428 ◽  
pp. 349-386 ◽  
Author(s):  
E. J. STRANG ◽  
H. J. S. FERNANDO
Keyword(s):  
Internal Waves ◽  
Richardson Number ◽  
Transition Period ◽  
Lower Layer ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Turbulent Eddies

The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.

scholarly journals Stratified Inertial Subrange Inferred from In Situ Measurements in the Bottom Boundary Layer of the Rockall Channel

2010 ◽  
Vol 40 (11) ◽  
pp. 2401-2417 ◽  
Author(s):  
Pascale Bouruet-Aubertot ◽  
Hans van Haren ◽  
M. Pascale Lelong
Keyword(s):  
Boundary Layer ◽  
Energy Levels ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Bottom Boundary Layer ◽  
Inertial Subrange ◽  
Buoyancy Frequency ◽  
Bottom Boundary ◽  
Wide Range ◽  
Taylor Hypothesis

Abstract Deep-ocean high-resolution moored temperature data are analyzed with a focus on superbuoyant frequencies. A local Taylor hypothesis based on the horizontal velocity averaged over 2 h is used to infer horizontal wavenumber spectra of temperature variance. The inertial subrange extends over fairly low horizontal wavenumbers, typically within 2 × 10−3 and 2 × 10−1 cycles per minute (cpm). It is therefore interpreted as a stratified inertial subrange for most of this wavenumber interval, whereas in some cases the convective inertial subrange is resolved as well. Kinetic energy dissipation rate ε is inferred using theoretical expressions for the stratified inertial subrange. A wide range of values within 10−9 and 4 × 10−7 m2 s−3 is obtained for time periods either dominated by semidiurnal tides or by significant subinertial variability. A scaling for ε that depends on the potential energy within the inertio-gravity waves (IGW) frequency band PEIGW and the buoyancy frequency N is proposed for these two cases. When semidiurnal tides dominate, ε ≃ (PEIGWN)3/2, whereas ε ≃ PEIGWN in the presence of significant subinertial variability. This result is obtained for energy levels ranging from 1 to 30 times the Garrett–Munk energy level and is in contrast with classical finescale parameterization in which ε ∼ (PEIGW)2 that applies far from energy sources. The specificities of the stratified bottom boundary layer, namely a weak stratification, may account for this difference.

scholarly journals Buoyancy Arrest and Bottom Ekman Transport. Part II: Oscillating Flow

2010 ◽  
Vol 40 (4) ◽  
pp. 636-655 ◽  
Author(s):  
K. H. Brink ◽  
S. J. Lentz
Keyword(s):  
Boundary Layer ◽  
Mixed Boundary ◽  
Broad Band ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Buoyancy Frequency ◽  
Bottom Boundary ◽  
Bottom Stress ◽  
Interior Flow ◽  
Lower Frequencies

Abstract The effects of a sloping bottom and stratification on a turbulent bottom boundary layer are investigated for cases where the interior flow oscillates monochromatically with frequency ω. At higher frequencies, or small slope Burger numbers s = αN/f (where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter), the bottom boundary layer is well mixed and the bottom stress is nearly what it would be over a flat bottom. For lower frequencies, or larger slope Burger number, the bottom boundary layer consists of a thick, weakly stratified outer layer and a thinner, more strongly stratified inner layer. Approximate expressions are derived for the different boundary layer thicknesses as functions of s and σ = ω/f. Further, buoyancy arrest causes the amplitude of the fluctuating bottom stress to decrease with decreasing σ (the s dependence, although important, is more complicated). For typical oceanic parameters, arrest is unimportant for fluctuation periods shorter than a few days. Substantial positive (toward the right when looking toward deeper water in the Northern Hemisphere) time-mean flows develop within the well-mixed boundary layer, and negative mean flows exist in the weakly stratified outer boundary layer for lower frequencies and larger s. If the interior flow is realistically broad band in frequency, the numerical model predicts stress reduction over all frequencies because of the nonlinearity associated with a quadratic bottom stress. It appears that the present one-dimensional model is reliable only for time scales less than the advective time scale that governs interior stratification.

The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

2009 ◽  
Vol 619 ◽  
pp. 235-259 ◽  
Author(s):  
KEI SAKAMOTO ◽  
KAZUNORI AKITOMO
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Interfacial Layer ◽  
Rapid Development ◽  
Tidal Mixing ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Rotating Frame ◽  
Three Dimensional Model ◽  
Bottom Boundary

To investigate turbulent properties and the developing mechanisms of the tidally induced bottom boundary layer in the linearly stratified ocean, numerical experiments have been executed with a non-hydrostatic three-dimensional model in the rotating frame, changing the temporal Rossby number Rot = |σ/f|, i.e. the ratio of the tidal frequency σ to the Coriolis parameter f. After the flow transitions to turbulence, the entire water column can be characterized by three layers: the mixed layer where density is homogenized and the flow is turbulent (z < zm); the stratified layer where the initial stratification remains and the flow is laminar (z > zt); and the interfacial layer between them where the flow is turbulent but the stratification remains (zm < z < zt). Turbulence is scaled by the frictional velocity uτ and the mixed-layer thickness zm (uτ and uτ/N where N is the buoyancy frequency) in the mixed (interfacial) layer, and has similarity. The mixed layer is thickened by the process where light water of the upper stratified layer is mixed with the lower unstratified layer water through the interfacial layer. As Rot approaches unity, i.e. near the critical latitude, the mixed layer develops more rapidly according to the following mechanism. As becomes Rot closer to unity, the current shear in the interfacial layer is intensified, since the difference of velocity becomes larger between the lower turbulent mixed and upper laminar stratified layers, and this leads to thickening of the interfacial layer. As a result, density deviation of the water entrained from above becomes larger, and this causes more rapid development of the mixed layer. In terms of the energy conversion from the eddy kinetic energy (EKE) to the potential energy (PE), the efficiency factor β which is the ratio of the conversion rate from EKE to PE to that from the tidal shear to EKE increased from 0.25% for Rot = 0.5 to 3.5% for Rot = 1.05 on average. When the time is normalized by the period required for the mixed layer to be thickened to the unstratified turbulent boundary layer δ = uτ/|f+σ|, the mixed layer development occurred in a similar manner in all cases. This similarity suggests the possibility of universal formulation for the turbulent tidal mixing under stratification.

The Scaling and Structure of the Estuarine Bottom Boundary Layer

2005 ◽  
Vol 35 (1) ◽  
pp. 55-71 ◽  
Author(s):  
Mark T. Stacey ◽  
David K. Ralston
Keyword(s):  
Boundary Layer ◽  
Reynolds Stress ◽  
Friction Velocity ◽  
Turbulent Energy ◽  
Buoyancy Flux ◽  
Bottom Boundary Layer ◽  
Stress Profile ◽  
Layer Height ◽  
Bottom Boundary ◽  
Boundary Layer Height

Abstract A two-week dataset from a partially and periodically stratified estuary quantifies variability in the turbulence across the tidal and spring–neap time scales. These observations have been fit with a two-parameter model of the Reynolds stress profile, which produces estimates of the time variation of the bottom boundary layer height and the friction velocity. Conditions at the top of the bottom boundary layer indicate that the dynamics governing the development of the estuarine bottom boundary layer are different on ebb tides than on flood tides. The asymmetry in the flow is explained by consideration of the strain-induced buoyancy flux, which is stabilizing on ebb tides and destabilizing on flood tides. Based on these observations, a scaling approach to estimating estuarine bottom boundary layer parameters (height and friction velocity) is presented, which includes a modified Monin–Obukhov length scale to account for the horizontal buoyancy flux created by the sheared advection. Comparison with the observations of boundary layer height and friction velocity suggests that this approach may be successful in predicting bottom boundary layer parameters in estuaries and coastal regions with significant horizontal buoyancy fluxes. Comparison between the strain-induced buoyancy flux and shear production indicates that the straining of the density field is an important contributor to the turbulent kinetic energy budget and creates an asymmetry in turbulent energy between ebb and flood tides. It appears that the structure of the turbulence, specifically the ratio of the Reynolds stress to the turbulent energy, is also modified by tidal straining, further accentuating the ebb–flood asymmetries.

Vertical Structure of Dissipation in the Nearshore

2007 ◽  
Vol 37 (7) ◽  
pp. 1764-1777 ◽  
Author(s):  
Falk Feddersen ◽  
J. H. Trowbridge ◽  
A. J. Williams
Keyword(s):  
Boundary Layer ◽  
Wave Breaking ◽  
Vertical Structure ◽  
Vertical Shear ◽  
Bottom Boundary Layer ◽  
Breaking Wave ◽  
Vertical Diffusion ◽  
Turbulent Length Scale ◽  
Bottom Boundary ◽  
Shear Production

Abstract The vertical structure of the dissipation of turbulence kinetic energy was observed in the nearshore region (3.2-m mean water depth) with a tripod of three acoustic Doppler current meters off a sandy ocean beach. Surface and bottom boundary layer dissipation scaling concepts overlap in this region. No depth-limited wave breaking occurred at the tripod, but wind-induced whitecapping wave breaking did occur. Dissipation is maximum near the surface and minimum at middepth, with a secondary maximum near the bed. The observed dissipation does not follow a surfzone scaling, nor does it follow a “log layer” surface or bottom boundary layer scaling. At the upper two current meters, dissipation follows a modified deep-water breaking-wave scaling. Vertical shear in the mean currents is negligible and shear production magnitude is much less than dissipation, implying that the vertical diffusion of turbulence is important. The increased near-bed secondary dissipation maximum results from a decrease in the turbulent length scale.

scholarly journals Acceleration of a Stratified Current over a Sloping Bottom, Driven by an Alongshelf Pressure Gradient*

2005 ◽  
Vol 35 (8) ◽  
pp. 1305-1317 ◽  
Author(s):  
David C. Chapman ◽  
Steven J. Lentz
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Vertical Shear ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Model Calculations ◽  
Bottom Boundary ◽  
Bottom Stress ◽  
Sloping Bottom

Abstract An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S &gt; 0.2) has a major impact. These results are supported by numerical model calculations.

scholarly journals Friction and Diapycnal Mixing at a Slope: Boundary Control of Potential Vorticity

2012 ◽  
Vol 42 (9) ◽  
pp. 1509-1523 ◽  
Author(s):  
Jessica Benthuysen ◽  
Leif N. Thomas
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Potential Vorticity ◽  
Slip Boundary Condition ◽  
Bottom Boundary Layer ◽  
Speed Ratio ◽  
Kelvin Wave ◽  
Geostrophic Current ◽  
Diapycnal Mixing ◽  
Bottom Boundary

Abstract Although atmospheric forcing by wind stress or buoyancy flux is known to change the ocean’s potential vorticity (PV) at the surface, less is understood about PV modification in the bottom boundary layer. The adjustment of a geostrophic current over a sloped bottom in a stratified ocean generates PV sources and sinks through friction and diapycnal mixing. The time-dependent problem is solved analytically for a no-slip boundary condition, and scalings are identified for the change in PV that arises during the adjustment to steady state. Numerical experiments are run to test the scalings with different turbulent closure schemes. The key parameters that control whether PV is injected into or extracted from the fluid are the direction of the geostrophic current and the ratio of its initial speed to its steady-state speed. When the current is in the direction of Kelvin wave propagation, downslope Ekman flow advects lighter water under denser water, driving diabatic mixing and extracting PV. For a current in the opposite direction, Ekman advection tends to restratify the bottom boundary layer and increase the PV. Mixing near the bottom counteracts this restratification, however, and an increase in PV will only occur for current speeds exceeding a critical value. Consequently, the change in PV is asymmetric for currents of the opposite sign but the same speed, with a bias toward PV removal. In the limit of a large speed ratio, the change in PV is independent of diapycnal mixing.

scholarly journals Buoyancy Arrest and Shelf–Ocean Exchange

2012 ◽  
Vol 42 (4) ◽  
pp. 644-658 ◽  
Author(s):  
K. H. Brink
Keyword(s):  
Boundary Layer ◽  
Numerical Models ◽  
Spatial Scales ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Buoyancy Frequency ◽  
Coriolis Parameter ◽  
Strong Constraint ◽  
Bottom Boundary ◽  
Stratified Ocean

Abstract When steady flow in a stratified ocean passes between the continental slope and open ocean, its ability to cross isobaths is potentially limited by buoyancy arrest. If the bottom Ekman transport vanishes and there are no interior stresses, then steady linear flow on an f plane must be geostrophic and follow isobaths exactly. The influence of arrest on cross-shelf transport is investigated here to establish 1) whether there are substantial penetration asymmetries between cases with upwelling and downwelling in the bottom boundary layer; 2) over what spatial scales, hence in what parameter regime, buoyancy arrest is important; and 3) the effects of depth-dependent interior flow. The problem is approached using scalings and idealized numerical models. The results show that there is little or no asymmetry introduced by bottom boundary layer behavior. Further, if the stratification is weak or moderate, as measured by a slope Burger number s = αN/f (where α is the bottom slope, N is buoyancy frequency, and f is the Coriolis parameter), buoyancy arrest does not exert a strong constraint on cross-isobath exchange.

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