Downstream Motion Research Articles

Unsteady boundary-layer transition measurements and computations on a rotating blade under cyclic pitch conditions

The presented work tackles the lack of experimental investigations of unsteady laminar-turbulent boundary-layer transition on rotor blades at cyclic pitch actuation, which are important for accurate performance predictions of helicopters in forward flight. Unsteady transition positions were measured on the blade suction side of a four-bladed subscale rotor by means of non-intrusive differential infrared thermography (DIT). Experiments were conducted at different rotation rates corresponding to Mach and Reynolds numbers at 75% rotor radius of up to {M}_{75} = 0.21 and {mathrm {Re}}_{75} = 3.3 times 10^5 and with varying cyclic blade pitch settings. The setup allowed transition to be measured across the outer 54% of the rotor radius. For comparison, transition was also measured using conventional infrared thermography for steady cases with collective pitch settings only. The study is complemented by numerical simulations including boundary-layer transition modeling based on semi-empirical criteria. DIT results reveal the upstream and downstream motion of boundary-layer transition during upstroke and downstroke, a reasonable comparison to experimental results obtained using the already established sigma c_p method, and noticeable agreement with numerical simulations. The result is the first systematic study of unsteady boundary-layer transition on a rotor suction side by means of DIT including a comparison to numerical computations.

Heterogeneous Temporal Contrast Adaptation in Drosophila Direction-Selective Circuits.

In visual systems, neurons adapt both to the mean light level and to the range of light levels, or the contrast. Contrast adaptation has been studied extensively, but it remains unclear how it is distributed among neurons in connected circuits, and how early adaptation affects subsequent computations. Here, we investigated temporal contrast adaptation in neurons across Drosophila's visual motion circuitry. Several ON-pathway neurons showed strong adaptation to changes in contrast over time. One of these neurons, Mi1, showed almost complete adaptation on fast timescales, and experiments ruled out several potential mechanisms for its adaptive properties. When contrast adaptation reduced the gain in ON-pathway cells, it was accompanied by decreased motion responses in downstream direction-selective cells. Simulations show that contrast adaptation can substantially improve motion estimates in natural scenes. The benefits are larger for ON-pathway adaptation, which helps explain the heterogeneous distribution of contrast adaptation in these circuits.

Drosophila Vision: An Eye for Change.

Two new studies show that neuronal adaptation to changes in visual contrast is widespread in the early Drosophila visual system, improving velocity estimation in downstream motion detectors.

Numerical investigation of flow-induced vibrations of two cylinders in tandem arrangement with full wake interference

This paper presents a numerical investigation on flow-induced vibration (FIV) of two elastically mounted cylinders in a tandem arrangement at subcritical Reynolds numbers. The tandem spacing between the cylinder centers is set at four cylinder diameters, placing the FIV problem within the full wake interference regime. A fluid-structure interaction numerical methodology based on a two-dimensional discrete vortex method is developed and applied to the FIV simulation of two cylinders. To investigate the effect of the upstream wake frequency and Reynolds number on the FIV response of the downstream cylinder separately, two experimental cases are designed. In one case, the FIV response is investigated with the Reynolds number varying and the upstream wake frequency fixed. In another case, the Reynolds number is fixed and the upstream wake frequency varies. In both cases, the FIV response of the upstream cylinder roughly resembles the lower branch of the typical vortex-induced vibration response of the single cylinder with the upstream reduced velocity varying from 6 to 9. For the downstream cylinder, the FIV response is characterized by two frequency branches: a dominant frequency branch associated with the wake interference mechanism and a secondary frequency branch associated with the upstream vortex shedding mechanism. It is found that the variation of the vortex shedding frequency in the upstream wake has little effect on the amplitude and dominant frequency of the downstream FIV response but directly causes the variation of the secondary frequency as the secondary frequency strictly follows the upstream vortex shedding frequency. The FIV response amplitude and dominant frequency of the downstream cylinder shows a strong dependence on the Reynolds number. The wake pattern of FIV shows that the FIV vortex shedding of each cylinder is directly related to the motion of itself but slightly modified by the wake of other cylinders for the full wake interference regime. The upstream wake vortices interfering with the downstream motion induce a flow in favor of the downstream FIV response.

Near-lean blowoff dynamics in a liquid fueled combustor

This paper describes an analysis of the near-lean blow off (LBO) dynamics of spray flames, including the influence of fuel composition upon these dynamics. It is motivated by the fact that, while reasonable correlations exist for predicting blowoff conditions, the fundamental reasons for why flames supported by flow recirculation actually blow off are not well understood. Prior work on gaseous systems has shown that the blowoff event is a culmination of several intermediate processes, initiating with local extinction of reactions (“stage 1”), followed by large scale changes in flame and flow dynamics (“stage 2”), finally leading to blowoff. In this study, near-LBO dynamics were characterized for ten liquid fuels with widely varying kinetic and physical properties. Results were compared at two air inlet temperatures, 450 and 300 K, as this influences the relative importance of physical and kinetic properties in controlling LBO. Extinction, re-ignition, and recovery of the flame are evident from these data, and grow in frequency as blowoff is approached. Results show that after a near-blowoff event, the flame can move upstream at velocities much faster than the flow velocity, corresponding to re-ignition. Nonetheless, the majority of the flame recovery events appear to be associated with convection of hot products back upstream, not re-ignition. In contrast, downstream motion of the flame faster than the flow, which would correspond to bulk flame extinction, was never observed. This indicates that “extinction events” actually correspond to convection of the flame downstream by the flow when it loses its stabilization point. The dependence of the equivalence ratio when these events appear, their frequency, and event duration were quantified as a function of fuel composition and air inlet temperature. For example, the data shows a higher percentage of recovery from near-blowoff events through re-ignition for high DCN fuels at the 450 K air temperature condition. These extinction/re-ignition results suggest that high DCN fuels are harder to blow off than low DCN fuels through two mechanisms: (1) by delaying the onset of LBO precursor events, and (2) because they are able to recover from these precursor events through re-ignition more often.

Dynamics of separation bubble dilation and collapse in shock wave/turbulent boundary layer interactions

Although several mechanisms have been suggested as explanations for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions, questions remain on causes and effects. In this effort, we examine the observed asymmetry in large-scale shock motions to highlight which of the suggested mechanisms is most consistent with shock-speed observations and accompanying separation dynamics. The analysis is based on a flowfield obtained from a validated large eddy simulation of a fully separated interaction. A statistical analysis is used to determine the speed of bubble collapse relative to dilation. The low-pass filtering required to separate upstream from downstream motions in the presence of higher-frequency jitter is accomplished with a relatively new technique, empirical mode decomposition, that is very appropriate for this purpose. The dynamics of bubble dilation versus collapse are then elaborated with conditional dynamic mode decomposition (DMD) analyses on the respective pressure fields. Bubble breathing is shown to have a different structure during dilation than during collapse—larger structures are observed during collapse when fluid is expelled from the bubble. The nature of the DMD mode associated with Kelvin–Helmholtz (K–H) shedding in the mixing layer also differs between dilation and collapse: When the bubble is dilating, the structures at the dominant K–H frequency are larger than when the bubble is collapsing. Additionally, a link is established between the convecting K–H structures and corrugation observed along the reflected shock. Some aspects of the nature of the asymmetry are linked to the ease of eddy formation (K–H structures), which plays an important role in the collapse of the bubble.

Observation of surface wave patterns modified by sub-surface shear currents

We report experimental observations of two canonical surface wave patterns – ship waves and ring waves – skewed by sub-surface shear, thus confirming effects predicted by recent theory. Observed ring waves on a still surface with sub-surface shear current are strikingly asymmetric, an effect of strongly anisotropic wave dispersion. Ship waves for motion across a sub-surface current on a still surface exhibit striking asymmetry about the ship’s line of motion, and large differences in transverse wavelength for upstream versus downstream motion are demonstrated, all of which is in good agreement with theoretical predictions. Neither of these phenomena can occur on a depth-uniform current. A quantitative comparison of measured versus predicted average phase shift for a ring wave is grossly mispredicted by no-shear theory, but in good agreement with predictions for the measured shear current. A clear difference in wave frequency within the ring wave packet is observed in the upstream versus downstream direction for all shear flows, while wave dispersive behaviour is identical to that for quiescent water for propagation normal to the shear current, as expected. Peak values of the measured two-dimensional Fourier spectrum for ship waves are shown to agree well with the predicted criterion of stationary ship waves, with the exception of some cases where results are imperfect due to the limited wavenumber resolution, transient effects and/or experimental noise. Experiments were performed on controlled shear currents created in two different ways, with a curved mesh and beneath a blocked stagnant-surface flow. Velocity profiles were measured with particle image velocimetry, and surface waves with a synthetic schlieren method. Our observations lend strong empirical support to recent predictions that wave forces on vessels and structures can be greatly affected by shear in estuarine and tidal waters.

Experimental study of the onset of downstream motion of adhering droplets in turbulent shear flows

In this study, the dynamics of adhering liquid droplets on various solid surfaces in shear flow, which is driven by a controlled air flow, are investigated experimentally. A series of experiments are carried out to understand the effects of fluid properties, wetting characteristics, droplet sizes and flow velocities. A rectangular Plexiglas-channel is used for the experiments. Droplets are placed on the bottom wall of that channel. The droplet shape and contour position are measured by the transmitted light technique and are further analyzed by using image processing. The shear flow leads to a deformation and oscillation of the droplet and eventually to a movement downstream. Three regimes are identified: regime I corresponds to a deformation and oscillation, whereas in regime II the deformed and still oscillating droplets moves downstream. Regime III characterizes a continuous downstream movement in a gliding manner. The start of regime II, i.e. the onset of downstream motion is defined by a critical air velocity. Results show that the contact angle hysteresis and surface energy have a strong influence on the critical air velocity for the onset of droplet motion, as well as the wetting characteristics and droplet volume. To find a global empirical law for the critical velocity, a dimensionless approach is derived based on the droplet Reynolds number and a modified Laplace number. The empirical law is in good agreement with experimental data and may serve as an estimator of the critical velocity for the onset of droplet motion.

Observations on the Role of Auto-Ignition in Flame Stabilization in Turbulent Non-Premixed Jet Flames in Vitiated Coflow

Turbulent combustion of non-premixed jets issuing into a vitiated coflow is studied at coflow temperatures that do not significantly exceed the fuel auto-ignition temperatures, with the objective of observing the global features of lifted flames in this operating temperature regime and the role played by auto-ignition in flame stabilization. Three distinct modes of flame base motions are identified, which include a fluctuating lifted flame base (mode A), avalanche downstream motion of the flame base (mode B), and the formation and propagation of auto-ignition kernels (mode C). Reducing the confinement length of the hot coflow serves to highlight the role of auto-ignition in flame stabilization when the flame is subjected to destabilization by ambient air entrainment. The influence of auto-ignition is further assessed by computing ignition delay times for homogeneous CH4/air mixtures using chemical kinetic simulations and comparing them against the flow transit time corresponding to mean flame liftoff height of the bulk flame base. It is inferred from these studies that while auto-ignition is an active flame stabilization mechanism in this regime, the effect of turbulence may be crucial in determining the importance of auto-ignition toward stabilizing the flame at the conditions studied. An experimental investigation of auto-ignition characteristics at various jet Reynolds numbers reveals that turbulence appears to have a suppressing effect on the active role of auto-ignition in flame stabilization.

Role of Rostral Fastigial Neurons in Encoding a Body-Centered Representation of Translation in Three Dimensions.

Many daily behaviors rely critically on estimates of our body motion. Such estimates must be computed by combining neck proprioceptive signals with vestibular signals that have been transformed from a head- to a body-centered reference frame. Recent studies showed that deep cerebellar neurons in the rostral fastigial nucleus (rFN) reflect these computations, but whether they explicitly encode estimates of body motion remains unclear. A key limitation in addressing this question is that, to date, cell tuning properties have only been characterized for a restricted set of motions across head-re-body orientations in the horizontal plane. Here we examined, for the first time, how 3D spatiotemporal tuning for translational motion varies with head-re-body orientation in both horizontal and vertical planes in the rFN of male macaques. While vestibular coding was profoundly influenced by head-re-body position in both planes, neurons typically reflected at most a partial transformation. However, their tuning shifts were not random but followed the specific spatial trajectories predicted for a 3D transformation. We show that these properties facilitate the linear decoding of fully body-centered motion representations in 3D with a broad range of temporal characteristics from small groups of 5-7 cells. These results demonstrate that the vestibular reference frame transformation required to compute body motion is indeed encoded by cerebellar neurons. We propose that maintaining partially transformed rFN responses with different spatiotemporal properties facilitates the creation of downstream body motion representations with a range of dynamic characteristics, consistent with the functional requirements for tasks such as postural control and reaching.SIGNIFICANCE STATEMENT Estimates of body motion are essential for many daily activities. Vestibular signals are important contributors to such estimates but must be transformed from a head- to a body-centered reference frame. Here, we provide the first direct demonstration that the cerebellum computes this transformation fully in 3D. We show that the output of these computations is reflected in the tuning properties of deep cerebellar rostral fastigial nucleus neurons in a specific distributed fashion that facilitates the efficient creation of body-centered translation estimates with a broad range of temporal properties (i.e., from acceleration to position). These findings support an important role for the rostral fastigial nucleus as a source of body translation estimates functionally relevant for behaviors ranging from postural control to perception.

Limited Impact of Subglacial Supercooling Freeze‐on for Greenland Ice Sheet Stratigraphy

AbstractLarge units of disrupted radiostratigraphy (UDR) are visible in many radio‐echo sounding data sets from the Greenland Ice Sheet. This study investigates whether supercooling freeze‐on rates at the bed can cause the observed UDR. We use a subglacial hydrology model to calculate both freezing and melting rates at the base of the ice sheet in a distributed sheet and within basal channels. We find that while supercooling freeze‐on is a phenomenon that occurs in many areas of the ice sheet, there is no discernible correlation with the occurrence of UDR. The supercooling freeze‐on rates are so low that it would require tens of thousands of years with minimal downstream ice motion to form the hundreds of meters of disrupted radiostratigraphy. Overall, the melt rates at the base of the ice sheet greatly overwhelm the freeze‐on rates, which has implications for mass balance calculations of Greenland ice.

Dynamic linear response of a shock/turbulent-boundary-layer interaction using constrained perturbations

Comprehensive experimental and computational investigations have revealed possible mechanisms underlying low-frequency unsteadiness observed in spanwise homogeneous shock-wave/turbulent-boundary-layer interactions (STBLI). In the present work, we extend this understanding by examining the dynamic linear response of a moderately separated Mach 2.3 STBLI to small perturbations. The statistically stationary linear response is analysed to identify potential time-local and time-mean linear tendencies present in the unsteady base flow: these provide insight into the selective amplification properties of the flow at various points in the limit cycle, as well as asymmetry and restoring mechanisms in the dynamics of the separation bubble. The numerical technique uses the synchronized large-eddy simulation method, previously developed for free shear flows, significantly extended to include a linear constraint necessary for wall-bounded flows. The results demonstrate that the STBLI fosters a global absolute linear instability corresponding to a time-mean linear tendency for upstream shock motion. The absolute instability is maintained through constructive feedback of perturbations through the recirculation: it is self-sustaining and insensitive to external forcing. The dynamics are characterized for key frequency bands corresponding to high–mid-frequency Kelvin–Helmholtz shedding along the separated shear layer$(St_{L}\sim 0.5)$, low–mid-frequency oscillations of the separation bubble$(St_{L}\sim 0.1)$and low-frequency large-scale bubble breathing and shock motion$(St_{L}\sim 0.03)$, where the Strouhal number is based on the nominal length of the separation bubble,$L$:$St_{L}=fL/U_{\infty }$. A band-pass filtering decomposition isolates the dynamic flow features and linear responses associated with these mechanisms. For example, in the low-frequency band, extreme shock displacements are shown to correlate with time-local linear tendencies toward more moderate displacements, indicating a restoring mechanism in the linear dynamics. However, a disparity between the linearly stable shock position and the mean shock position leads to an observed asymmetry in the low-frequency shock motion cycle, in which upstream motion occurs more rapidly than downstream motion. This is explained through competing linear and nonlinear (mass depletion through shedding) mechanisms and discussed in the context of an oscillator model. The analysis successfully illustrates how time-local linear dynamics sustain several key unsteady broadband flow features in a causal manner.

Transient wave resistance upon a real shear current

We study the waves and wave-making forces acting on ships travelling on currents which vary as a function of depth. Our concern is realism; we consider a real current profile from the Columbia River, and model ships with dimensions and Froude numbers typical of three classes of vessels operating in these waters. To this end we employ the most general theory of waves from free-surface sources on shear current to date, which we derive and present here. Expressions are derived for ship waves which satisfy an arbitrary dispersion relation and are generated by a wave source acting on the free surface, with the source’s shape and time-dependence is also being arbitrary. Practical calculation procedures for numerically calculating dispersion on a shear current which may vary arbitrarily with depth both in direction and magnitude, are indicated.For ships travelling at an oblique angle to a shear-current, the ship wave pattern is asymmetrical, and wave-making radiation forces have a lateral component in addition to the conventional wave resistance, the sternward component. No corresponding lateral force exists in the absence of shear. We consider the dependence of wave resistance and lateral force for upstream, downstream and cross-stream motion on the Columbia River current, both in steady motion and during two different manoeuvres: a ship suddenly set in motion, and a ship turning through 360∘. We find that for smaller ships (tugboats, fishing-boats) the wave resistance can differ drastically from that in quiescent water, and depends strongly on Froude number and direction of motion. For Froude numbers typical of such boats, wave resistance can vary by a factor 3 between upstream and downstream motion, and the strong Froude number dependence is made more complicated by interference effects. The lateral radiation force is approximately 20% of the wave resistance for cross-current motion for these ships, and can reach more than 50% for short periods during manoeuvring; this is by no means a small force, and will have an effect on seakeeping, economy, optimal choice of route and operational safety. For an example ship (tugboat) doing a turning motion, both the lateral force and wave resistance are predicted to undergo variations whose amplitude amounts to approximately 100% of their constant values in quiescent water.

Response of an oblique shock train to downstream periodic pressure perturbations

An experimental investigation of the response of an oblique shock train to downstream periodic pressure perturbations was conducted. The oblique shock train is generated in a Mach 2.7 ducted flow and controlled by a downstream elliptical shaft. Cyclic rotating of the shaft leads to a periodic oscillatory motion of the oblique shock train. Six cases of perturbation frequency are studied. The results indicate that the downstream pressure perturbations propagate upstream to cause the oblique shock train to oscillate with a translational motion back and forth and the wall pressure to fluctuate with the same frequency. There is no distinct relative motion between the first oblique shock and the second shock during the motion process of the oblique shock train. The entire oblique shock train exhibits its behaviour of rigid motion and the strength of the first oblique shock of the oblique shock train is nearly stable during its periodic motion. There is a clear hysteresis effect in that the oblique shock train travels along a different path for the upstream and downstream motions. A simple analytical model was built based on these experimental data to analyse the oblique shock train dynamics.

T7 RNA polymerase translocation is facilitated by a helix opening on the fingers domain that may also prevent backtracking.

Here, we studied the complete process of a viral T7 RNA polymerase (RNAP) translocation on DNA during transcription elongation by implementing extensive all-atom molecular dynamics (MD) simulations to construct a Markov state model (MSM). Our studies show that translocation proceeds in a Brownian motion, and the RNAP thermally transits among multiple metastable states. We observed non-synchronized backbone movements of the nucleic acid (NA) chains with the RNA translocation accomplished first, while the template DNA lagged. Notably, both the O-helix and Y-helix on the fingers domain play key roles in facilitating NA translocation through the helix opening. The helix opening allows a key residue Tyr639 to become inserted into the active site, which pushes the RNA–DNA hybrid forward. Another key residue, Phe644, coordinates the downstream template DNA motions by stacking and un-stacking with a transition nucleotide (TN) and its adjacent nucleotide. Moreover, the O-helix opening at pre-translocation (pre-trans) likely resists backtracking. To test this hypothesis, we computationally designed mutants of T7 RNAP by replacing the amino acids on the O-helix with counterpart residues from a mitochondrial RNAP that is capable of backtracking. The current experimental results support the hypothesis.

The effect of building spacing on near-field temporal evolution of triple building plumes

Building plume is important for ventilation and pollutants dispersion along and above buildings in an urban canopy layer. This study fundamentally explores the merging process and temporal penetration of triple uniformly distributed starting building plumes, with a focus of the spacing effect on near-field flow dynamics. Instantaneous velocity and vorticity distributions, penetrating velocities, and stream-wise penetrated heights are quantitatively examined using 2-D particle image velocimetry (PIV) measurements at spacing ratios S/W (building spacing/building width) of 0.2, 0.5, and 1.0.We identified a four-stage merging progress and captured three main spacing-induced merging features. A compact layout at S/W = 0.2 introduces a strong upward channel flow. The wall flows beside the channel tend to draw together first and the unstable channel flow determines the flow pattern transition. In contrast, wider layouts at S/W = 0.5 and 1.0 exhibit intensive downward flow. The wall flows tend to exhibit self-merging initially and the downstream natural swaying motion dominates the merged pattern variations.Merging effect and buoyancy force jointly determine the temporal penetrating velocities. Temporal series of maximum axial velocities above the middle source fits into a power law profile at S/W = 0.2 but a linear function of time at S/W = 0.5 and 1.0. The normalized penetrated heights at S/W = 1.0 are notably faster than in the other two cases before the normalized time is at 3.00 probably because the weaker entrainment and interaction with neighbors lead to less energy and momentum dissipation, quicker self-merging, and faster penetration.

Monitoring of vertical deformations by means high-precision geodetic levelling. Test case: The Arenoso dam (South of Spain)

Abstract The Arenoso reservoir is created by an embankment dam, with central clay core, slates and greywacke shoulders. This kind of engineering structure is subject of deformation due to factors such as changes of water level of the reservoir, seat structure, climate changes, etc. In general, dam monitoring involves measurements both outside (external shell) and inside the structure. A number of control points is established around the area of the dam and the measurements of the displacements of the control points take place at several epochs. In this study high-precision levelling techniques have been used to monitor the vertical deformations. In particular five high-precision levelling profiles were measured in five surveys: February and July 2008, March and July 2013 and August 2014. In this study the design, observations and results are presented. On the one hand the results put in evidence the precision of the observations that are always under 1-mm level. On the other hand these results indicate downstream (southeastward) motion of the thrust block center of the dam probably during the fall and winter. The subsidence reachs here the maximum with a value of −14 cm in 2014 (in respect of February 2008). The displacements observed at the berms of the dam exhibit a similar trend to the displacements observed at the crest but they are significantly smaller, as expected. The accumulative vertical displacements and the settlement index indicate the magnitude of the movements decrease in time, confirming the dam tends to stabilize.

Experimental investigation on spark ignition of annular premixed combustors

The ignition behaviour of a multiple-burner annular combustion chamber consisting of 12 or 18 bluff-body premixed methane-air swirl burners was investigated experimentally. The study focusses on the mechanism of lightround, namely the burner-to-burner flame propagation. Side visualization of the spreading flame by 5 kHz OH* chemiluminescence showed that propagation from burner to burner did not follow a purely azimuthal direction, but a sawtooth pattern with downstream and sideways motion from one burner to the following, bringing flame to the downstream part of the recirculation zone of the adjacent burner before being convected upstream leading to full burner ignition. This pattern was more pronounced when the burners where fitted with swirlers. Top visualization and image processing were used to quantify the speed of lightround as a function of inter-burner spacing, bulk velocity, equivalence ratio, and swirling feature. It was found that flame spread from burner to burner following two balanced modes of propagation. These are turbulent flame propagation combined with volumetric expansion in the inter-burner region and convection within the next un-ignited burner. The results presented in this paper bring new insights into the ignition of realistic gas turbines.

Speed and structure of turbulent fronts in pipe flow

Using extensive direct numerical simulations, the dynamics of laminar–turbulent fronts in pipe flow is investigated for Reynolds numbers between $Re=2000$ and 5500. We here investigate the physical distinction between the fronts of weak and strong slugs both by analysing the turbulent kinetic energy budget and by comparing the downstream front motion to the advection speed of bulk turbulent structures. Our study shows that weak downstream fronts travel slower than turbulent structures in the bulk and correspond to decaying turbulence at the front. At $Re\simeq 2900$ the downstream front speed becomes faster than the advection speed, marking the onset of strong fronts. In contrast to weak fronts, turbulent eddies are generated at strong fronts by feeding on the downstream laminar flow. Our study also suggests that temporal fluctuations of production and dissipation at the downstream laminar–turbulent front drive the dynamical switches between the two types of front observed up to $Re\simeq 3200$.

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current (Ellingsen, J. Fluid Mech., vol. 742, 2014, R2). We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth and the angle between the shear current and the ship’s motion. Formulae for both the normal and lateral wave resistance forces are derived, and we analyse their dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to 10–20 % of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. The theory is fully laid out and far-field contributions are carefully separated off by means of Cauchy’s integral theorem, exposing potential pitfalls associated with a slightly different method (Sokhotsky–Plemelj) used in several previous works.