Skip to main content

Research Repository

Advanced Search

Outputs (21)

The Batchelor–Howells–Townsend spectrum: large velocity case (2024)
Journal Article
Jolly, M. S., & Wirosoetisno, D. (2024). The Batchelor–Howells–Townsend spectrum: large velocity case. Nonlinearity, 37(7), Article 075025. https://doi.org/10.1088/1361-6544/ad5265

We consider the behaviour of a passive tracer θ governed by ∂tθ+u⋅∇θ=Δθ+g in two space dimensions with prescribed smooth random incompressible velocity u(x, t) and source g(x). In 1959, Batchelor et al (J. Fluid Mech. 5 113) predicted that the tracer... Read More about The Batchelor–Howells–Townsend spectrum: large velocity case.

The Batchelor–Howells–Townsend spectrum: Three-dimensional case (2022)
Journal Article
Jolly, M., & Wirosoetisno, D. (2023). The Batchelor–Howells–Townsend spectrum: Three-dimensional case. Physica D: Nonlinear Phenomena, 445, Article 133615. https://doi.org/10.1016/j.physd.2022.133615

Given a velocity field u(x, t), we consider the evolution of a passive tracer governed by @t + u · ∇ = + g with time-independent source g(x). When u is small in some sense, Batchelor, Howells and Townsend (1959, J. Fluid Mech. 5:134; henceforth BHT59... Read More about The Batchelor–Howells–Townsend spectrum: Three-dimensional case.

Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited (2020)
Journal Article
Jolly, M., & Wirosoetisno, D. (2020). Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited. Journal of Mathematical Fluid Mechanics, 22(2), Article 18. https://doi.org/10.1007/s00021-019-0478-6

Given a velocity field u(x, t), we consider the evolution of a passive tracer θ governed by ∂tθ + u · ∇θ = Δθ + g with time-independent source g(x). When u is small in some sense, Batchelor, Howells and Townsend (J Fluid Mech 5:134, 1959) predicted t... Read More about Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited.

Navier–Stokes equations on the β-plane: Determining modes and nodes (2018)
Journal Article
Miyajima, N., & Wirosoetisno, D. (2019). Navier–Stokes equations on the β-plane: Determining modes and nodes. Physica D: Nonlinear Phenomena, 386-387, 31-37. https://doi.org/10.1016/j.physd.2018.08.005

We revisit the 2d Navier–Stokes equations on the periodic β-plane, with the Coriolis parameter varying asβy, and obtain bounds on the number of determining modes and nodes of the flow. The number of modesand nodes scale as c G1/20+ c′(M/β)1/2and c G2... Read More about Navier–Stokes equations on the β-plane: Determining modes and nodes.

Energy spectra and passive tracer cascades in turbulent flows (2018)
Journal Article
Jolly, M., & Wirosoetisno, D. (2018). Energy spectra and passive tracer cascades in turbulent flows. Journal of Mathematical Physics, 59(7), Article 073104. https://doi.org/10.1063/1.5046773

We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spectra over the potential range of the tracer cascade (in 2D when the tra... Read More about Energy spectra and passive tracer cascades in turbulent flows.

Averaging method applied to the three-dimensional primitive equations (2016)
Journal Article
Petcu, M., Temam, R., & Wirosoetisno, D. (2016). Averaging method applied to the three-dimensional primitive equations. Discrete and Continuous Dynamical Systems - Series A, 36(10), 5681-5707. https://doi.org/10.3934/dcds.2016049

In this article we study the small Rossby number asymptotics for the three-dimensional primitive equations of the oceans and of the atmosphere. The fast oscillations present in the exact solution are eliminated using an averaging method, the so-calle... Read More about Averaging method applied to the three-dimensional primitive equations.

Timestepping schemes for the 3d Navier-Stokes equations (2015)
Journal Article
Hong, Y., & Wirosoetisno, D. (2015). Timestepping schemes for the 3d Navier-Stokes equations. Applied Numerical Mathematics, 96, 153-164. https://doi.org/10.1016/j.apnum.2015.05.006

It is well known that the (exact) solutions of the 3d Navier–Stokes equations remain bounded for all time if the initial data and the forcing are sufficiently small relative to the viscosity. They also remain bounded for a finite time for arbitrary i... Read More about Timestepping schemes for the 3d Navier-Stokes equations.

Navier-Stokes equations on a rapidly rotating sphere (2015)
Journal Article
Wirosoetisno, D. (2015). Navier-Stokes equations on a rapidly rotating sphere. Discrete and Continuous Dynamical Systems - Series B, 20(4), 1251-1259. https://doi.org/10.3934/dcdsb.2015.20.1251

We extend our earlier β-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes equations on a sphere rotating with angular velocity 1/ϵ becomes zonal i... Read More about Navier-Stokes equations on a rapidly rotating sphere.

Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics (2014)
Journal Article
Tone, F., Wang, X., & Wirosoetisno, D. (2014). Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics. Numerische Mathematik, 130(3), 541-566. https://doi.org/10.1007/s00211-014-0670-9

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds... Read More about Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics.