Mixing Associated with Submesoscale Processes

Closely spaced vertical profiles through the bottom boundary layer over a sloping continental shelf during relaxation from coastal upwelling reveal structure that is consistent with convectively driven mixing. Parcels of fluid were observed adjacent to the bottom that were warm (by several millikelvin) relative to fluid immediately above. On average, the vertical gradient of potential temperature in the superadiabatic (statically unstable) bottom layer was found to be 21.7 3 1024 Km 21, or 6.0 3 1025 kg m24 in potential density. Turbulent dissipation rates («) increased toward the bottom but were relatively constant over the dimensionless depth range 0.4‐1.0z/D (where D is the mixed layer height). The Rayleigh number Ra associated with buoyancy anomalies in the bottom mixed layer is estimated to be approximately 1011, much larger than the value of approximately 10 3 required to initiate convection in simple laboratory or numerical experiments. An evaluation of the data in which the bottom boundary layer was unstably stratified indicates that the greater the buoyancy anomaly is, the greater the turbulent dissipation rate in the neutral layer away from the bottom will be. The vertical structures of averaged profiles of potential density, potential temperature, and turbulent dissipation rate versus nondimensional depth are similar to their distinctive structure in the upper ocean during convection. Nearby moored observations indicate that periods of static instability near the bottom follow events of northward flow and local fluid warming by lateral advection. The rate of local fluid warming is consistent with several estimates of offshore buoyancy transport near the bottom. It is suggested that the concentration of offshore Ekman transport near the bottom of the Ekman layer when the flow atop the layer is northward can provide the differential transport of buoyant bottom fluid when the density in the bottom boundary layer decreases up the slope.

Chapter 8 - Submesoscale processes and mixing

Studies of internal wave-driven mixing in the coastal ocean have been mainly focused on internal tides, while wind-driven near-inertial waves (NIWs) have received less attention in this regard. This study demonstrates a scenario of NIW-driven mixing over the Texas-Louisiana shelf. Supported by a high-resolution simulation over the shelf, the NIWs driven by land-sea breeze radiate downward at a sharp front and enhance the mixing in the bottom boundary layer where the NIWs are focused due to slantwise critical reflection. The criterion for slantwise critical reflection of NIWs is (where ω is the wave frequency, Sbot is the bottom slope, and Sp is the isopycnal slope) under the assumption that the mean flow is in a thermal wind balance and only varies in the slope-normal direction. The mechanism driving the enhanced mixing is explored in an idealized simulation. During slantwise critical reflection, NIWs are amplified with enhanced shear and periodically destratify a bottom boundary layer via differential buoyancy advection, leading to periodically enhanced mixing. Turbulent transport of tracers is also enhanced during slantwise critical reflection of NIWs, which has implications for bottom hypoxia over the Texas-Louisiana shelf.

Processes influencing the circulation and bottom mixing across the shelf slope: the importance of the slope topography and the coast

[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.

A suspended‐sediment‐induced, stably stratified oceanic bottom boundary layer is examined with the Mellor‐Yamada level II turbulence closure model. The boundary layer equations are coupled through the eddy diffusion coefficients for momentum and mass. The bottom boundary layer of the Florida Current is modeled using flow and sediment properties as input parameters. Model results indicate that the boundary layer response to a suspended sediment concentration gradient is to reduce appreciably the level of turbulence. Turbulent kinetic energy and eddy conductivity are reduced by about 40% and 25%, respectively, and bottom stress is reduced by approximately 45%. Increases of veering angle of ≅5°, together with enhancement of the Ekman‐like nature of the current spiral with sediment‐induced stability, are noted. The boundary layer adjusts to the reduced turbulence level by a decrease in the slope of the velocity profile and by diminution of the thicknesses of the boundary layer and contained logarithmic layer by as much as 50%. The predictions are consistent with findings from studies of stably stratified atmospheric boundary layers and sediment‐carrying channel flows. The velocity field near the bottom of a neutrally stratified bottom boundary layer is governed by the relationship U = (u*/κ) ln z/z0. To recover the predicted velocity distribution from this relationship in the sediment‐stratified case, von Karman's constant κ must be reduced by about 15%. The model, however, treats κ as an internal constant. Similarity theory suggests that a more appropriate expression for the near‐bottom velocity field in the sediment‐stratified bottom boundary layer is U = (u*/κ)(ln z/z0 + A ∫Z0z dz/L(z)) where the Monin‐Obukhov length L = z/Rƒ, A = 5.5, and Rf is the flux Richardson number. For the thermally stratified atmospheric boundary layer, L(z) is nearly constant, which yields the familiar log‐linear profile. Our model predicts that in the sediment‐stratified bottom boundary layer, L is nearly linear in z (i.e., Rƒ ≅ const). This yields U ≅ (u*/k′) ln z/Z0, where κ′ = κ/(1 + ARƒ) and κ′ may be interpreted as a modified von Karman constant. The results suggest that u* values inferred from logarithmic speed profiles in sediment‐laden flows may be significant overestimates of the actual u*.

Flocculation under combined effects of hydrodynamic and subaqueous biomass in the bottom boundary layer (BBL) of a microtidal estuary

: This grant consisted of two components, development of new instruments followed by three field investigations of the dynamics of the wave surface and bottom boundary layers in shallow nearshore waters. Standard (daytime) and intensified (night-time) video systems were developed and tested in the field experiments, and were used to measure the temporal and spatial variability in wave breaking occurrences on both land atop towers and at sea aboard ships. Video data obtained coincident with in situ pressure, bi-directional velocity, turbulence, and void fraction were used to calibrate new models for the transformation of wave energy across the surf zone, the forcing of nearshore circulation patterns, and characteristics of breaking waves including turbulence and bubble injection into the water column. Methods for measuring wave breaking on the continental shelf from shipboard video observations were developed in a series of cruises, and used to quantify whitecapping events in relation to sea and swell in the vicinity of a directional waverider buoy.

The hydrographic properties of the bottom boundary layer (BBL) are investigated in a synoptic cross section of the Middle Atlantic Bight shelfbreak frontal jet. The dataset consists of closely spaced conductivity–temperature–depth stations and concurrent shipboard acoustic Doppler current profiler measurements. An extremum in BBL properties occurs in the frontal region where the layer becomes thinner (disappearing briefly), more stratified, and more strongly capped. These changes are apparently related to the significant cross-slope variation in interior stratification. Where the BBL vanishes, at the shoreward edge of the front, it detaches into the interior along an (nearly) isopycnal layer. This is revealed both by weak vertical stratification as well as weak isopycnal gradients of potential temperature (θ) and salinity (S) along the layer. An advective–diffusive model of the detachment in density space is used to explain the observed θ, S distribution as well as estimate the pumping speed along the detached BBL. The detided ADCP velocity fields are analyzed in light of the observed detached BBL. The mechanism of detachment is discussed in relation to existing models, and the secondary circulation in the cross-stream plane is inferred. This reveals a deep interior upwelling cell, apparently tied to the local bathymetry, which enhances the flow along the detached BBL.

Internal solitary waves enhancing turbulent mixing in the bottom boundary layer of continental slope

In October of 2003 a fleet of autonomous underwater gliders began a time series of transects across the New Jersey shelf. The gliders are equipped with a conductivity‐temperature‐depth sensor, and some carry optical ECO‐sensor pucks. The physical‐optical data are used to examine storm‐induced sediment resuspension. There are two types of storm response found. In summer, the seasonal stratification limits midshelf sediment resuspension to below the pycnocline even during hurricanes. In contrast, winter storms suspend sediment throughout the full water column. The transition between summer and winter seasons starts with surface cooling that preconditions the shelf for rapid mixing during fall storms. The mixing storm of October 2003 was a classic northeaster. Early in the storm when waves were high, sediment resuspension was limited to below the pycnocline. After the pycnocline eroded through growth of the bottom boundary layer, particles immediately filled the full water column. The spectral ratio of backscatter indicated that the particles were likely similar materials both before and after the stratification was eroded. The backscatter profiles in the bottom boundary layer decay with distance from the bed at rates consistent with theory but with variable slopes. The reduced slope of the backscatter profiles increased after stratification was lost, which is consistent with an increase in vertical transport or turbulent mixing. Wave bottom orbital velocities during this time were decreasing, and the glider vertical velocities showed no enhancement consistent with Langmuir cells. Enhanced mixing was related to the interaction of the surface and bottom boundary layers while the stratification was eroded, and the observed variability in the resuspension during the event was also due to the tide.

We study the dynamical (three-dimensional box, axisymmetric and spherical shell geometry) and parameterized models of the mantle convection with the core-cooling. The viscosity is constant in space and dependent on the volume averaged mantle temperature. Core is treated as a hot bath. To understand the process of cooling, we use the ‘local’ Rayleigh (Ral ) and Nusselt (Nul) numbers, which are defined in each thermal boundary layer. In the dynamical calculations, we check the various combinations of Ral and Nul, and find that the local Rayleigh number either at the top or bottom surface may control both the top and bottom local Nusselt numbers. This result suggests that the core-cooling in this case may be controlled by the flow either at top or bottom boundary layer. The least-square-fitting of Nul-Ral relationship shows that its power-law index is around 0.3, despite of the different geometry. Comparing the thermal history calculated by the dynamical and parameterized models, we find that the parameterized convection theory based on the local Ra-Nu relationship obtained by the dynamical calculation is useful for investigating the thermal history of the mantle and core. Applying the parameterized theory to the Earth, we find that the plausible Urey ratio is smaller than that obtained by the previous works which ignored the bottom thermal boundary layer.

An analysis of the stabilization of fire whirls

Fluid–particle interaction and generation of coherent structures over permeable beds: an experimental analysis

The ability to accurately measure long-term time-series of tidal currents in bays and estuaries is critical in estuarine hydrodynamic studies. Accurate measurements of tidal currents near the air-water interface and in the bottom boundary layer remain difficult in spite of the significant advances in technology for measuring tidal currents which have been achieved in recent years. One of the objectives of this study is to demonstrate that turbulent mean velocity distribution within the bottom boundary layer can be determined accurately by using a broad-band acoustic Doppler current profiler (BB-ADCP). A suite of instruments, including two BB-ADCPs and four electromagnetic (EM) current meters was deployed in San Francisco Bay, California in an investigation of resuspension and transport of sediment during March 1995. The velocity measurements obtained in the bottom boundary layer by BB-ADCP were highly coherent (r2>0.94) with the velocity measurements obtained by EM current meters. During early March 1995, both BB-ADCPs and EM current meters recorded a very unusual flow event. Agreement among independent measurements by these instruments in describing such an atypical hydrodynamic occurrence further validates the velocity measurements obtained by BB-ADCP in the bottom boundary layer.