Mathew G. Wells

Oriented cell motility and division underlie early limb bud morphogenesis

The vertebrate limb bud arises from lateral plate mesoderm and its overlying ectoderm. Despite progress regarding the genetic requirements for limb development, morphogenetic mechanisms that generate early outgrowth remain relatively undefined. We show by live imaging and lineage tracing in different vertebrate models that the lateral plate contributes mesoderm to the early limb bud through directional cell movement. The direction of cell motion, longitudinal cell axes and bias in cell division planes lie largely parallel to one another along the rostrocaudal (head-tail) axis in lateral plate mesoderm. Transition of these parameters from a rostrocaudal to a mediolateral (outward from the body wall) orientation accompanies early limb bud outgrowth. Furthermore, we provide evidence that Wnt5a acts as a chemoattractant in the emerging limb bud where it contributes to the establishment of cell polarity that is likely to underlie the oriented cell behaviours.

The Relationship between Flux Coefficient and Entrainment Ratio in Density Currents

Abstract The authors explore the theoretical and empirical relationship between the nonlocal quantities of the entrainment ratio E, the appropriately depth- and time-averaged flux coefficient Γ, and the bulk Froude number Fro in density currents. The main theoretical result is that E = 0.125 Γ Fro2(CU3/CL)/cosθ, where θ is the angle of the slope over which the density current flows, CL is the ratio the turbulent length scale to the depth of the density current, and CU is the ratio of the turbulent velocity scale to the mean velocity of the density current. In the case of high bulk Froude numbers Γ ∼ Fro−2 and (CU3/CL) = Cϵ ∼ 1, so E ∼ 0.1, consistent with observations of a constant entrainment ratio in unstratified jets and weakly stratified plumes. For bulk Froude numbers close to one, Γ is constant and has a value in the range of 0.1–0.3, which means that E ∼ Fro2, again in agreement with observations and previous experiments. For bulk Froude numbers less than one, Γ decreases rapidly with bulk Froude n...

A plume head melting under a rifting margin

Abstract A large igneous province (LIP), in the form of a long narrow band of thickened oceanic crust, runs along the Atlantic margin of North America abutting the rifted continental shelf. We propose that this, like many other LIPs, has a mantle plume origin. There is evidence that when the central Atlantic Ocean opened the rift was underlain by the flattened head of a mantle plume, and that the rift site had drifted away from the plume tail by the time of the rifting, so that the tail took little part in the formation of the LIP. We carried out numerical simulations in which we rifted the lithosphere over various model plume heads and calculated the volumes of melt produced. We found that the thickness and width of the resulting thickened oceanic crust is very sensitive to the thermal structure directly under the rift and the structure of the lithosphere. To fit observations of the LIP, a thin flat plume head is required. Such a plume head results when a mantle plume with temperature-dependent viscosity passes through a significant step reduction in the background mantle viscosity at 660 km depth. However, an extensive layer of low viscosity under the rift results in a region of thickened crust much wider than the layer is deep, by decoupling the mantle flow from the lithosphere. To avoid decoupling, we propose that there must be significant topography on the lithosphere, and the rift site is a region of thinned lithosphere. Very thick crust next to the margin can be explained by lithospheric necking and the resulting fast initial upflow under the rift.

The long-term circulation driven by density currents in a two-layer stratified basin

Experimentation and theory are used to study the long-term dynamics of a two-dimensional density current flowing into a two-layer stratified basin. When the initial Richardson number, Ri in ρ , characterizing the ratio of the background stratification to the buoyancy flux of the density current, is less than the critical value of Rip = 21-27, it is found that the density current penetrates the stratified interface. This result is ostensibly independent of slope for angles between 30° and 90°. If the current does not initially penetrate the interface, then it slowly increases the density of the top layer until the interfacial density difference is reduced sufficiently to drive penetration. The time scale for this to occur, t p = (Ri in ρ - Ri* ρ )L/B 1/3 , is explicitly a function of the buoyancy flux B and the length of the basin L. The initial Richardson number, Ri in ρ , is a function of depth, the initial reduced gravity of the interface and a weak function of slope angle. In the absence of initial penetration for very steep slopes of 75° and 90°, we observe that penetrative convection at the interface leads to significant local entrainment. In consequence, the top layer thickens and the interfacial entrainment rate increases as the fifth power of the interfacial Froude number. In contrast, such a process is not observed at comparable interfacial Froude numbers on lower slopes of 30°, 45° and 60°, thereby demonstrating the important role of impact angle on penetrative convection. We attribute the increased interfacial entrainment by the steep density currents as the result of the transition from an undular bore to a turbulent hydraulic jump at the point where the density current intrudes. We discuss the applicability of the observed circulation to the stability of the Arctic halocline where we find 0.56 ≤t p ≤1.2 years for a range of contemporary oceanographic conditions.

Global (latitudinal) variation in submarine channel sinuosity

Current classifications of submarine channels and fans link channel sinuosity to gradient, and in turn to sediment caliber, with end members being high-sinuosity, low-gradient, fine-grained systems and low-sinuosity, high-gradient, coarse-grained systems. However, the most sinuous modern submarine channels, such as the Amazon, Bengal, Indus, and Zaire, along with ancient sinuous submarine channels, are located in equatorial regions. Here we quantitatively compare slope versus latitude controls on submarine channel sinuosity and show that the latitudinal control is strong, while that of slope is weak. Variation in sinuosity with latitude is shown to occur uniquely in submarine channels; no comparable relationship is observed for terrestrial river channels. Possible causal mechanisms for this latitudinal variation are explored, focusing on the influence of the Coriolis force, flow type, and sediment type. Although climate does not vary straightforwardly with latitude, climatic controls on flow and sediment type may explain some of the latitudinal variation; Coriolis force, however, varies with latitude alone and produces an excellent fit to the observed sinuosity-latitude distribution. Regardless of which control predominates, latitudinal global variation in channel sinuosity should have changed over geologic time. Since deposit architecture and facies are linked directly with sinuosity, submarine channel deposits should also systematically vary in space and time.

Coriolis forces influence the secondary circulation of gravity currents flowing in large-scale sinuous submarine channel systems

A combination of centrifugal and Coriolis forces drive the secondary circulation of turbidity currents in sinuous channels, and hence determine where erosion and deposition of sediment occur. Using laboratory experiments we show that when centrifugal forces dominate, the density interface shows a superelevation at the outside of a channel bend. However when Coriolis forces dominate, the interface is always deflected to the right (in the Northern Hemisphere) for both left and right turning bends. The relative importance of either centrifugal or Coriolis forces can be described in terms of a Rossby number defined as Ro = U/fR, where U is the mean downstream velocity, f the Coriolis parameter and R the radius of curvature of the channel bend. Channels with larger bends at high latitudes have ∣Ro∣ < 1 and are dominated by Coriolis forces, whereas smaller, tighter bends at low latitudes have ∣Ro∣ ≫ 1 and are dominated by centrifugal forces.

Two-dimensional density currents in a confined basin

We present new experimental results on the mechanisms through which steady two-dimensional density currents lead to the formation of a stratification in a closed basin. A motivation for this work is to test the underlying assumptions in a diffusive “filling box” model that describes the oceanic thermohaline circulation (Hughes, G.O. and Griffiths, R.W., A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions, Ocean Modeling, 2005, submitted.). In particular, they hypothesized that a non-uniform upwelling velocity is due to weak along-slope entrainment in density currents associated with a large horizontal entrainment ratio of E eq  ∼ 0.1. We experimentally measure the relationship between the along-slope entrainment ratio, E, of a density current to the horizontal entrainment ratio, E eq, of an equivalent vertical plume. The along-slope entrainment ratios show the same quantitative decrease with slope as observed by Ellison and Turner (Ellison, T.H. and Turner, J.S., Turbulent entrainment in stratified flows, J. Fluid Mech., 1959, 6, 423–448.), whereas the horizontal entrainment ratio E eq appears to asymptote to a value of E eq = 0.08 at low slopes. Using the measured values of E eq we show that two-dimensional density currents drive circulations that are in good agreement with the two-dimensional filling box model of Baines and Turner (Baines, W.D. and Turner, J.S., Turbulent buoyant convection from a source in a confined region, J. Fluid. Mech., 1969, 37, 51–80.). We find that the vertical velocities of density fronts collapse onto their theoretical prediction that U =-2−2/3 B 1/3 E eq 2/3 (H/R) ζ, where U is the velocity, H the depth, B the buoyancy flux, R the basin width, E eq the horizontal entrainment ratio and ζ = z/H the dimensionless depth. The density profiles are well fitted with Δ = 2−1/3 B 2/3 E eq −2/3 H -1 [ln(ζ ) + τ ], where τ is the dimensionless time. Finally, we provide a simple example of a diffusive filling box model, where we show how the density stratification of the deep Caribbean waters (below 1850 m depth) can be described by a balance between a steady two-dimensional entraining density current and vertical diffusion in a triangular basin.

The Interaction of Large Amplitude Internal Seiches with a Shallow Sloping Lakebed: Observations of Benthic Turbulence in Lake Simcoe, Ontario, Canada

Observations of the interactions of large amplitude internal seiches with the sloping boundary of Lake Simcoe, Canada show a pronounced asymmetry between up- and downwelling. Data were obtained during a 42-day period in late summer with an ADCP and an array of four thermistor chains located in a 5 km line at the depths where the thermocline intersects the shallow slope of the lakebed. The thermocline is located at depths of 12–14 m during the strongly stratified period of late summer. During periods of strong westerly winds the thermocline is deflected as much as 8 m vertically and interacts directly with the lakebed at depth between 14–18 m. When the thermocline was rising at the boundary, the stratification resembles a turbulent bore that propagates up the sloping lakebed with a speed of 0.05–0.15 m s−1 and a Froude number close to unity. There were strong temperature overturns associated with the abrupt changes in temperature across the bore. Based on the size of overturns in the near bed stratification, we show that the inferred turbulent diffusivity varies by up to two orders of magnitude between up- and downwellings. When the thermocline was rising, estimates of turbulent diffusivity were high with KZ ∼10−4 m2s−1, whereas during downwelling events the near-bed stratification was greatly increased and the turbulence was reduced. This asymmetry is consistent with previous field observations and underlines the importance of shear-induced convection in benthic bottom boundary layers of stratified lakes.

The thermal variability of the waters of Fathom Five National Marine Park, Lake Huron

ABSTRACT Measurements of the thermal stratification at 3 locations within Fathom Five National Marine Park in Lake Huron, Ontario during the summers of 2006 and 2007 found large oscillations in the position of the thermocline. These oscillations led to considerable variability in the temperature at a given depth, with frequent changes in temperature at a rate of 5 °C per hour, and brief periods where temperatures changed at the rate of 10 °C per hour. The thermal stress due to such fast rates of temperature change has been previously implicated in negative effects on many aquatic organisms. The thermocline was observed to move by as much as 20 m vertically, and had dominant periods of oscillation of 12, 17 and 24 h. The strongest temperature variability occurs in the depth range of 10–20 m, which accounts for 20% of the total lakebed area within Fathom Five. The temperature variability was lowest in deep regions well below the thermocline and at a sheltered area behind a reef. This variability was a ubiquitous feature of the water column of Fathom Five during the summer stratification, and the impact of these frequent short-term thermal fluctuations on benthic and fish habitat is discussed in this note.

The Intrusion Depth of Density Currents Flowing into Stratified Water Bodies

Abstract Theory and laboratory experiments are presented describing the depth at which a density current intrudes into a linearly stratified water column, as a function of the entrainment ratio E, the buoyancy flux in the dense current B, and the magnitude of the stratification N. The main result is that Z ∼ E−1/3B1/3/N. It is shown that the depth of the intrusion scales as Z ∼ (3 ± 1)B1/3/N for laboratory experiments, and as for oceanic density currents. The velocity of a large-scale density current is controlled by a geostrophic balance defined as Ugeo = 0.25g′s/f, where s is the slope and f is the Coriolis parameter. The geostrophic buoyancy flux is then defined by Bgeo = g′Ugeoh, with g′ the reduced gravity and h the thickness of the current. The scaling herein implies that the depth of an oceanic intrusion is relatively insensitive to changes in source water properties but is very sensitive to changes in the stratification of the water column, consistent with the previous scaling of Price and Baringe...