Jeffrey R. Carpenter

Instability in Stratified Shear Flow: Review of a Physical Interpretation Based on Interacting Waves

Instability in homogeneous and density stratified shear flows may be interpreted in terms of the interaction of two (or more) otherwise free waves in the velocity and density profiles. These waves exist on gradients of vorticity and density, and instability results when two fundamental conditions are satisfied: (I) the phase speeds of the waves are stationary with respect to each other (“phase-locking“), and (II) the relative phase of the waves is such that a mutual growth occurs. The advantage of the wave interaction approach is that it provides a physical interpretation to shear flow instability. This paper is largely intended to purvey the basics of this physical interpretation to the reader, while both reviewing and consolidating previous work on the topic. The interpretation is shown to provide a framework for understanding many classical and nonintuitive results from the stability of stratified shear flows, such as the Rayleigh and Fjortoft theorems, and the destabilizing effect of an otherwise stable density stratification. Finally, we describe an application of the theory to a geophysical-scale flow in the Fraser River estuary. [DOI: 10.1115/1.4007909]

Interface structure and flux laws in a natural double‐diffusive layering

The diffusive regime of double-diffusive convection generates staircases consisting of thin high-gradient interfaces sandwiched between convectively mixed layers. Simultaneous microstructure measurements of both temperature and conductivity from the staircases in Lake Kivu are used to test flux laws and theoretical models for double diffusion. Density ratios in Lake Kivu are between one and ten and mixed layer thicknesses on average 0.7 m. The larger interface thickness of temperature (average 9 cm) compared to dissolved substances (6 cm) confirms the boundary-layer structure of the interface. Our observations suggest that the boundary-layer break-off cannot be characterized by a single critical boundary-layer Rayleigh number, but occurs within a range of O(10(2)) to O(10(4)). Heat flux parameterizations which assume that the Nusselt number follows a power law increase with the Rayleigh number Ra are tested for their exponent . In contrast to the standard estimate =1/3, we found =0.200.03 for density ratios between two and six. Therefore, we suggest a correction of heat flux estimates which are based on =1/3. The magnitude of the correction depends on Ra in the system of interest. For Lake Kivu (average heat flux 0.10 W m(-2)) with Ra=O(10(8)), corrections are marginal. In the Arctic Ocean with Ra=O(10(8)) to O(10(12)), however, heat fluxes can be overestimated by a factor of four.

Does Rotation Influence Double-Diffusive Fluxes in Polar Oceans?

AbstractThe diffusive (or semiconvection) regime of double-diffusive convection (DDC) is widespread in the polar oceans, generating “staircases” consisting of high-gradient interfaces of temperature and salinity separated by convectively mixed layers. Using two-dimensional direct numerical simulations, support is provided for a previous theory that rotation can influence DDC heat fluxes when the thickness of the thermal interface sufficiently exceeds that of the Ekman layer. This study finds, therefore, that the earth’s rotation places constraints on small-scale vertical heat fluxes through double-diffusive layers. This leads to departures from laboratory-based parameterizations that can significantly change estimates of Arctic Ocean heat fluxes in certain regions, although most of the upper Arctic Ocean thermocline is not expected to be dominated by rotation.

Stability of a Double-Diffusive Interface in the Diffusive Convection Regime

AbstractIn this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are ...

Revisiting Microstructure Sensor Responses with Implications for Double-Diffusive Fluxes

Thinhigh-gradientinterfacesthatoccurnaturallywithindouble-diffusivestaircasesareusedtoestimatethe response characteristics of temperature and conductivity microstructure sensors. The knowledge of these responses is essentialfor resolvingsmall-scaleturbulencein natural waterbodies and for determining doublediffusive fluxes of heat and salt. Here, the authors derive microstructure sensor responses from observed differences in the statistical distributions of interface thicknesses at various profiling speeds in Lake Kivu (central Africa). In contrast to the standard approach for determining sensor responses, this method is independent of any knowledge of the true in situ temperature and salinity structure. Assuming double-pole frequency response functions, the time constants for the Sea-Bird Electronics SBE-7 conductivity sensor and the Rockland Scientific International FP07 thermistor are estimated to be 2.2 and 10ms, respectively. In contrast to previous assumptions, the frequency response for the SBE-7 is found to be substantial and dominates the wavenumber response for profiling speeds larger than 0.19ms 21 .

Effect of resuscitation with hydroxyethyl starch and lactated Ringers on macrophage activity after hemorrhagic shock and sepsis.

Hemorrhagic shock appears to predispose patients to subsequent sepsis. This study examined the effect of different resuscitation fluids on macrophage function following hemorrhagic shock. Male Sprague-Dawley rats were bled to a blood pressure of 50 mmHg for 60 min and then resuscitated with 6% hydroxyethyl starch (HES) or Lactated Ringers (LR). Phagocytic function was assessed by clearance of IV colloidal carbon (C). Carbon clearance was not statistically different between control (154.89), shock LR (169.16), and shock HES (144.60). Computerized image analysis of C distribution in sections of liver and spleen taken 4 h after C infusion exhibits a significant decrease in C distribution after resuscitation with HES compared to control and animals resuscitated with LR (Students t test, p < .05). Male CBA/J mice were bled to a mean blood pressure of 50 mmHg for 60 min and then resuscitated with either LR (N = 18) or HES (N = 17). In separate experiments CBA/J mice had no shock, but were given LR or HES followed by cecal ligation and puncture and later excision (CLPE). A final group had shock with either LR or HES resuscitation and then CLPE as above. Splenocytes were harvested 48 h after shock for mixed lymphocyte culture (MLC). Animals undergoing shock with subsequent septic challenge (Shock/CLPE) showed significantly increased mortality 40 vs. 0% (chi square, p < .05) and immunosuppression on MLC 2,088(LR)/3,300 (HES) vs. 18,570 (LR)/17,705 (HES) compared to CLPE alone (Students/test, P < .05). Resuscitation with HES significantly decreased phagocytic function compared to LR in rats. There were no differences in survival or MLC data, however, between LR or HES resuscitation.

Spatial variability of the Arctic Ocean's double‐diffusive staircase

The Arctic Ocean thermohaline stratification frequently exhibits a staircase structure overlying the Atlantic Water Layer that can be attributed to the diffusive form of double-diffusive convection. The staircase consists of multiple layers of O(1) m in thickness separated by sharp interfaces, across which temperature and salinity change abruptly. Through a detailed analysis of Ice-Tethered Profiler measurements from 2004-2013, the double-diffusive staircase structure is characterized across the entire Arctic Ocean. We demonstrate how the large-scale Arctic Ocean circulation influences the small-scale staircase properties. These staircase properties (layer thicknesses and temperature and salinity jumps across interfaces) are examined in relation to a bulk vertical density ratio spanning the staircase stratification. We show that the Lomonosov Ridge serves as an approximate boundary between regions of low density ratio (approximately 3 to 4) on the Eurasian side and higher density ratio (approximately 6 to 7) on the Canadian side. We find that the Eurasian Basin staircase is characterized by fewer, thinner layers than that in the Canadian Basin, although the margins of all basins are characterized by relatively thin layers and the absence of a well-defined staircase. A double-diffusive 4/3-flux law parametrization is used to estimate vertical heat fluxes in the Canadian Basin to be O(0.1) Wm-2. It is shown that the 4/3-flux law may not be an appropriate representation of heat fluxes through the Eurasian Basin staircase. Here, molecular heat fluxes are estimated to be between O(0.01) Wm-2 and O(0.1) Wm-2. However, many uncertainties remain about the exact nature of these fluxes. This article is protected by copyright. All rights reserved.

Temperature steps in salty seas

With the right combination of temperature and salinity, the water column of a lake or ocean exhibits a layered, staircase structure. Such aquatic staircases have been observed throughout the world, from tropical Africa to the Arctic Ocean.

A Physical Interpretation of the Wind-Wave Instability as Interacting Waves

AbstractOne mechanism for the growth of ocean surface waves by wind is through a shear instability that was first described by Miles in 1957. A physical interpretation of this wind-wave instability is provided in terms of the interaction of the surface gravity wave with perturbations of vorticity within the critical layer—a near-singularity in the airflow where the background flow speed matches that of the surface gravity wave. This physical interpretation relies on the fact that the vertical velocity field is slowly varying across the critical layer, whereas both the displacement and vorticity fields vary rapidly. Realizing this allows for the construction of a physically intuitive description of the critical layer vorticity perturbations that may be approximated by a simple vortex sheet model, the essence of the wind-wave instability can then be captured through the interaction of the critical layer vorticity with the surface gravity wave. This simple model is then extended to account for vorticity pert...

Turbulence and Mixing in a Shallow Shelf Sea From Underwater Gliders

The seasonal thermocline in shallow shelf seas acts as a natural barrier for boundary-generated turbulence, damping scalar transport to the upper regions of the water column, and controlling primary production to a certain extent. To better understand turbulence and mixing conditions within the thermocline, two unique 12- and 17-day datasets with continuous measurements of the dissipation rate of turbulent kinetic energy (e) collected by autonomous underwater gliders under stratified to well-mixed conditions are presented. A highly intermittent e signal was observed in the stratified thermocline region, which was mainly characterized by quiescent flow (turbulent activity index below 7). The rate of diapycnal mixing remained relatively constant for the majority of the time with peaks of higher fluxes that were responsible for much of the increase in bottom mixed layer temperature. The water column stayed predominantly strongly stratified, with a bulk Richardson number across the thermocline well above 2. A positive relationship between the intensity of turbulence, shear and stratification was found. The trend between turbulence levels and the bulk Richardson number was relatively weak, but suggests that e increases as the bulk Richardson number approaches 1. The results also highlight the interpretation difficulties in both quantifying turbulent thermocline fluxes, as well as the responsible mechanisms.