Turbulent Bottom Boundary Layer Research Articles

Effect of spatial inhomogeneity of the resistance coefficient on the dynamics of the M 2 tidal wave in the White Sea

To find variations in the dynamics of the surface M2 tide in the White Sea induced by the spatially inhomogeneity of the resistance coefficient, we use a modified version of the QUODDY-4 three-dimensional finite-element hydrostatic model. This version differs from the original version in that it has a module introduced to calculate the resistance coefficient in the bottom boundary layer (BBL). The resistance coefficient is found from resistance laws for an oscillating rotating turbulent BBL over hydrodynamically rough and partially rough (smoothly rough) underlying surfaces describing the dependence of the resistance coefficient and other integral characteristics of resistance on dimensionless similarity parameters: the sea-bottom Rossby number Ro, the streaming Reynolds number Re, and the relative (normalized to tidal frequency) inertial frequency f/σ. The use of spatial inhomogeneity of the resistance coefficient was shown not to lead to considerable changes in tidal characteristics. The values of these characteristics are several times larger than the instrumental measurement errors for the level and velocity but less than the errors in their calculation.

The Baltic Sea Tracer Release Experiment: 2. Mixing processes

Deep water mixing processes in the largest basin of the Baltic Sea (Gotland Basin) are investigated here with the help of long‐term moored instrumentation and turbulence microstructure measurements. Budgets for heat and salinity reveal a strong temporal variability in the deep water mixing coefficients that is shown to be coupled to the wind forcing down to time scales of individual wind events. Consistent with the results from a simultaneously conducted tracer release experiment, near‐boundary turbulence was identified as the key processes for basin‐scale mixing. Turbulent bottom boundary layers were found to be thick and stable in the flat, deep part of the basin, where highest dissipation rates were observed, and comparatively thin, less energetic, and highly variable on the slopes due to a permanent tendency for boundary layer restratification. In the absence of internal tides, strongly damped basin‐scale topographic waves with periods of a few days, a deep rim current, and, to a smaller extent, near‐inertial waves were identified as the main energy sources for boundary mixing. These results are likely to be relevant also for other medium‐sized stratified basins.

Numerical Modeling of Turbulent Bottom Boundary Layer over Rough Bed under Irregular Waves

A numerical model of turbulent bottom boundary layer over rough bed under irregular waves is reviewed. The turbulence model is based upon Shear Stress Transport (SST) k- model. The non-linear governing equations of the boundary layer for each turbulence models were solved by using a Crank-Nicolson type implicit finite-difference scheme. Typical the main velocity distribution, turbulence kinetic energy and time series of the bottom shear stress are presented. These results are shown to be in generally good agreement with experimental result. The roughness effects in the properties of turbulent bottom boundary layer for irregular waves are also presented with several values of the roughness parameter (am/ks) from am/ks=5 to am/ks=3122. The roughness effect tends to decrease the main velocity distribution and to increase the turbulent kinetic energy in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the mean velocity distribution and the kinetic energy turbulent is relatively unaffected. The effect of bed roughness on the bottom shear stress under irregular waves is found that the higher roughness elements increase the magnitude of bottom shear stress along wave cycle. And further, the bottom shear stress under irregular waves is examined with the existing calculation method and the newly proposed method.

The Modification of Bottom Boundary Layer Turbulence and Mixing by Internal Waves Shoaling on a Barrier Reef

Abstract Results are presented from an observational study of stratified, turbulent flow in the bottom boundary layer on the outer southeast Florida shelf. Measurements of momentum and heat fluxes were made using an array of acoustic Doppler velocimeters and fast-response temperature sensors in the bottom 3 m over a rough reef slope. Direct estimates of flux Richardson number Rf confirm previous laboratory, numerical, and observational work, which find mixing efficiency not to be a constant but rather to vary with Frt, Reb, and Rig. These results depart from previous observations in that the highest levels of mixing efficiency occur for Frt < 1, suggesting that efficient mixing can also happen in regions of buoyancy-controlled turbulence. Generally, the authors find that turbulence in the reef bottom boundary layer is highly variable in time and modified by near-bed flow, shear, and stratification driven by shoaling internal waves.

Boundary mixing in lakes: 1. Modeling the effect of shear-induced convection

[1] Recent studies in lakes have shown evidence for a strong influence of shear-induced stratification on mixing in turbulent bottom boundary layers (BBLs) on sloping topography. These observations suggest that the periodic near-bottom shear resulting from internal wave motions may lead to alternating periods of gravitationally stable and unstable stratification in the BBL with relevant implications for turbulence and mixing in the entire basin. The impact of these processes for basin-scale mixing is investigated here in a three-dimensional processes-oriented modeling study, using a well-investigated system (Lake Alpnach, Switzerland) as an example. Consistent with available observations, our results indicate that the BBL becomes gravitationally unstable in areas with upslope flow, covering a substantial fraction of the total bottom area of the lake. While near-bottom convection associated with the unstable stratification in these areas results in strong turbulence, its contribution to net mixing is negligible since the BBL is already well mixed. Conversely, in areas with downslope flow the near-bottom shear generates stable stratification, leading to a suppression of turbulence but also to larger mixing rates due to an enhanced mixing efficiency. Overall, BBL mixing is found to dominate basin-scale mixing. These mechanisms are likely to be important for a large class of stratified natural waters, in which boundary layer mixing is energized by periodic internal waves or basin-scale motions.

Boundary mixing in lakes: 2. Combined effects of shear- and convectively induced turbulence on basin-scale mixing

[1] A detailed comparison of results from a numerical three-dimensional hydrostatic lake model with high-resolution observations of the vertical structure of the turbulent bottom boundary layer (BBL) in a medium-size lake (Lake Alpnach, Switzerland) is provided. The focus of this study is on the shear-induced generation and destruction of stratification in the BBL that may ultimately lead to unstable layers (convection). The model was shown to provide a reliable description of the internal seiching dynamics, as well as the local BBL properties, including the generation of shear-induced convection in two data sets from 2003 and 2007. Basin-scale mixing parameters, inferred from the simulations, are closely connected to the seiching motions, with the hypolimnetic mixing reacting almost immediately to the variable wind-forcing and seiching activity. During upslope flow, the BBL becomes convectively turbulent, causing low mixing efficiency on a basin-scale, whereas during downslope flow, the BBL is restratifying and shear-induced turbulence is weak but leads to a higher mixing efficiency. The overall deep-water mixing efficiency varied in the range of 5 to 10% in this system dominated by turbulent boundary processes.

Cyclonic Spirals in Tidally Accelerating Bottom Boundary Layers in the Zhujiang (Pearl River) Estuary

Abstract A velocity spiral in the tidally accelerating bottom boundary layer (BBL) was defined as a directional shear of the prevailing flow with the elevation and the tidal phase. However, so far there is no information on the spiral for the oscillatory BBL flows or a valid explanation for its origin, life history, and persistence. To investigate this rotating current in the tidally accelerating BBL flow, the authors performed instrumented tripod observations in the tidally energetic Zhujiang (Pearl River) estuary. The tidal BBL flows may fall into three distinct regimes: (i) the quasi-steady phase in the peak tide; (ii) the accelerating–decelerating phase at the slack tide; and (iii) the transition between (i) and (ii), when a cyclonic spiral occurs only in the early–late ebb. The subcritical spiral, defined by a Froude number of the oscillatory BBL flow, may be analytically examined by unsteady linearized turbulent BBL equations. The spiral is formed under the momentum balance between local acceleration and bottom friction, independent of stratification conditions. The spiral consists of the “diffusive” and oscillatory boundary layers in the streamwise and spanwise direction, respectively. The streamwise spiral presents an exponential degradation (growth) in the decelerating (accelerating) ebb, indicating its limited life history over a tidal cycle. The transient in bottom stresses induced by the growth or the degradation of the spiral may be the mechanism for sediment trapping in the very little bed friction in the tidal estuary.

A New Method for Modeling Bottom Shear Stress under Irregular Waves

The bottom shear stress estimation is the most important step to device an input to all the practical sediment transport models. In this paper, the modeling of bottom shear stress in a rough turbulent bottom boundary layer under irregular waves of experimental result is examined by a new calculation method of bottom shear stress based on incorporating velocity and acceleration terms simultaneously. A new acceleration coefficient is proposed to formulate the bottom shear stress under irregular waves. The new formula is further examined with a basic harmonic wave cycle modified with the phase difference and square of the instantaneous friction velocity incorporating the acceleration effect as proposed by the previous researchers. The new method gave the smallest the RMSE value indicating that the new method has the best agreement with the bottom shear stress of experimental results. Therefore, it can effectively be utilized in a beach evolution model by combining it with the irregular wave transformation model.

Turbulent mixing in a strongly forced salt wedge estuary

Turbulent mixing of salt is examined in a shallow salt wedge estuary with strong fluvial and tidal forcing. A numerical model of the Merrimack River estuary is used to quantify turbulent stress, shear production, and buoyancy flux. Little mixing occurs during flood tides despite strong velocities because bottom boundary layer turbulence is dislocated from stratification elevated in the water column. During ebbs, bottom salinity fronts form at a series of bathymetric transitions. At the fronts, near‐bottom velocity and shear stress are low, but shear, stress, and buoyancy flux are elevated at the pycnocline. Internal shear layers provide the dominant source of mixing during the early ebb. Later in the ebb, the pycnocline broadens and moves down such that boundary layer turbulence dominates mixing. Mixing occurs primarily during ebbs, with internal shear mixing accounting for about 50% of the total buoyancy flux. Both the relative contribution of internal shear mixing and the mixing efficiency increase with discharge, with bulk mixing efficiencies between 0.02 and 0.07. Buoyancy fluxes in the estuary increase with discharge up to about 400 m3 s−1 above which a majority of the mixing occurs offshore. Observed buoyancy fluxes were more consistent with the k‐ɛ turbulence closure than the Mellor‐Yamada closure, and more total mixing occurred in the estuary with k‐ɛ. Calculated buoyancy fluxes were sensitive to horizontal grid resolution, as a lower resolution grid yielded less integrated buoyancy flux in the estuary and exported lower salinity water but likely had greater numerical mixing.

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

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.

Effect of water depth and the bottom boundary layer upon internal wave generation over abrupt topography

The role of water depth and bottom boundary layer turbulence upon lee-wave generation in sill regions is examined. Their effect upon vertical mixing is also considered. Calculations are performed using a non-hydrostatic model in cross-section form with a specified tidal forcing. Initial calculations in deeper water and a sill height such that the sill top is well removed from the surrounding bed region showed that downstream lee-wave generation and associated mixing increased as bottom friction coefficient k increased. This was associated with an increase in current shear across the sill. However, for a given k, increasing vertical eddy viscosity A v reduced vertical shear in the across sill velocity, leading to a reduction in lee-wave amplitude and associated mixing. Subsequent calculations using shallower water showed that for a given k and A v, lee-wave generation was reduced due to the shallower water depth and changes in the bottom boundary layer. However, in this case (unlike in the deepwater case), there is an appreciable bottom current. This gives rise to bottom mixing which in shallow water extends to mid-depth and enhances the mid-water mixing that is found on the lee side of the sill. Final calculations with deeper water but small sill height showed that lee waves could propagate over the sill, thereby reducing their contribution to mixing. In this case, bottom mixing was the major source of mixing which was mainly confined to the near bed region, with little mid-water mixing.

Modelling coupled turbulence – Dissolved oxygen dynamics near the sediment–water interface under wind waves and sea swell

A one-dimensional vertical unsteady numerical model for diffusion-consumption of dissolved oxygen (DO) above and below the sediment–water interface was developed to investigate DO profile dynamics under wind waves and sea swell (high-frequency oscillatory flows with periods ranging from 2 to 30 s). We tested a new approach to modelling DO profiles that coupled an oscillatory turbulent bottom boundary layer model with a Michaelis–Menten based consumption model. The flow regime controls both the mean value and the fluctuations of the oxygen mass transfer efficiency during a wave cycle, as expressed by the non-dimensional Sherwood number defined with the maximum shear velocity ( Sh). The Sherwood number was found to be non-dependent on the sediment biogeochemical activity ( μ). In the laminar regime, both cycle-averaged and variance of the Sherwood number are very low ( S h ¯ < 0.05 , VAR ( S h ) < 0.1 % ) . In the turbulent regime, the cycle-averaged Sherwood number is larger ( S h ¯ ≈ 0.2 ) . The Sherwood number also has intra-wave cycle fluctuations that increase with the wave Reynolds number (VAR( Sh) up to 30%). Our computations show that DO mass transfer efficiency under high-frequency oscillatory flows in the turbulent regime are water-side controlled by: (a) the diffusion time across the diffusive boundary layer and (b) diffusive boundary layer dynamics during a wave cycle. As a result of these two processes, when the wave period decreases, the Sh minimum increases and the Sh maximum decreases. S h ¯ values vary little, ranging from 0.17 to 0.23. For periods up to 30 s, oxygen penetration depth into the sediment did not show any intra-wave fluctuations. Values for the laminar regime are small (≤1 mm for μ = 2000 g m −3 d −1) and decrease when the flow period increases. In the turbulent regime, the oxygen penetration depth reaches values up to five times larger than those in the laminar regime, becoming asymptotic as the maximum shear velocity increases.

Turbulence‐plankton interactions: a new cartoon

AbstractClimate change redistributes turbulence in both space and time, adding urgency to understanding of turbulence effects. Many analytic and analog models used to simulate and assess effects of turbulence on plankton rely on simple Couette flow. There shear rates are constant and spatially uniform, and hence so is vorticity. Over the last decade, however, turbulence research within fluid dynamics has focused on the structure of dissipative vortices in space and time. Vorticity gradients, finite net diffusion of vorticity and small radii of curvature of streamlines are ubiquitous features of turbulent vortices at dissipation scales but are explicitly excluded from simple, steady Couette flows. All of these flow components contribute instabilities that cause rotation of particles and so are important to simulate in future laboratory devices designed to assess effects of turbulence on nutrient uptake, particle coagulation, motility and predator‐prey encounter in the plankton. The Burgers vortex retains these signature features of turbulence and provides a simplified “cartoon” of vortex structure and dynamics that nevertheless obeys the Navier‐Stokes equations. Moreover, this idealization closely resembles many dissipative vortices observed in both the laboratory and the field as well as in direct numerical simulations of turbulence. It is simple enough to allow both simulation in numerical models and fabrication of analog devices that selectively reproduce its features. Exercise of such numerical and analog models promises additional insights into mechanisms of turbulence effects on passive trajectories and local accumulations of both living and nonliving particles, into solute exchange with living and nonliving particles and into more subtle influences on sensory processes and swimming trajectories of plankton, including demersal organisms and settling larvae in turbulent bottom boundary layers. The literature on biological consequences of vortical turbulence has focused primarily on the smallest, Kolmogorov‐scale vortices of length scale η. Theoretical dissipation spectra and direct numerical simulation, however, indicate that typical dissipative vortices with radii of 7η to 8η, peak azimuthal speeds of order 1 cm s−1 and lifetimes of order 10 s or longer (and much longer for moderate pelagic turbulence intensities) deserve new attention in studies of biological effects of turbulence.

Flow separation and resuspension beneath shoaling nonlinear internal waves

Laboratory observations are presented showing the structure and dynamics of the turbulent bottom boundary layer beneath nonlinear internal waves (NLIWs) of depression shoaling upon sloping topography. The adverse pressure gradient beneath the shoaling waves causes the rear face to steepen, flow separation to occur, and wave‐induced near‐bottom vortices to suspend bed material. The resuspension is directly attributed to the near‐bed viscous stress and to near‐bed patches of elevated positive Reynolds stress generated by the vortical structures. These results are consistent with published field observations of resuspension events beneath shoaling NLIWs. Elevated near‐bed viscous stresses are found throughout the domain at locations that are not correlated to the resuspension events. Near‐bed viscous stress is thus required for incipient sediment motion but is not necessarily a precursor for resuspension. Resuspension is dependent on the vertical velocity field associated with positive Reynolds stress and is also found to occur where the mean (wave‐averaged) vertical velocity is directed away from the bed. The results are interpreted by analogy to the eddy‐stress and turbulent bursting resuspension models developed for turbulent channel flows.

Energetics of the Beamed Zombie Turbulence Maser Action Mechanism for Remote Detection of Submerged Oceanic Turbulence

Sea surface brightness spectral anomalies from a Honolulu municipal outfall have been detected from space satellites in 200 km areas extending 20 km from the wastewater diffuser (Leung and Gibson 2004, Bondur 2005, Keeler et al. 2005, Gibson et al. 2006). Dropsonde and towed body microstructure measurements show greatly enhanced viscous and temperature dissipation rates above the outfall trapping-layer. Fossil-turbulencewaves (FTWs) and secondary zombie-turbulence-waves (ZTWs) break as they propagate near-vertically and then break again near the surface to produce wind-ripple smoothing with narrow-wavelength λ patterns from the soliton-like internal waves that supply turbulence energy to advected outfall fossils and to the ZTWs they radiate. The λ = 30-250 m solitons reflect an efficient maser-action conversion of horizontal tidal and current kinetic energy by bottom boundary layer turbulence events to near-vertical FTWs with λ the Ozmidov scale of the events at fossilization. Secondary (zombie) turbulence amplifies, channels in chimneys, and near-vertically beams ambient internal wave energy at scales λ just as energized metastable molecules amplify and beam quantum wavelengths in astrophysical lasers and masers around stars. Kilowatts of buoyancy power from the treatment plant produce fossil turbulence patches trapped below the thermocline. Beamed zombie turbulence maser action (BZTMA) in mixing chimneys amplifies these kilowatts into the megawatts of surface turbulence dissipation required to affect brightness on wide sea surface areas. The BZTMA vertical mixing mechanism appears critical to vertical oceanic transport of information, heat, mass and momentum, and to the conversion of barotropic tides to baroclinic tides.

Variability of internally generated turbulence in an estuary, from 100 days of continuous observations

We present detailed observations of internally generated turbulence in a sheared, stratified natural flow, as well as an analysis of the external factors leading to its generation and temporal variability. Multi-month time series of vertical profiles of velocity, acoustic backscatter (0.5 Hz), and turbulence parameters were collected with two moored acoustic Doppler current profilers (ADCPs) in the Hudson River estuary, and estuary-long transects of water density were collected 30 times. ADCP backscatter is used for visualization of coherent turbulent structures and evaluation of surface wave biases to the turbulence measurements. Benefits of the continuous long-term turbulence record include our capturing: (1) the seasonality of turbulence due to changing riverflow, (2) hysteresis in stratification and turbulence over the fortnightly cycle of tidal range, and (3) intermittent events such as breaking internal waves. Internal mixing layers (IMLs) are defined as turbulent regions above the logarithmic velocity layer, and the bottom boundary layer (BBL) is defined as the continuously turbulent range of heights above the bed. A cross-correlation analysis reveals how IML and BBL turbulence vary with stratification and external forcing from tidal range, river flow, and winds. Turbulence in both layers is maximal at spring tide and minimal when most stratified, with one exception—IML turbulence at a site with changing channel depth and width is maximal at times of maximum stratification and freshwater input.

Effect of hydrodynamic properties of the sea bottom on the tidal dynamics in a rectangular basin

Expressions derived for the friction coefficient in an oscillatory rotating turbulent bottom boundary layer (BBL) over rough, incompletely rough (smoothly rough), and smooth underlying surfaces are incorporated as an individual module into a two-dimensional nonlinear tidal model, and the standard version of the model and its modified analogue are used to discuss the titular subject. It is established that the dynamics of tides in the Taylor basin can change noticeably under the effect of hydrodynamic properties of the sea bottom. Such changes occur mainly in the influence domains of amphidromies. In the remaining parts of the basin, relative changes in the amplitudes and phases of tidal sea-surface level elevations do not exceed ±10% and ±10°, respectively. The largest discrepancies of tidal characteristics take place in the cases of the incompletely rough and smooth sea bottoms; the smallest discrepancies, in the case of the rough sea bottom. Estimates for the changes in tidal characteristics that are caused by the usually neglected effects of rotation and phase difference between the bottom friction and the tidal velocity at the upper BBL boundary are presented as well.

Turbulent boundary-layer effects on transient wave propagation in shallow water

The depth-integrated continuity and momentum equations developed by Liu &amp; Orfila are extended to include the effects of turbulent bottom boundary layer. The eddy viscosity model is employed in the boundary layer, in which the eddy viscosity is assumed to be a power function of the vertical elevation from the bottom. The leading-order effects of the turbulent boundary layer appear as a convolution integral in the depth-integrated continuity equation because of the boundary-layer displacement. The bottom stress is also expressed as a convolution integral of the depth-averaged horizontal velocity. For simple harmonic progressive waves, the analytical expression for the phase shift between the bottom stress and the depth-averaged velocity is obtained. The analytical solutions for the solitary wave damping rate due to a turbulent boundary layer are also derived. Prandtl's one-seventh power law is described in detail as an example.

Prediction of instantaneous bottom shear stress for smooth turbulent bottom boundary layers under irregular waves

A method has been proposed to compute instantaneous turbulent bottom shear stress from the variation in free stream velocity under irregular waves for hydraulically smooth plane bed condition. Instantaneous free stream velocity and a modified relationship for turbulent wave friction factor have been introduced as the basis for the correlation with bottom shear stress. Turbulent friction factor and phase difference, obtained through spectral analysis of generated free stream velocity and corresponding bottom shear stress from k–e model computation, corresponds quite well to those from laboratory data. Instantaneous bottom shear stress computed by the proposed method has been compared with those from experimental data for irregular waves. The proposed method presents a high degree of accuracy and has been found to be very convenient in defining the asymptotic behavior of bottom shear stress variation under smooth plane bed condition

Interbasin exchange and mixing in the hypolimnion of a large lake: The role of long internal waves

We conducted a combined field and numerical study of the effects of episodic internal Kelvin-type waves on bottom boundary turbulence and the exchange of a passive tracer between the main basin and the side basin of a large lake (Lake Geneva). High-resolution measurements of the vertical current structure near the entrance of the 25-km-long and 70-m-deep side basin revealed that hypolimnetic current speeds frequently exceed 0.2 m s™1, leading to a turbulent bottom boundary layer several meters thick with logarithmic current profiles and to a region of strong shear across the thermocline. The time series and vertical structure of the currents were reproduced by a threedimensional numerical model of the lake. It was demonstrated that, after episodes of strong winds from the northeast and southwest, exchange flows due to internal Kelvin waves were able to temporarily half or double the hypolimnetic volume of the side basin, leading to an irreversible exchange of up to 40% of the hypolimnetic water in the side basin of Lake Geneva within only a few wave cycles. With the help of the numerical model, it was shown that the key mechanisms of exchange are horizontal dispersion by resolved scales and, to a small extent, shear dispersion in the bottom boundary layer. It is suggested that bottom boundary-layer turbulence and the interbasin exchange can explain the structural differences in the oxygen profiles observed in the side basin and the main basin, respectively.